Use Ed25519 keys.

This uses the portable Ed25519 library made by Orson Peters, which in turn uses
the reference implementation made by Daniel J. Bernstein.

This implementation also allows Ed25519 keys to be used for key exchange, so
there is no need to add a separate implementation of Curve25519.

diff --git a/src/Makefile.am b/src/Makefile.am
index 64c845d60e278a305e3aa8bdb84d3bcf4472b8e5..ec1da980fd5af774b43861eba5e3778e6b81979c 100644 (file)
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -1,6 +1,6 @@
 ## Produce this file with automake to get Makefile.in
 
-sbin_PROGRAMS = tincd tinc sptps_test
+sbin_PROGRAMS = tincd tinc sptps_test sptps_keypair
 
 if LINUX
 sbin_PROGRAMS += sptps_speed
@@ -8,6 +8,21 @@ endif
 
 DEFAULT_INCLUDES =
 
+ed25519_SOURCES = \
+       ed25519/add_scalar.c \
+       ed25519/ed25519.h \
+       ed25519/fe.c ed25519/fe.h \
+       ed25519/fixedint.h \
+       ed25519/ge.c ed25519/ge.h \
+       ed25519/key_exchange.c \
+       ed25519/keypair.c \
+       ed25519/precomp_data.h \
+       ed25519/sc.c ed25519/sc.h \
+       ed25519/seed.c \
+       ed25519/sha512.c ed25519/sha512.h \
+       ed25519/sign.c \
+       ed25519/verify.c
+
 tincd_SOURCES = \
        buffer.c buffer.h \
        cipher.h \
@@ -67,7 +82,8 @@ tincd_SOURCES = \
        system.h \
        tincd.c \
        utils.c utils.h \
-       xalloc.h
+       xalloc.h \
+       $(ed25519_SOURCES)
 
 tinc_SOURCES = \
        dropin.c dropin.h \
@@ -83,19 +99,27 @@ tinc_SOURCES = \
        subnet_parse.c subnet.h \
        tincctl.c tincctl.h \
        top.c top.h \
-       utils.c utils.h
+       utils.c utils.h \
+       $(ed25519_SOURCES)
 
 sptps_test_SOURCES = \
        logger.c logger.h \
        sptps.c sptps.h \
        sptps_test.c \
-       utils.c utils.h
+       utils.c utils.h \
+       $(ed25519_SOURCES)
+
+sptps_keypair_SOURCES = \
+       sptps_keypair.c \
+       utils.c utils.h \
+       $(ed25519_SOURCES)
 
 sptps_speed_SOURCES = \
        logger.c logger.h \
        sptps.c sptps.h \
        sptps_speed.c \
-       utils.c utils.h
+       utils.c utils.h \
+       $(ed25519_SOURCES)
 
 ## Conditionally compile device drivers
        
@@ -135,17 +159,17 @@ tincd_SOURCES += \
        openssl/cipher.c \
        openssl/crypto.c \
        openssl/digest.c openssl/digest.h \
-       openssl/ecdh.c \
-       openssl/ecdsa.c \
+       ed25519/ecdh.c \
+       ed25519/ecdsa.c \
        openssl/prf.c \
        openssl/rsa.c
 tinc_SOURCES += \
        openssl/cipher.c \
        openssl/crypto.c \
        openssl/digest.c openssl/digest.h \
-       openssl/ecdh.c \
-       openssl/ecdsa.c \
-       openssl/ecdsagen.c \
+       ed25519/ecdh.c \
+       ed25519/ecdsa.c \
+       ed25519/ecdsagen.c \
        openssl/prf.c \
        openssl/rsa.c \
        openssl/rsagen.c
@@ -153,16 +177,19 @@ sptps_test_SOURCES += \
        openssl/cipher.c \
        openssl/crypto.c \
        openssl/digest.c openssl/digest.h \
-       openssl/ecdh.c \
-       openssl/ecdsa.c \
+       ed25519/ecdh.c \
+       ed25519/ecdsa.c \
        openssl/prf.c
+sptps_keypair_SOURCES += \
+       openssl/crypto.c \
+       ed25519/ecdsagen.c
 sptps_speed_SOURCES += \
        openssl/cipher.c \
        openssl/crypto.c \
        openssl/digest.c openssl/digest.h \
-       openssl/ecdh.c \
-       openssl/ecdsa.c \
-       openssl/ecdsagen.c \
+       ed25519/ecdh.c \
+       ed25519/ecdsa.c \
+       ed25519/ecdsagen.c \
        openssl/prf.c
 endif
 

diff --git a/src/ecdh.h b/src/ecdh.h
index fbd47292b614ca06098dd3153974b918918266c8..c5ea3efbb6d64b593de3d789785b8264c8b9d4a2 100644 (file)
--- a/src/ecdh.h
+++ b/src/ecdh.h
@@ -20,8 +20,8 @@
 #ifndef __TINC_ECDH_H__
 #define __TINC_ECDH_H__
 
-#define ECDH_SIZE 67
-#define ECDH_SHARED_SIZE 66
+#define ECDH_SIZE 32
+#define ECDH_SHARED_SIZE 32
 
 #ifndef __TINC_ECDH_INTERNAL__
 typedef struct ecdh ecdh_t;

diff --git a/src/ed25519/.dirstamp b/src/ed25519/.dirstamp
new file mode 100644 (file)
index 0000000..e69de29

diff --git a/src/ed25519/add_scalar.c b/src/ed25519/add_scalar.c
new file mode 100644 (file)
index 0000000..262ec72
--- /dev/null
+++ b/src/ed25519/add_scalar.c
@@ -0,0 +1,56 @@
+#include "ed25519.h"
+#include "ge.h"
+#include "sc.h"
+
+
+/* see http://crypto.stackexchange.com/a/6215/4697 */
+void ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar) {
+    const unsigned char SC_1[32] = {1}; /* scalar with value 1 */
+    
+    unsigned char n[32]; 
+    ge_p3 nB;
+    ge_p1p1 A_p1p1;
+    ge_p3 A;
+    ge_p3 public_key_unpacked;
+    ge_cached T;
+
+    int i;
+
+    /* copy the scalar and clear highest bit */
+    for (i = 0; i < 31; ++i) {
+        n[i] = scalar[i];
+    }
+    n[31] = scalar[31] & 127;
+
+    /* private key: a = n + t */
+    if (private_key) {
+        sc_muladd(private_key, SC_1, n, private_key);
+    }
+
+    /* public key: A = nB + T */
+    if (public_key) {
+        /* if we know the private key we don't need a point addition, which is faster */
+        /* using a "timing attack" you could find out wether or not we know the private
+           key, but this information seems rather useless - if this is important pass
+           public_key and private_key seperately in 2 function calls */
+        if (private_key) {
+            ge_scalarmult_base(&A, private_key);
+        } else {
+            /* unpack public key into T */
+            ge_frombytes_negate_vartime(&public_key_unpacked, public_key);
+            fe_neg(public_key_unpacked.X, public_key_unpacked.X); // undo negate
+            fe_neg(public_key_unpacked.T, public_key_unpacked.T); // undo negate
+            ge_p3_to_cached(&T, &public_key_unpacked);
+
+            /* calculate n*B */
+            ge_scalarmult_base(&nB, n);
+
+            /* A = n*B + T */
+            ge_add(&A_p1p1, &nB, &T);
+            ge_p1p1_to_p3(&A, &A_p1p1);
+        }
+            
+        /* pack public key */
+        ge_p3_tobytes(public_key, &A);
+    }
+}

diff --git a/src/ed25519/ecdh.c b/src/ed25519/ecdh.c
new file mode 100644 (file)
index 0000000..d0cd7e0
--- /dev/null
+++ b/src/ed25519/ecdh.c
@@ -0,0 +1,51 @@
+/*
+    ecdh.c -- Diffie-Hellman key exchange handling
+    Copyright (C) 2011-2013 Guus Sliepen <guus@tinc-vpn.org>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+*/
+
+#include "../system.h"
+
+#include "ed25519.h"
+
+#define __TINC_ECDH_INTERNAL__
+typedef struct ecdh_t {
+       uint8_t private[64];
+} ecdh_t;
+
+#include "../crypto.h"
+#include "../ecdh.h"
+#include "../xalloc.h"
+
+ecdh_t *ecdh_generate_public(void *pubkey) {
+       ecdh_t *ecdh = xzalloc(sizeof *ecdh);
+
+       uint8_t seed[32];
+       randomize(seed, sizeof seed);
+       ed25519_create_keypair(pubkey, ecdh->private, seed);
+
+       return ecdh;
+}
+
+bool ecdh_compute_shared(ecdh_t *ecdh, const void *pubkey, void *shared) {
+       ed25519_key_exchange(shared, pubkey, ecdh->private);
+       free(ecdh);
+       return true;
+}
+
+void ecdh_free(ecdh_t *ecdh) {
+       free(ecdh);
+}

diff --git a/src/ed25519/ecdsa.c b/src/ed25519/ecdsa.c
new file mode 100644 (file)
index 0000000..1da2797
--- /dev/null
+++ b/src/ed25519/ecdsa.c
@@ -0,0 +1,102 @@
+/*
+    ecdsa.c -- ECDSA key handling
+    Copyright (C) 2011-2013 Guus Sliepen <guus@tinc-vpn.org>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+*/
+
+#include "../system.h"
+
+#include "ed25519.h"
+
+#define __TINC_ECDSA_INTERNAL__
+typedef struct {
+       uint8_t private[64];
+       uint8_t public[32];
+} ecdsa_t;
+
+#include "../logger.h"
+#include "../ecdsa.h"
+#include "../utils.h"
+#include "../xalloc.h"
+
+// Get and set ECDSA keys
+//
+ecdsa_t *ecdsa_set_base64_public_key(const char *p) {
+       int len = strlen(p);
+
+       if(len != 43) {
+               logger(DEBUG_ALWAYS, LOG_ERR, "Invalid size %s for public key!", len);
+               return 0;
+       }
+
+       ecdsa_t *ecdsa = xzalloc(sizeof *ecdsa);
+       len = b64decode(p, ecdsa->public, len);
+       if(len != 32) {
+               logger(DEBUG_ALWAYS, LOG_ERR, "Invalid format of public key! len = %d", len);
+               free(ecdsa);
+               return 0;
+       }
+
+       return ecdsa;
+}
+
+char *ecdsa_get_base64_public_key(ecdsa_t *ecdsa) {
+       char *base64 = xmalloc(44);
+       b64encode(ecdsa->public, base64, sizeof ecdsa->public);
+
+       return base64;
+}
+
+// Read PEM ECDSA keys
+
+ecdsa_t *ecdsa_read_pem_public_key(FILE *fp) {
+       ecdsa_t *ecdsa = xzalloc(sizeof *ecdsa);
+       if(fread(ecdsa->public, sizeof ecdsa->public, 1, fp) == 1)
+               return ecdsa;
+       free(ecdsa);
+       return 0;
+}
+
+ecdsa_t *ecdsa_read_pem_private_key(FILE *fp) {
+       ecdsa_t *ecdsa = xmalloc(sizeof *ecdsa);
+       if(fread(ecdsa, sizeof *ecdsa, 1, fp) == 1)
+               return ecdsa;
+       free(ecdsa);
+       return 0;
+}
+
+size_t ecdsa_size(ecdsa_t *ecdsa) {
+       return 64;
+}
+
+// TODO: standardise output format?
+
+bool ecdsa_sign(ecdsa_t *ecdsa, const void *in, size_t len, void *sig) {
+       ed25519_sign(sig, in, len, ecdsa->public, ecdsa->private);
+       return true;
+}
+
+bool ecdsa_verify(ecdsa_t *ecdsa, const void *in, size_t len, const void *sig) {
+       return ed25519_verify(sig, in, len, ecdsa->public);
+}
+
+bool ecdsa_active(ecdsa_t *ecdsa) {
+       return ecdsa;
+}
+
+void ecdsa_free(ecdsa_t *ecdsa) {
+       free(ecdsa);
+}

diff --git a/src/ed25519/ecdsagen.c b/src/ed25519/ecdsagen.c
new file mode 100644 (file)
index 0000000..4184573
--- /dev/null
+++ b/src/ed25519/ecdsagen.c
@@ -0,0 +1,55 @@
+/*
+    ecdsagen.c -- ECDSA key generation and export
+    Copyright (C) 2011-2013 Guus Sliepen <guus@tinc-vpn.org>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+*/
+
+#include "../system.h"
+
+#include "ed25519.h"
+
+#define __TINC_ECDSA_INTERNAL__
+typedef struct {
+       uint8_t private[64];
+       uint8_t public[32];
+} ecdsa_t;
+
+#include "../crypto.h"
+#include "../ecdsagen.h"
+#include "../utils.h"
+#include "../xalloc.h"
+
+// Generate ECDSA key
+
+ecdsa_t *ecdsa_generate(void) {
+       ecdsa_t *ecdsa = xzalloc(sizeof *ecdsa);
+
+       uint8_t seed[32];
+       randomize(seed, sizeof seed);
+       ed25519_create_keypair(ecdsa->public, ecdsa->private, seed);
+
+       return ecdsa;
+}
+
+// Write PEM ECDSA keys
+
+bool ecdsa_write_pem_public_key(ecdsa_t *ecdsa, FILE *fp) {
+       return fwrite(ecdsa->public, sizeof ecdsa->public, 1, fp) == 1;
+}
+
+bool ecdsa_write_pem_private_key(ecdsa_t *ecdsa, FILE *fp) {
+       return fwrite(ecdsa, sizeof *ecdsa, 1, fp) == 1;
+}

diff --git a/src/ed25519/ed25519.h b/src/ed25519/ed25519.h
new file mode 100644 (file)
index 0000000..bb34f89
--- /dev/null
+++ b/src/ed25519/ed25519.h
@@ -0,0 +1,38 @@
+#ifndef ED25519_H
+#define ED25519_H
+
+#include <stddef.h>
+
+#if defined(_WIN32)
+    #if defined(ED25519_BUILD_DLL)
+        #define ED25519_DECLSPEC __declspec(dllexport)
+    #elif defined(ED25519_DLL)
+        #define ED25519_DECLSPEC __declspec(dllimport)
+    #else
+        #define ED25519_DECLSPEC
+    #endif
+#else
+    #define ED25519_DECLSPEC
+#endif
+
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef ED25519_NO_SEED
+int ED25519_DECLSPEC ed25519_create_seed(unsigned char *seed);
+#endif
+
+void ED25519_DECLSPEC ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed);
+void ED25519_DECLSPEC ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key);
+int ED25519_DECLSPEC ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *private_key);
+void ED25519_DECLSPEC ed25519_add_scalar(unsigned char *public_key, unsigned char *private_key, const unsigned char *scalar);
+void ED25519_DECLSPEC ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key);
+
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

diff --git a/src/ed25519/fe.c b/src/ed25519/fe.c
new file mode 100644 (file)
index 0000000..448e3e9
--- /dev/null
+++ b/src/ed25519/fe.c
@@ -0,0 +1,1491 @@
+#include "fixedint.h"
+#include "fe.h"
+
+
+/*
+    helper functions
+*/
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+
+
+/*
+    h = 0
+*/
+
+void fe_0(fe h) {
+    h[0] = 0;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = 1
+*/
+
+void fe_1(fe h) {
+    h[0] = 1;
+    h[1] = 0;
+    h[2] = 0;
+    h[3] = 0;
+    h[4] = 0;
+    h[5] = 0;
+    h[6] = 0;
+    h[7] = 0;
+    h[8] = 0;
+    h[9] = 0;
+}
+
+
+
+/*
+    h = f + g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+    Postconditions:
+       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 + g0;
+    int32_t h1 = f1 + g1;
+    int32_t h2 = f2 + g2;
+    int32_t h3 = f3 + g3;
+    int32_t h4 = f4 + g4;
+    int32_t h5 = f5 + g5;
+    int32_t h6 = f6 + g6;
+    int32_t h7 = f7 + g7;
+    int32_t h8 = f8 + g8;
+    int32_t h9 = f9 + g9;
+    
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+    Replace (f,g) with (g,g) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cmov(fe f, const fe g, unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+
+    b = (unsigned int) (- (int) b); /* silence warning */
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+}
+
+/*
+    Replace (f,g) with (g,f) if b == 1;
+    replace (f,g) with (f,g) if b == 0.
+
+    Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,fe g,unsigned int b) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t x0 = f0 ^ g0;
+    int32_t x1 = f1 ^ g1;
+    int32_t x2 = f2 ^ g2;
+    int32_t x3 = f3 ^ g3;
+    int32_t x4 = f4 ^ g4;
+    int32_t x5 = f5 ^ g5;
+    int32_t x6 = f6 ^ g6;
+    int32_t x7 = f7 ^ g7;
+    int32_t x8 = f8 ^ g8;
+    int32_t x9 = f9 ^ g9;
+    b = -b;
+    x0 &= b;
+    x1 &= b;
+    x2 &= b;
+    x3 &= b;
+    x4 &= b;
+    x5 &= b;
+    x6 &= b;
+    x7 &= b;
+    x8 &= b;
+    x9 &= b;
+    f[0] = f0 ^ x0;
+    f[1] = f1 ^ x1;
+    f[2] = f2 ^ x2;
+    f[3] = f3 ^ x3;
+    f[4] = f4 ^ x4;
+    f[5] = f5 ^ x5;
+    f[6] = f6 ^ x6;
+    f[7] = f7 ^ x7;
+    f[8] = f8 ^ x8;
+    f[9] = f9 ^ x9;
+    g[0] = g0 ^ x0;
+    g[1] = g1 ^ x1;
+    g[2] = g2 ^ x2;
+    g[3] = g3 ^ x3;
+    g[4] = g4 ^ x4;
+    g[5] = g5 ^ x5;
+    g[6] = g6 ^ x6;
+    g[7] = g7 ^ x7;
+    g[8] = g8 ^ x8;
+    g[9] = g9 ^ x9;
+}
+
+
+
+/*
+    h = f
+*/
+
+void fe_copy(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    
+    h[0] = f0;
+    h[1] = f1;
+    h[2] = f2;
+    h[3] = f3;
+    h[4] = f4;
+    h[5] = f5;
+    h[6] = f6;
+    h[7] = f7;
+    h[8] = f8;
+    h[9] = f9;
+}
+
+
+
+/*
+    Ignores top bit of h.
+*/
+
+void fe_frombytes(fe h, const unsigned char *s) {
+    int64_t h0 = load_4(s);
+    int64_t h1 = load_3(s + 4) << 6;
+    int64_t h2 = load_3(s + 7) << 5;
+    int64_t h3 = load_3(s + 10) << 3;
+    int64_t h4 = load_3(s + 13) << 2;
+    int64_t h5 = load_4(s + 16);
+    int64_t h6 = load_3(s + 20) << 7;
+    int64_t h7 = load_3(s + 23) << 5;
+    int64_t h8 = load_3(s + 26) << 4;
+    int64_t h9 = (load_3(s + 29) & 8388607) << 2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+
+void fe_invert(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    fe t3;
+    int i;
+
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t2, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t1, t2);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t2, t2, t1);
+    fe_sq(t3, t2);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t3, t3);
+    }
+
+    fe_mul(t2, t3, t2);
+    fe_sq(t2, t2);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(out, t1, t0);
+}
+
+
+
+/*
+    return 1 if f is in {1,3,5,...,q-2}
+    return 0 if f is in {0,2,4,...,q-1}
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnegative(const fe f) {
+    unsigned char s[32];
+
+    fe_tobytes(s, f);
+    
+    return s[0] & 1;
+}
+
+
+
+/*
+    return 1 if f == 0
+    return 0 if f != 0
+
+    Preconditions:
+       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+int fe_isnonzero(const fe f) {
+    unsigned char s[32];
+    unsigned char r;
+
+    fe_tobytes(s, f);
+
+    r = s[0];
+    #define F(i) r |= s[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return r != 0;
+}
+
+
+
+/*
+    h = f * g
+    Can overlap h with f or g.
+
+    Preconditions:
+       |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+       |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+    Postconditions:
+       |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+    */
+
+    /*
+    Notes on implementation strategy:
+
+    Using schoolbook multiplication.
+    Karatsuba would save a little in some cost models.
+
+    Most multiplications by 2 and 19 are 32-bit precomputations;
+    cheaper than 64-bit postcomputations.
+
+    There is one remaining multiplication by 19 in the carry chain;
+    one *19 precomputation can be merged into this,
+    but the resulting data flow is considerably less clean.
+
+    There are 12 carries below.
+    10 of them are 2-way parallelizable and vectorizable.
+    Can get away with 11 carries, but then data flow is much deeper.
+
+    With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+void fe_mul(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
+    int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+    int32_t g3_19 = 19 * g3;
+    int32_t g4_19 = 19 * g4;
+    int32_t g5_19 = 19 * g5;
+    int32_t g6_19 = 19 * g6;
+    int32_t g7_19 = 19 * g7;
+    int32_t g8_19 = 19 * g8;
+    int32_t g9_19 = 19 * g9;
+    int32_t f1_2 = 2 * f1;
+    int32_t f3_2 = 2 * f3;
+    int32_t f5_2 = 2 * f5;
+    int32_t f7_2 = 2 * f7;
+    int32_t f9_2 = 2 * f9;
+    int64_t f0g0    = f0   * (int64_t) g0;
+    int64_t f0g1    = f0   * (int64_t) g1;
+    int64_t f0g2    = f0   * (int64_t) g2;
+    int64_t f0g3    = f0   * (int64_t) g3;
+    int64_t f0g4    = f0   * (int64_t) g4;
+    int64_t f0g5    = f0   * (int64_t) g5;
+    int64_t f0g6    = f0   * (int64_t) g6;
+    int64_t f0g7    = f0   * (int64_t) g7;
+    int64_t f0g8    = f0   * (int64_t) g8;
+    int64_t f0g9    = f0   * (int64_t) g9;
+    int64_t f1g0    = f1   * (int64_t) g0;
+    int64_t f1g1_2  = f1_2 * (int64_t) g1;
+    int64_t f1g2    = f1   * (int64_t) g2;
+    int64_t f1g3_2  = f1_2 * (int64_t) g3;
+    int64_t f1g4    = f1   * (int64_t) g4;
+    int64_t f1g5_2  = f1_2 * (int64_t) g5;
+    int64_t f1g6    = f1   * (int64_t) g6;
+    int64_t f1g7_2  = f1_2 * (int64_t) g7;
+    int64_t f1g8    = f1   * (int64_t) g8;
+    int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
+    int64_t f2g0    = f2   * (int64_t) g0;
+    int64_t f2g1    = f2   * (int64_t) g1;
+    int64_t f2g2    = f2   * (int64_t) g2;
+    int64_t f2g3    = f2   * (int64_t) g3;
+    int64_t f2g4    = f2   * (int64_t) g4;
+    int64_t f2g5    = f2   * (int64_t) g5;
+    int64_t f2g6    = f2   * (int64_t) g6;
+    int64_t f2g7    = f2   * (int64_t) g7;
+    int64_t f2g8_19 = f2   * (int64_t) g8_19;
+    int64_t f2g9_19 = f2   * (int64_t) g9_19;
+    int64_t f3g0    = f3   * (int64_t) g0;
+    int64_t f3g1_2  = f3_2 * (int64_t) g1;
+    int64_t f3g2    = f3   * (int64_t) g2;
+    int64_t f3g3_2  = f3_2 * (int64_t) g3;
+    int64_t f3g4    = f3   * (int64_t) g4;
+    int64_t f3g5_2  = f3_2 * (int64_t) g5;
+    int64_t f3g6    = f3   * (int64_t) g6;
+    int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
+    int64_t f3g8_19 = f3   * (int64_t) g8_19;
+    int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
+    int64_t f4g0    = f4   * (int64_t) g0;
+    int64_t f4g1    = f4   * (int64_t) g1;
+    int64_t f4g2    = f4   * (int64_t) g2;
+    int64_t f4g3    = f4   * (int64_t) g3;
+    int64_t f4g4    = f4   * (int64_t) g4;
+    int64_t f4g5    = f4   * (int64_t) g5;
+    int64_t f4g6_19 = f4   * (int64_t) g6_19;
+    int64_t f4g7_19 = f4   * (int64_t) g7_19;
+    int64_t f4g8_19 = f4   * (int64_t) g8_19;
+    int64_t f4g9_19 = f4   * (int64_t) g9_19;
+    int64_t f5g0    = f5   * (int64_t) g0;
+    int64_t f5g1_2  = f5_2 * (int64_t) g1;
+    int64_t f5g2    = f5   * (int64_t) g2;
+    int64_t f5g3_2  = f5_2 * (int64_t) g3;
+    int64_t f5g4    = f5   * (int64_t) g4;
+    int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
+    int64_t f5g6_19 = f5   * (int64_t) g6_19;
+    int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
+    int64_t f5g8_19 = f5   * (int64_t) g8_19;
+    int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
+    int64_t f6g0    = f6   * (int64_t) g0;
+    int64_t f6g1    = f6   * (int64_t) g1;
+    int64_t f6g2    = f6   * (int64_t) g2;
+    int64_t f6g3    = f6   * (int64_t) g3;
+    int64_t f6g4_19 = f6   * (int64_t) g4_19;
+    int64_t f6g5_19 = f6   * (int64_t) g5_19;
+    int64_t f6g6_19 = f6   * (int64_t) g6_19;
+    int64_t f6g7_19 = f6   * (int64_t) g7_19;
+    int64_t f6g8_19 = f6   * (int64_t) g8_19;
+    int64_t f6g9_19 = f6   * (int64_t) g9_19;
+    int64_t f7g0    = f7   * (int64_t) g0;
+    int64_t f7g1_2  = f7_2 * (int64_t) g1;
+    int64_t f7g2    = f7   * (int64_t) g2;
+    int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
+    int64_t f7g4_19 = f7   * (int64_t) g4_19;
+    int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
+    int64_t f7g6_19 = f7   * (int64_t) g6_19;
+    int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
+    int64_t f7g8_19 = f7   * (int64_t) g8_19;
+    int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
+    int64_t f8g0    = f8   * (int64_t) g0;
+    int64_t f8g1    = f8   * (int64_t) g1;
+    int64_t f8g2_19 = f8   * (int64_t) g2_19;
+    int64_t f8g3_19 = f8   * (int64_t) g3_19;
+    int64_t f8g4_19 = f8   * (int64_t) g4_19;
+    int64_t f8g5_19 = f8   * (int64_t) g5_19;
+    int64_t f8g6_19 = f8   * (int64_t) g6_19;
+    int64_t f8g7_19 = f8   * (int64_t) g7_19;
+    int64_t f8g8_19 = f8   * (int64_t) g8_19;
+    int64_t f8g9_19 = f8   * (int64_t) g9_19;
+    int64_t f9g0    = f9   * (int64_t) g0;
+    int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
+    int64_t f9g2_19 = f9   * (int64_t) g2_19;
+    int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
+    int64_t f9g4_19 = f9   * (int64_t) g4_19;
+    int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
+    int64_t f9g6_19 = f9   * (int64_t) g6_19;
+    int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
+    int64_t f9g8_19 = f9   * (int64_t) g8_19;
+    int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
+    int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
+    int64_t h1 = f0g1 + f1g0   + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
+    int64_t h2 = f0g2 + f1g1_2 + f2g0   + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
+    int64_t h3 = f0g3 + f1g2   + f2g1   + f3g0   + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
+    int64_t h4 = f0g4 + f1g3_2 + f2g2   + f3g1_2 + f4g0   + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
+    int64_t h5 = f0g5 + f1g4   + f2g3   + f3g2   + f4g1   + f5g0   + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
+    int64_t h6 = f0g6 + f1g5_2 + f2g4   + f3g3_2 + f4g2   + f5g1_2 + f6g0   + f7g9_38 + f8g8_19 + f9g7_38;
+    int64_t h7 = f0g7 + f1g6   + f2g5   + f3g4   + f4g3   + f5g2   + f6g1   + f7g0   + f8g9_19 + f9g8_19;
+    int64_t h8 = f0g8 + f1g7_2 + f2g6   + f3g5_2 + f4g4   + f5g3_2 + f6g2   + f7g1_2 + f8g0   + f9g9_38;
+    int64_t h9 = f0g9 + f1g8   + f2g7   + f3g6   + f4g5   + f5g4   + f6g3   + f7g2   + f8g1   + f9g0   ;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f * 121666
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_mul121666(fe h, fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int64_t h0 = f0 * (int64_t) 121666;
+    int64_t h1 = f1 * (int64_t) 121666;
+    int64_t h2 = f2 * (int64_t) 121666;
+    int64_t h3 = f3 * (int64_t) 121666;
+    int64_t h4 = f4 * (int64_t) 121666;
+    int64_t h5 = f5 * (int64_t) 121666;
+    int64_t h6 = f6 * (int64_t) 121666;
+    int64_t h7 = f7 * (int64_t) 121666;
+    int64_t h8 = f8 * (int64_t) 121666;
+    int64_t h9 = f9 * (int64_t) 121666;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+
+    carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+    carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+    carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+    carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+    carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+    carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+    carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+    carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+    carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+    carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_neg(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t h0 = -f0;
+    int32_t h1 = -f1;
+    int32_t h2 = -f2;
+    int32_t h3 = -f3;
+    int32_t h4 = -f4;
+    int32_t h5 = -f5;
+    int32_t h6 = -f6;
+    int32_t h7 = -f7;
+    int32_t h8 = -f8;
+    int32_t h9 = -f9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+void fe_pow22523(fe out, const fe z) {
+    fe t0;
+    fe t1;
+    fe t2;
+    int i;
+    fe_sq(t0, z);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, z, t1);
+    fe_mul(t0, t0, t1);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 1; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 5; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 20; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 10; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t1, t0);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t1, t1, t0);
+    fe_sq(t2, t1);
+
+    for (i = 1; i < 100; ++i) {
+        fe_sq(t2, t2);
+    }
+
+    fe_mul(t1, t2, t1);
+    fe_sq(t1, t1);
+
+    for (i = 1; i < 50; ++i) {
+        fe_sq(t1, t1);
+    }
+
+    fe_mul(t0, t1, t0);
+    fe_sq(t0, t0);
+
+    for (i = 1; i < 2; ++i) {
+        fe_sq(t0, t0);
+    }
+
+    fe_mul(out, t0, z);
+    return;
+}
+
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq2(fe h, const fe f) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t f0_2 = 2 * f0;
+    int32_t f1_2 = 2 * f1;
+    int32_t f2_2 = 2 * f2;
+    int32_t f3_2 = 2 * f3;
+    int32_t f4_2 = 2 * f4;
+    int32_t f5_2 = 2 * f5;
+    int32_t f6_2 = 2 * f6;
+    int32_t f7_2 = 2 * f7;
+    int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
+    int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
+    int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
+    int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
+    int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
+    int64_t f0f0    = f0   * (int64_t) f0;
+    int64_t f0f1_2  = f0_2 * (int64_t) f1;
+    int64_t f0f2_2  = f0_2 * (int64_t) f2;
+    int64_t f0f3_2  = f0_2 * (int64_t) f3;
+    int64_t f0f4_2  = f0_2 * (int64_t) f4;
+    int64_t f0f5_2  = f0_2 * (int64_t) f5;
+    int64_t f0f6_2  = f0_2 * (int64_t) f6;
+    int64_t f0f7_2  = f0_2 * (int64_t) f7;
+    int64_t f0f8_2  = f0_2 * (int64_t) f8;
+    int64_t f0f9_2  = f0_2 * (int64_t) f9;
+    int64_t f1f1_2  = f1_2 * (int64_t) f1;
+    int64_t f1f2_2  = f1_2 * (int64_t) f2;
+    int64_t f1f3_4  = f1_2 * (int64_t) f3_2;
+    int64_t f1f4_2  = f1_2 * (int64_t) f4;
+    int64_t f1f5_4  = f1_2 * (int64_t) f5_2;
+    int64_t f1f6_2  = f1_2 * (int64_t) f6;
+    int64_t f1f7_4  = f1_2 * (int64_t) f7_2;
+    int64_t f1f8_2  = f1_2 * (int64_t) f8;
+    int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
+    int64_t f2f2    = f2   * (int64_t) f2;
+    int64_t f2f3_2  = f2_2 * (int64_t) f3;
+    int64_t f2f4_2  = f2_2 * (int64_t) f4;
+    int64_t f2f5_2  = f2_2 * (int64_t) f5;
+    int64_t f2f6_2  = f2_2 * (int64_t) f6;
+    int64_t f2f7_2  = f2_2 * (int64_t) f7;
+    int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
+    int64_t f2f9_38 = f2   * (int64_t) f9_38;
+    int64_t f3f3_2  = f3_2 * (int64_t) f3;
+    int64_t f3f4_2  = f3_2 * (int64_t) f4;
+    int64_t f3f5_4  = f3_2 * (int64_t) f5_2;
+    int64_t f3f6_2  = f3_2 * (int64_t) f6;
+    int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
+    int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
+    int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
+    int64_t f4f4    = f4   * (int64_t) f4;
+    int64_t f4f5_2  = f4_2 * (int64_t) f5;
+    int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
+    int64_t f4f7_38 = f4   * (int64_t) f7_38;
+    int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
+    int64_t f4f9_38 = f4   * (int64_t) f9_38;
+    int64_t f5f5_38 = f5   * (int64_t) f5_38;
+    int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
+    int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
+    int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
+    int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
+    int64_t f6f6_19 = f6   * (int64_t) f6_19;
+    int64_t f6f7_38 = f6   * (int64_t) f7_38;
+    int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
+    int64_t f6f9_38 = f6   * (int64_t) f9_38;
+    int64_t f7f7_38 = f7   * (int64_t) f7_38;
+    int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
+    int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
+    int64_t f8f8_19 = f8   * (int64_t) f8_19;
+    int64_t f8f9_38 = f8   * (int64_t) f9_38;
+    int64_t f9f9_38 = f9   * (int64_t) f9_38;
+    int64_t h0 = f0f0  + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
+    int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
+    int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
+    int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
+    int64_t h4 = f0f4_2 + f1f3_4 + f2f2   + f5f9_76 + f6f8_38 + f7f7_38;
+    int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
+    int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
+    int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
+    int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4   + f9f9_38;
+    int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    h0 += h0;
+    h1 += h1;
+    h2 += h2;
+    h3 += h3;
+    h4 += h4;
+    h5 += h5;
+    h6 += h6;
+    h7 += h7;
+    h8 += h8;
+    h9 += h9;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
+    h0 += carry9 * 19;
+    h9 -= carry9 << 25;
+    carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    h[0] = (int32_t) h0;
+    h[1] = (int32_t) h1;
+    h[2] = (int32_t) h2;
+    h[3] = (int32_t) h3;
+    h[4] = (int32_t) h4;
+    h[5] = (int32_t) h5;
+    h[6] = (int32_t) h6;
+    h[7] = (int32_t) h7;
+    h[8] = (int32_t) h8;
+    h[9] = (int32_t) h9;
+}
+
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h, const fe f, const fe g) {
+    int32_t f0 = f[0];
+    int32_t f1 = f[1];
+    int32_t f2 = f[2];
+    int32_t f3 = f[3];
+    int32_t f4 = f[4];
+    int32_t f5 = f[5];
+    int32_t f6 = f[6];
+    int32_t f7 = f[7];
+    int32_t f8 = f[8];
+    int32_t f9 = f[9];
+    int32_t g0 = g[0];
+    int32_t g1 = g[1];
+    int32_t g2 = g[2];
+    int32_t g3 = g[3];
+    int32_t g4 = g[4];
+    int32_t g5 = g[5];
+    int32_t g6 = g[6];
+    int32_t g7 = g[7];
+    int32_t g8 = g[8];
+    int32_t g9 = g[9];
+    int32_t h0 = f0 - g0;
+    int32_t h1 = f1 - g1;
+    int32_t h2 = f2 - g2;
+    int32_t h3 = f3 - g3;
+    int32_t h4 = f4 - g4;
+    int32_t h5 = f5 - g5;
+    int32_t h6 = f6 - g6;
+    int32_t h7 = f7 - g7;
+    int32_t h8 = f8 - g8;
+    int32_t h9 = f9 - g9;
+
+    h[0] = h0;
+    h[1] = h1;
+    h[2] = h2;
+    h[3] = h3;
+    h[4] = h4;
+    h[5] = h5;
+    h[6] = h6;
+    h[7] = h7;
+    h[8] = h8;
+    h[9] = h9;
+}
+
+
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+void fe_tobytes(unsigned char *s, const fe h) {
+    int32_t h0 = h[0];
+    int32_t h1 = h[1];
+    int32_t h2 = h[2];
+    int32_t h3 = h[3];
+    int32_t h4 = h[4];
+    int32_t h5 = h[5];
+    int32_t h6 = h[6];
+    int32_t h7 = h[7];
+    int32_t h8 = h[8];
+    int32_t h9 = h[9];
+    int32_t q;
+    int32_t carry0;
+    int32_t carry1;
+    int32_t carry2;
+    int32_t carry3;
+    int32_t carry4;
+    int32_t carry5;
+    int32_t carry6;
+    int32_t carry7;
+    int32_t carry8;
+    int32_t carry9;
+    q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
+    q = (h0 + q) >> 26;
+    q = (h1 + q) >> 25;
+    q = (h2 + q) >> 26;
+    q = (h3 + q) >> 25;
+    q = (h4 + q) >> 26;
+    q = (h5 + q) >> 25;
+    q = (h6 + q) >> 26;
+    q = (h7 + q) >> 25;
+    q = (h8 + q) >> 26;
+    q = (h9 + q) >> 25;
+    /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+    h0 += 19 * q;
+    /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+    carry0 = h0 >> 26;
+    h1 += carry0;
+    h0 -= carry0 << 26;
+    carry1 = h1 >> 25;
+    h2 += carry1;
+    h1 -= carry1 << 25;
+    carry2 = h2 >> 26;
+    h3 += carry2;
+    h2 -= carry2 << 26;
+    carry3 = h3 >> 25;
+    h4 += carry3;
+    h3 -= carry3 << 25;
+    carry4 = h4 >> 26;
+    h5 += carry4;
+    h4 -= carry4 << 26;
+    carry5 = h5 >> 25;
+    h6 += carry5;
+    h5 -= carry5 << 25;
+    carry6 = h6 >> 26;
+    h7 += carry6;
+    h6 -= carry6 << 26;
+    carry7 = h7 >> 25;
+    h8 += carry7;
+    h7 -= carry7 << 25;
+    carry8 = h8 >> 26;
+    h9 += carry8;
+    h8 -= carry8 << 26;
+    carry9 = h9 >> 25;
+    h9 -= carry9 << 25;
+
+    /* h10 = carry9 */
+    /*
+    Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+    Have h0+...+2^230 h9 between 0 and 2^255-1;
+    evidently 2^255 h10-2^255 q = 0.
+    Goal: Output h0+...+2^230 h9.
+    */
+    s[0] = (unsigned char) (h0 >> 0);
+    s[1] = (unsigned char) (h0 >> 8);
+    s[2] = (unsigned char) (h0 >> 16);
+    s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
+    s[4] = (unsigned char) (h1 >> 6);
+    s[5] = (unsigned char) (h1 >> 14);
+    s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
+    s[7] = (unsigned char) (h2 >> 5);
+    s[8] = (unsigned char) (h2 >> 13);
+    s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
+    s[10] = (unsigned char) (h3 >> 3);
+    s[11] = (unsigned char) (h3 >> 11);
+    s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
+    s[13] = (unsigned char) (h4 >> 2);
+    s[14] = (unsigned char) (h4 >> 10);
+    s[15] = (unsigned char) (h4 >> 18);
+    s[16] = (unsigned char) (h5 >> 0);
+    s[17] = (unsigned char) (h5 >> 8);
+    s[18] = (unsigned char) (h5 >> 16);
+    s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
+    s[20] = (unsigned char) (h6 >> 7);
+    s[21] = (unsigned char) (h6 >> 15);
+    s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
+    s[23] = (unsigned char) (h7 >> 5);
+    s[24] = (unsigned char) (h7 >> 13);
+    s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
+    s[26] = (unsigned char) (h8 >> 4);
+    s[27] = (unsigned char) (h8 >> 12);
+    s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
+    s[29] = (unsigned char) (h9 >> 2);
+    s[30] = (unsigned char) (h9 >> 10);
+    s[31] = (unsigned char) (h9 >> 18);
+}

diff --git a/src/ed25519/fe.h b/src/ed25519/fe.h
new file mode 100644 (file)
index 0000000..b4b62d2
--- /dev/null
+++ b/src/ed25519/fe.h
@@ -0,0 +1,41 @@
+#ifndef FE_H
+#define FE_H
+
+#include "fixedint.h"
+
+
+/*
+    fe means field element.
+    Here the field is \Z/(2^255-19).
+    An element t, entries t[0]...t[9], represents the integer
+    t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
+    Bounds on each t[i] vary depending on context.
+*/
+
+
+typedef int32_t fe[10];
+
+
+void fe_0(fe h);
+void fe_1(fe h);
+
+void fe_frombytes(fe h, const unsigned char *s);
+void fe_tobytes(unsigned char *s, const fe h);
+
+void fe_copy(fe h, const fe f);
+int fe_isnegative(const fe f);
+int fe_isnonzero(const fe f);
+void fe_cmov(fe f, const fe g, unsigned int b);
+void fe_cswap(fe f, fe g, unsigned int b);
+
+void fe_neg(fe h, const fe f);
+void fe_add(fe h, const fe f, const fe g);
+void fe_invert(fe out, const fe z);
+void fe_sq(fe h, const fe f);
+void fe_sq2(fe h, const fe f);
+void fe_mul(fe h, const fe f, const fe g);
+void fe_mul121666(fe h, fe f);
+void fe_pow22523(fe out, const fe z);
+void fe_sub(fe h, const fe f, const fe g);
+
+#endif

diff --git a/src/ed25519/fixedint.h b/src/ed25519/fixedint.h
new file mode 100644 (file)
index 0000000..d03e4bd
--- /dev/null
+++ b/src/ed25519/fixedint.h
@@ -0,0 +1,70 @@
+/*
+    Portable header to provide the 32 and 64 bits type.
+
+    Not a compatible replacement for <stdint.h>, do not blindly use it as such.
+*/
+
+#if ((defined(__STDC__) && __STDC__ && __STDC_VERSION__ >= 199901L) || (defined(__WATCOMC__) && (defined(_STDINT_H_INCLUDED) || __WATCOMC__ >= 1250)) || (defined(__GNUC__) && (defined(_STDINT_H) || defined(_STDINT_H_) || defined(__UINT_FAST64_TYPE__)) )) && !defined(FIXEDINT_H_INCLUDED)
+    #include <stdint.h>
+    #define FIXEDINT_H_INCLUDED
+
+    #if defined(__WATCOMC__) && __WATCOMC__ >= 1250 && !defined(UINT64_C)
+        #include <limits.h>
+        #define UINT64_C(x) (x + (UINT64_MAX - UINT64_MAX))
+    #endif
+#endif
+
+
+#ifndef FIXEDINT_H_INCLUDED
+    #define FIXEDINT_H_INCLUDED
+
+    /* (u)int32_t */
+    #ifndef uint32_t
+        #if (ULONG_MAX == 0xffffffffUL)
+            typedef unsigned long uint32_t;
+        #elif (UINT_MAX == 0xffffffffUL)
+            typedef unsigned int uint32_t;
+        #elif (USHRT_MAX == 0xffffffffUL)
+            typedef unsigned short uint32_t;
+        #endif
+    #endif
+
+
+    #ifndef int32_t
+        #if (LONG_MAX == 0x7fffffffL)
+            typedef signed long int32_t;
+        #elif (INT_MAX == 0x7fffffffL)
+            typedef signed int int32_t;
+        #elif (SHRT_MAX == 0x7fffffffL)
+            typedef signed short int32_t;
+        #endif
+    #endif
+
+
+    /* (u)int64_t */
+    #if (defined(__STDC__) && defined(__STDC_VERSION__) && __STDC__ && __STDC_VERSION__ >= 199901L)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__GNUC__)
+        __extension__ typedef long long int64_t;
+        __extension__ typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif defined(__MWERKS__) || defined(__SUNPRO_C) || defined(__SUNPRO_CC) || defined(__APPLE_CC__) || defined(_LONG_LONG) || defined(_CRAYC)
+        typedef long long int64_t;
+        typedef unsigned long long uint64_t;
+
+        #define UINT64_C(v) v ##ULL
+        #define INT64_C(v) v ##LL
+    #elif (defined(__WATCOMC__) && defined(__WATCOM_INT64__)) || (defined(_MSC_VER) && _INTEGRAL_MAX_BITS >= 64) || (defined(__BORLANDC__) && __BORLANDC__ > 0x460) || defined(__alpha) || defined(__DECC)
+        typedef __int64 int64_t;
+        typedef unsigned __int64 uint64_t;
+
+        #define UINT64_C(v) v ##UI64
+        #define INT64_C(v) v ##I64
+    #endif
+#endif

diff --git a/src/ed25519/ge.c b/src/ed25519/ge.c
new file mode 100644 (file)
index 0000000..3c342b1
--- /dev/null
+++ b/src/ed25519/ge.c
@@ -0,0 +1,467 @@
+#include "ge.h"
+#include "precomp_data.h"
+
+
+/*
+r = p + q
+*/
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YplusX);
+    fe_mul(r->Y, r->Y, q->YminusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+static void slide(signed char *r, const unsigned char *a) {
+    int i;
+    int b;
+    int k;
+
+    for (i = 0; i < 256; ++i) {
+        r[i] = 1 & (a[i >> 3] >> (i & 7));
+    }
+
+    for (i = 0; i < 256; ++i)
+        if (r[i]) {
+            for (b = 1; b <= 6 && i + b < 256; ++b) {
+                if (r[i + b]) {
+                    if (r[i] + (r[i + b] << b) <= 15) {
+                        r[i] += r[i + b] << b;
+                        r[i + b] = 0;
+                    } else if (r[i] - (r[i + b] << b) >= -15) {
+                        r[i] -= r[i + b] << b;
+
+                        for (k = i + b; k < 256; ++k) {
+                            if (!r[k]) {
+                                r[k] = 1;
+                                break;
+                            }
+
+                            r[k] = 0;
+                        }
+                    } else {
+                        break;
+                    }
+                }
+            }
+        }
+}
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) {
+    signed char aslide[256];
+    signed char bslide[256];
+    ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+    ge_p1p1 t;
+    ge_p3 u;
+    ge_p3 A2;
+    int i;
+    slide(aslide, a);
+    slide(bslide, b);
+    ge_p3_to_cached(&Ai[0], A);
+    ge_p3_dbl(&t, A);
+    ge_p1p1_to_p3(&A2, &t);
+    ge_add(&t, &A2, &Ai[0]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[1], &u);
+    ge_add(&t, &A2, &Ai[1]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[2], &u);
+    ge_add(&t, &A2, &Ai[2]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[3], &u);
+    ge_add(&t, &A2, &Ai[3]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[4], &u);
+    ge_add(&t, &A2, &Ai[4]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[5], &u);
+    ge_add(&t, &A2, &Ai[5]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[6], &u);
+    ge_add(&t, &A2, &Ai[6]);
+    ge_p1p1_to_p3(&u, &t);
+    ge_p3_to_cached(&Ai[7], &u);
+    ge_p2_0(r);
+
+    for (i = 255; i >= 0; --i) {
+        if (aslide[i] || bslide[i]) {
+            break;
+        }
+    }
+
+    for (; i >= 0; --i) {
+        ge_p2_dbl(&t, r);
+
+        if (aslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_add(&t, &u, &Ai[aslide[i] / 2]);
+        } else if (aslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
+        }
+
+        if (bslide[i] > 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_madd(&t, &u, &Bi[bslide[i] / 2]);
+        } else if (bslide[i] < 0) {
+            ge_p1p1_to_p3(&u, &t);
+            ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
+        }
+
+        ge_p1p1_to_p2(r, &t);
+    }
+}
+
+
+static const fe d = {
+    -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
+};
+
+static const fe sqrtm1 = {
+    -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
+};
+
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s) {
+    fe u;
+    fe v;
+    fe v3;
+    fe vxx;
+    fe check;
+    fe_frombytes(h->Y, s);
+    fe_1(h->Z);
+    fe_sq(u, h->Y);
+    fe_mul(v, u, d);
+    fe_sub(u, u, h->Z);     /* u = y^2-1 */
+    fe_add(v, v, h->Z);     /* v = dy^2+1 */
+    fe_sq(v3, v);
+    fe_mul(v3, v3, v);      /* v3 = v^3 */
+    fe_sq(h->X, v3);
+    fe_mul(h->X, h->X, v);
+    fe_mul(h->X, h->X, u);  /* x = uv^7 */
+    fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
+    fe_mul(h->X, h->X, v3);
+    fe_mul(h->X, h->X, u);  /* x = uv^3(uv^7)^((q-5)/8) */
+    fe_sq(vxx, h->X);
+    fe_mul(vxx, vxx, v);
+    fe_sub(check, vxx, u);  /* vx^2-u */
+
+    if (fe_isnonzero(check)) {
+        fe_add(check, vxx, u); /* vx^2+u */
+
+        if (fe_isnonzero(check)) {
+            return -1;
+        }
+
+        fe_mul(h->X, h->X, sqrtm1);
+    }
+
+    if (fe_isnegative(h->X) == (s[31] >> 7)) {
+        fe_neg(h->X, h->X);
+    }
+
+    fe_mul(h->T, h->X, h->Y);
+    return 0;
+}
+
+
+/*
+r = p + q
+*/
+
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yplusx);
+    fe_mul(r->Y, r->Y, q->yminusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_add(r->Z, t0, r->T);
+    fe_sub(r->T, t0, r->T);
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) {
+    fe t0;
+
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->yminusx);
+    fe_mul(r->Y, r->Y, q->yplusx);
+    fe_mul(r->T, q->xy2d, p->T);
+    fe_add(t0, p->Z, p->Z);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+}
+
+
+
+/*
+r = p
+*/
+
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) {
+    fe_mul(r->X, p->X, p->T);
+    fe_mul(r->Y, p->Y, p->Z);
+    fe_mul(r->Z, p->Z, p->T);
+    fe_mul(r->T, p->X, p->Y);
+}
+
+
+void ge_p2_0(ge_p2 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+}
+
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) {
+    fe t0;
+
+    fe_sq(r->X, p->X);
+    fe_sq(r->Z, p->Y);
+    fe_sq2(r->T, p->Z);
+    fe_add(r->Y, p->X, p->Y);
+    fe_sq(t0, r->Y);
+    fe_add(r->Y, r->Z, r->X);
+    fe_sub(r->Z, r->Z, r->X);
+    fe_sub(r->X, t0, r->Y);
+    fe_sub(r->T, r->T, r->Z);
+}
+
+
+void ge_p3_0(ge_p3 *h) {
+    fe_0(h->X);
+    fe_1(h->Y);
+    fe_1(h->Z);
+    fe_0(h->T);
+}
+
+
+/*
+r = 2 * p
+*/
+
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) {
+    ge_p2 q;
+    ge_p3_to_p2(&q, p);
+    ge_p2_dbl(r, &q);
+}
+
+
+
+/*
+r = p
+*/
+
+static const fe d2 = {
+    -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
+};
+
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) {
+    fe_add(r->YplusX, p->Y, p->X);
+    fe_sub(r->YminusX, p->Y, p->X);
+    fe_copy(r->Z, p->Z);
+    fe_mul(r->T2d, p->T, d2);
+}
+
+
+/*
+r = p
+*/
+
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) {
+    fe_copy(r->X, p->X);
+    fe_copy(r->Y, p->Y);
+    fe_copy(r->Z, p->Z);
+}
+
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}
+
+
+static unsigned char equal(signed char b, signed char c) {
+    unsigned char ub = b;
+    unsigned char uc = c;
+    unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+    uint64_t y = x; /* 0: yes; 1..255: no */
+    y -= 1; /* large: yes; 0..254: no */
+    y >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) y;
+}
+
+static unsigned char negative(signed char b) {
+    uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+    x >>= 63; /* 1: yes; 0: no */
+    return (unsigned char) x;
+}
+
+static void cmov(ge_precomp *t, ge_precomp *u, unsigned char b) {
+    fe_cmov(t->yplusx, u->yplusx, b);
+    fe_cmov(t->yminusx, u->yminusx, b);
+    fe_cmov(t->xy2d, u->xy2d, b);
+}
+
+
+static void select(ge_precomp *t, int pos, signed char b) {
+    ge_precomp minust;
+    unsigned char bnegative = negative(b);
+    unsigned char babs = b - (((-bnegative) & b) << 1);
+    fe_1(t->yplusx);
+    fe_1(t->yminusx);
+    fe_0(t->xy2d);
+    cmov(t, &base[pos][0], equal(babs, 1));
+    cmov(t, &base[pos][1], equal(babs, 2));
+    cmov(t, &base[pos][2], equal(babs, 3));
+    cmov(t, &base[pos][3], equal(babs, 4));
+    cmov(t, &base[pos][4], equal(babs, 5));
+    cmov(t, &base[pos][5], equal(babs, 6));
+    cmov(t, &base[pos][6], equal(babs, 7));
+    cmov(t, &base[pos][7], equal(babs, 8));
+    fe_copy(minust.yplusx, t->yminusx);
+    fe_copy(minust.yminusx, t->yplusx);
+    fe_neg(minust.xy2d, t->xy2d);
+    cmov(t, &minust, bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) {
+    signed char e[64];
+    signed char carry;
+    ge_p1p1 r;
+    ge_p2 s;
+    ge_precomp t;
+    int i;
+
+    for (i = 0; i < 32; ++i) {
+        e[2 * i + 0] = (a[i] >> 0) & 15;
+        e[2 * i + 1] = (a[i] >> 4) & 15;
+    }
+
+    /* each e[i] is between 0 and 15 */
+    /* e[63] is between 0 and 7 */
+    carry = 0;
+
+    for (i = 0; i < 63; ++i) {
+        e[i] += carry;
+        carry = e[i] + 8;
+        carry >>= 4;
+        e[i] -= carry << 4;
+    }
+
+    e[63] += carry;
+    /* each e[i] is between -8 and 8 */
+    ge_p3_0(h);
+
+    for (i = 1; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+
+    ge_p3_dbl(&r, h);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p2(&s, &r);
+    ge_p2_dbl(&r, &s);
+    ge_p1p1_to_p3(h, &r);
+
+    for (i = 0; i < 64; i += 2) {
+        select(&t, i / 2, e[i]);
+        ge_madd(&r, h, &t);
+        ge_p1p1_to_p3(h, &r);
+    }
+}
+
+
+/*
+r = p - q
+*/
+
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) {
+    fe t0;
+    
+    fe_add(r->X, p->Y, p->X);
+    fe_sub(r->Y, p->Y, p->X);
+    fe_mul(r->Z, r->X, q->YminusX);
+    fe_mul(r->Y, r->Y, q->YplusX);
+    fe_mul(r->T, q->T2d, p->T);
+    fe_mul(r->X, p->Z, q->Z);
+    fe_add(t0, r->X, r->X);
+    fe_sub(r->X, r->Z, r->Y);
+    fe_add(r->Y, r->Z, r->Y);
+    fe_sub(r->Z, t0, r->T);
+    fe_add(r->T, t0, r->T);
+}
+
+
+void ge_tobytes(unsigned char *s, const ge_p2 *h) {
+    fe recip;
+    fe x;
+    fe y;
+    fe_invert(recip, h->Z);
+    fe_mul(x, h->X, recip);
+    fe_mul(y, h->Y, recip);
+    fe_tobytes(s, y);
+    s[31] ^= fe_isnegative(x) << 7;
+}

diff --git a/src/ed25519/ge.h b/src/ed25519/ge.h
new file mode 100644 (file)
index 0000000..17fde2d
--- /dev/null
+++ b/src/ed25519/ge.h
@@ -0,0 +1,74 @@
+#ifndef GE_H
+#define GE_H
+
+#include "fe.h"
+
+
+/*
+ge means group element.
+
+Here the group is the set of pairs (x,y) of field elements (see fe.h)
+satisfying -x^2 + y^2 = 1 + d x^2y^2
+where d = -121665/121666.
+
+Representations:
+  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+  ge_precomp (Duif): (y+x,y-x,2dxy)
+*/
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+void ge_p3_tobytes(unsigned char *s, const ge_p3 *h);
+void ge_tobytes(unsigned char *s, const ge_p2 *h);
+int ge_frombytes_negate_vartime(ge_p3 *h, const unsigned char *s);
+
+void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q);
+void ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b);
+void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q);
+void ge_scalarmult_base(ge_p3 *h, const unsigned char *a);
+
+void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p);
+void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p);
+void ge_p2_0(ge_p2 *h);
+void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p);
+void ge_p3_0(ge_p3 *h);
+void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p);
+void ge_p3_to_cached(ge_cached *r, const ge_p3 *p);
+void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p);
+
+#endif

diff --git a/src/ed25519/key_exchange.c b/src/ed25519/key_exchange.c
new file mode 100644 (file)
index 0000000..abd75da
--- /dev/null
+++ b/src/ed25519/key_exchange.c
@@ -0,0 +1,79 @@
+#include "ed25519.h"
+#include "fe.h"
+
+void ed25519_key_exchange(unsigned char *shared_secret, const unsigned char *public_key, const unsigned char *private_key) {
+    unsigned char e[32];
+    unsigned int i;
+    
+    fe x1;
+    fe x2;
+    fe z2;
+    fe x3;
+    fe z3;
+    fe tmp0;
+    fe tmp1;
+
+    int pos;
+    unsigned int swap;
+    unsigned int b;
+
+    /* copy the private key and make sure it's valid */
+    for (i = 0; i < 32; ++i) {
+        e[i] = private_key[i];
+    }
+
+    e[0] &= 248;
+    e[31] &= 63;
+    e[31] |= 64;
+
+    /* unpack the public key and convert edwards to montgomery */
+    /* due to CodesInChaos: montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p */
+    fe_frombytes(x1, public_key);
+    fe_1(tmp1);
+    fe_add(tmp0, x1, tmp1);
+    fe_sub(tmp1, tmp1, x1);
+    fe_invert(tmp1, tmp1);
+    fe_mul(x1, tmp0, tmp1);
+
+    fe_1(x2);
+    fe_0(z2);
+    fe_copy(x3, x1);
+    fe_1(z3);
+
+    swap = 0;
+    for (pos = 254; pos >= 0; --pos) {
+        b = e[pos / 8] >> (pos & 7);
+        b &= 1;
+        swap ^= b;
+        fe_cswap(x2, x3, swap);
+        fe_cswap(z2, z3, swap);
+        swap = b;
+
+        /* from montgomery.h */
+        fe_sub(tmp0, x3, z3);
+        fe_sub(tmp1, x2, z2);
+        fe_add(x2, x2, z2);
+        fe_add(z2, x3, z3);
+        fe_mul(z3, tmp0, x2);
+        fe_mul(z2, z2, tmp1);
+        fe_sq(tmp0, tmp1);
+        fe_sq(tmp1, x2);
+        fe_add(x3, z3, z2);
+        fe_sub(z2, z3, z2);
+        fe_mul(x2, tmp1, tmp0);
+        fe_sub(tmp1, tmp1, tmp0);
+        fe_sq(z2, z2);
+        fe_mul121666(z3, tmp1);
+        fe_sq(x3, x3);
+        fe_add(tmp0, tmp0, z3);
+        fe_mul(z3, x1, z2);
+        fe_mul(z2, tmp1, tmp0);
+    }
+
+    fe_cswap(x2, x3, swap);
+    fe_cswap(z2, z3, swap);
+
+    fe_invert(z2, z2);
+    fe_mul(x2, x2, z2);
+    fe_tobytes(shared_secret, x2);
+}

diff --git a/src/ed25519/keypair.c b/src/ed25519/keypair.c
new file mode 100644 (file)
index 0000000..dc1b8ec
--- /dev/null
+++ b/src/ed25519/keypair.c
@@ -0,0 +1,16 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+
+
+void ed25519_create_keypair(unsigned char *public_key, unsigned char *private_key, const unsigned char *seed) {
+    ge_p3 A;
+
+    sha512(seed, 32, private_key);
+    private_key[0] &= 248;
+    private_key[31] &= 63;
+    private_key[31] |= 64;
+
+    ge_scalarmult_base(&A, private_key);
+    ge_p3_tobytes(public_key, &A);
+}

diff --git a/src/ed25519/precomp_data.h b/src/ed25519/precomp_data.h
new file mode 100644 (file)
index 0000000..776b84f
--- /dev/null
+++ b/src/ed25519/precomp_data.h
@@ -0,0 +1,1391 @@
+static ge_precomp Bi[8] = {
+    {
+        { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+        { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+        { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+    },
+    {
+        { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+        { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+        { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+    },
+    {
+        { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+        { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+        { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+    },
+    {
+        { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+        { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+        { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+    },
+    {
+        { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 },
+        { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 },
+        { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 },
+    },
+    {
+        { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 },
+        { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 },
+        { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 },
+    },
+    {
+        { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 },
+        { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 },
+        { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 },
+    },
+    {
+        { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 },
+        { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 },
+        { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 },
+    },
+};
+
+
+/* base[i][j] = (j+1)*256^i*B */
+static ge_precomp base[32][8] = {
+    {
+        {
+            { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
+            { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
+            { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
+        },
+        {
+            { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 },
+            { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 },
+            { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 },
+        },
+        {
+            { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
+            { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
+            { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
+        },
+        {
+            { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 },
+            { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 },
+            { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 },
+        },
+        {
+            { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
+            { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
+            { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
+        },
+        {
+            { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 },
+            { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 },
+            { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 },
+        },
+        {
+            { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
+            { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
+            { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
+        },
+        {
+            { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 },
+            { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 },
+            { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 },
+        },
+    },
+    {
+        {
+            { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 },
+            { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 },
+            { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 },
+        },
+        {
+            { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 },
+            { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 },
+            { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 },
+        },
+        {
+            { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 },
+            { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 },
+            { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 },
+        },
+        {
+            { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 },
+            { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 },
+            { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 },
+        },
+        {
+            { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 },
+            { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 },
+            { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 },
+        },
+        {
+            { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 },
+            { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 },
+            { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 },
+        },
+        {
+            { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 },
+            { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 },
+            { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 },
+        },
+        {
+            { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 },
+            { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 },
+            { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 },
+        },
+    },
+    {
+        {
+            { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 },
+            { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 },
+            { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 },
+        },
+        {
+            { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 },
+            { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 },
+            { -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 },
+        },
+        {
+            { -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 },
+            { 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 },
+            { 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 },
+        },
+        {
+            { -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 },
+            { 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 },
+            { 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 },
+        },
+        {
+            { -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 },
+            { 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 },
+            { -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 },
+        },
+        {
+            { -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 },
+            { -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 },
+            { 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 },
+        },
+        {
+            { 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 },
+            { -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 },
+            { -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 },
+        },
+        {
+            { 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 },
+            { 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 },
+            { -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 },
+        },
+    },
+    {
+        {
+            { 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 },
+            { -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 },
+            { -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 },
+        },
+        {
+            { -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 },
+            { 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 },
+            { -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 },
+        },
+        {
+            { 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 },
+            { 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 },
+            { -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 },
+        },
+        {
+            { 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556 },
+            { 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749 },
+            { 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930 },
+        },
+        {
+            { 1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391 },
+            { 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253 },
+            { 20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066 },
+        },
+        {
+            { 24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958 },
+            { -11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082 },
+            { -28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383 },
+        },
+        {
+            { -30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521 },
+            { -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807 },
+            { 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948 },
+        },
+        {
+            { 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134 },
+            { -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455 },
+            { 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629 },
+        },
+    },
+    {
+        {
+            { -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069 },
+            { -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746 },
+            { 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919 },
+        },
+        {
+            { 11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837 },
+            { 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906 },
+            { -28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771 },
+        },
+        {
+            { -25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817 },
+            { 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098 },
+            { 10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409 },
+        },
+        {
+            { -12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504 },
+            { -26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727 },
+            { 28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420 },
+        },
+        {
+            { -32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003 },
+            { -1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605 },
+            { -30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384 },
+        },
+        {
+            { -26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701 },
+            { -23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683 },
+            { 29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708 },
+        },
+        {
+            { -3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563 },
+            { -19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260 },
+            { -5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387 },
+        },
+        {
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+            { -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 },
+        },
+    },
+    {
+        {
+            { 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 },
+            { 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 },
+            { -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 },
+        },
+        {
+            { -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 },
+            { -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 },
+            { 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 },
+        },
+        {
+            { -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 },
+            { -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 },
+            { 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 },
+        },
+        {
+            { 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 },
+            { -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 },
+            { 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 },
+        },
+        {
+            { -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 },
+            { 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 },
+            { -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 },
+        },
+        {
+            { 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 },
+            { 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 },
+            { -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 },
+        },
+        {
+            { -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 },
+            { 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 },
+            { 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 },
+        },
+        {
+            { 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 },
+            { 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 },
+            { -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 },
+        },
+    },
+    {
+        {
+            { -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 },
+            { -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 },
+            { -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 },
+        },
+        {
+            { -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 },
+            { -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 },
+            { 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 },
+        },
+        {
+            { 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 },
+            { -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 },
+            { -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 },
+        },
+        {
+            { -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 },
+            { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 },
+            { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 },
+        },
+        {
+            { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 },
+            { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 },
+            { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 },
+        },
+        {
+            { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 },
+            { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 },
+            { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 },
+        },
+        {
+            { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 },
+            { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 },
+            { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 },
+        },
+        {
+            { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 },
+            { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 },
+            { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 },
+        },
+    },
+    {
+        {
+            { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 },
+            { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 },
+            { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 },
+        },
+        {
+            { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 },
+            { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 },
+            { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 },
+        },
+        {
+            { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 },
+            { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 },
+            { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 },
+        },
+        {
+            { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 },
+            { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 },
+            { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 },
+        },
+        {
+            { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 },
+            { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 },
+            { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 },
+        },
+        {
+            { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 },
+            { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 },
+            { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 },
+        },
+        {
+            { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 },
+            { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 },
+            { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 },
+        },
+        {
+            { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 },
+            { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 },
+            { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 },
+        },
+    },
+};
\ No newline at end of file

diff --git a/src/ed25519/sc.c b/src/ed25519/sc.c
new file mode 100644 (file)
index 0000000..ca5bad2
--- /dev/null
+++ b/src/ed25519/sc.c
@@ -0,0 +1,809 @@
+#include "fixedint.h"
+#include "sc.h"
+
+static uint64_t load_3(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+
+    return result;
+}
+
+static uint64_t load_4(const unsigned char *in) {
+    uint64_t result;
+
+    result = (uint64_t) in[0];
+    result |= ((uint64_t) in[1]) << 8;
+    result |= ((uint64_t) in[2]) << 16;
+    result |= ((uint64_t) in[3]) << 24;
+    
+    return result;
+}
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+void sc_reduce(unsigned char *s) {
+    int64_t s0 = 2097151 & load_3(s);
+    int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
+    int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
+    int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
+    int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
+    int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
+    int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
+    int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
+    int64_t s8 = 2097151 & load_3(s + 21);
+    int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
+    int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
+    int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
+    int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
+    int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
+    int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
+    int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
+    int64_t s16 = 2097151 & load_3(s + 42);
+    int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
+    int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
+    int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
+    int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
+    int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
+    int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
+    int64_t s23 = (load_4(s + 60) >> 3);
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}
+
+
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
+    int64_t a0 = 2097151 & load_3(a);
+    int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
+    int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
+    int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
+    int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
+    int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
+    int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
+    int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
+    int64_t a8 = 2097151 & load_3(a + 21);
+    int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
+    int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+    int64_t a11 = (load_4(a + 28) >> 7);
+    int64_t b0 = 2097151 & load_3(b);
+    int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
+    int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
+    int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
+    int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
+    int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
+    int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
+    int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
+    int64_t b8 = 2097151 & load_3(b + 21);
+    int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
+    int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+    int64_t b11 = (load_4(b + 28) >> 7);
+    int64_t c0 = 2097151 & load_3(c);
+    int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
+    int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
+    int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
+    int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
+    int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
+    int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
+    int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
+    int64_t c8 = 2097151 & load_3(c + 21);
+    int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
+    int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
+    int64_t c11 = (load_4(c + 28) >> 7);
+    int64_t s0;
+    int64_t s1;
+    int64_t s2;
+    int64_t s3;
+    int64_t s4;
+    int64_t s5;
+    int64_t s6;
+    int64_t s7;
+    int64_t s8;
+    int64_t s9;
+    int64_t s10;
+    int64_t s11;
+    int64_t s12;
+    int64_t s13;
+    int64_t s14;
+    int64_t s15;
+    int64_t s16;
+    int64_t s17;
+    int64_t s18;
+    int64_t s19;
+    int64_t s20;
+    int64_t s21;
+    int64_t s22;
+    int64_t s23;
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+    int64_t carry17;
+    int64_t carry18;
+    int64_t carry19;
+    int64_t carry20;
+    int64_t carry21;
+    int64_t carry22;
+
+    s0 = c0 + a0 * b0;
+    s1 = c1 + a0 * b1 + a1 * b0;
+    s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
+    s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+    s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+    s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+    s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+    s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
+    s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
+    s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+    s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+    s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+    s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+    s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+    s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
+    s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
+    s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+    s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+    s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+    s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+    s20 = a9 * b11 + a10 * b10 + a11 * b9;
+    s21 = a10 * b11 + a11 * b10;
+    s22 = a11 * b11;
+    s23 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry18 = (s18 + (1 << 20)) >> 21;
+    s19 += carry18;
+    s18 -= carry18 << 21;
+    carry20 = (s20 + (1 << 20)) >> 21;
+    s21 += carry20;
+    s20 -= carry20 << 21;
+    carry22 = (s22 + (1 << 20)) >> 21;
+    s23 += carry22;
+    s22 -= carry22 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    carry17 = (s17 + (1 << 20)) >> 21;
+    s18 += carry17;
+    s17 -= carry17 << 21;
+    carry19 = (s19 + (1 << 20)) >> 21;
+    s20 += carry19;
+    s19 -= carry19 << 21;
+    carry21 = (s21 + (1 << 20)) >> 21;
+    s22 += carry21;
+    s21 -= carry21 << 21;
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+    s23 = 0;
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+    s22 = 0;
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+    s21 = 0;
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+    s20 = 0;
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+    s19 = 0;
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+    s18 = 0;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry12 = (s12 + (1 << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 << 21;
+    carry14 = (s14 + (1 << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 << 21;
+    carry16 = (s16 + (1 << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    carry13 = (s13 + (1 << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 << 21;
+    carry15 = (s15 + (1 << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 << 21;
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+    s17 = 0;
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+    s16 = 0;
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+    s15 = 0;
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+    s14 = 0;
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+    s13 = 0;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = (s0 + (1 << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry2 = (s2 + (1 << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry4 = (s4 + (1 << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry6 = (s6 + (1 << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry8 = (s8 + (1 << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry10 = (s10 + (1 << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry1 = (s1 + (1 << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry3 = (s3 + (1 << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry5 = (s5 + (1 << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry7 = (s7 + (1 << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry9 = (s9 + (1 << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry11 = (s11 + (1 << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 << 21;
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 << 21;
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 << 21;
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 << 21;
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 << 21;
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 << 21;
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 << 21;
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 << 21;
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 << 21;
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 << 21;
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 << 21;
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 << 21;
+    
+    s[0] = (unsigned char) (s0 >> 0);
+    s[1] = (unsigned char) (s0 >> 8);
+    s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
+    s[3] = (unsigned char) (s1 >> 3);
+    s[4] = (unsigned char) (s1 >> 11);
+    s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
+    s[6] = (unsigned char) (s2 >> 6);
+    s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
+    s[8] = (unsigned char) (s3 >> 1);
+    s[9] = (unsigned char) (s3 >> 9);
+    s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
+    s[11] = (unsigned char) (s4 >> 4);
+    s[12] = (unsigned char) (s4 >> 12);
+    s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
+    s[14] = (unsigned char) (s5 >> 7);
+    s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
+    s[16] = (unsigned char) (s6 >> 2);
+    s[17] = (unsigned char) (s6 >> 10);
+    s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
+    s[19] = (unsigned char) (s7 >> 5);
+    s[20] = (unsigned char) (s7 >> 13);
+    s[21] = (unsigned char) (s8 >> 0);
+    s[22] = (unsigned char) (s8 >> 8);
+    s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
+    s[24] = (unsigned char) (s9 >> 3);
+    s[25] = (unsigned char) (s9 >> 11);
+    s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
+    s[27] = (unsigned char) (s10 >> 6);
+    s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
+    s[29] = (unsigned char) (s11 >> 1);
+    s[30] = (unsigned char) (s11 >> 9);
+    s[31] = (unsigned char) (s11 >> 17);
+}

diff --git a/src/ed25519/sc.h b/src/ed25519/sc.h
new file mode 100644 (file)
index 0000000..8fa727e
--- /dev/null
+++ b/src/ed25519/sc.h
@@ -0,0 +1,12 @@
+#ifndef SC_H
+#define SC_H
+
+/*
+The set of scalars is \Z/l
+where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+void sc_reduce(unsigned char *s);
+void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c);
+
+#endif
\ No newline at end of file

diff --git a/src/ed25519/seed.c b/src/ed25519/seed.c
new file mode 100644 (file)
index 0000000..25e5182
--- /dev/null
+++ b/src/ed25519/seed.c
@@ -0,0 +1,40 @@
+#include "ed25519.h"
+
+#ifndef ED25519_NO_SEED
+
+#ifdef _WIN32
+#include <Windows.h>
+#include <Wincrypt.h>
+#else
+#include <stdio.h>
+#endif
+
+int ed25519_create_seed(unsigned char *seed) {
+#ifdef _WIN32
+    HCRYPTPROV prov;
+
+    if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT))  {
+        return 1;
+    }
+
+    if (!CryptGenRandom(prov, 32, seed))  {
+        CryptReleaseContext(prov, 0);
+        return 1;
+    }
+
+    CryptReleaseContext(prov, 0);
+#else
+    FILE *f = fopen("/dev/urandom", "rb");
+
+    if (f == NULL) {
+        return 1;
+    }
+
+    fread(seed, 1, 32, f);
+    fclose(f);
+#endif
+
+    return 0;
+}
+
+#endif
\ No newline at end of file

diff --git a/src/ed25519/sha512.c b/src/ed25519/sha512.c
new file mode 100644 (file)
index 0000000..635d8ae
--- /dev/null
+++ b/src/ed25519/sha512.c
@@ -0,0 +1,275 @@
+/* LibTomCrypt, modular cryptographic library -- Tom St Denis
+ *
+ * LibTomCrypt is a library that provides various cryptographic
+ * algorithms in a highly modular and flexible manner.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+#include "fixedint.h"
+#include "sha512.h"
+
+/* the K array */
+static const uint64_t K[80] = {
+    UINT64_C(0x428a2f98d728ae22), UINT64_C(0x7137449123ef65cd), 
+    UINT64_C(0xb5c0fbcfec4d3b2f), UINT64_C(0xe9b5dba58189dbbc),
+    UINT64_C(0x3956c25bf348b538), UINT64_C(0x59f111f1b605d019), 
+    UINT64_C(0x923f82a4af194f9b), UINT64_C(0xab1c5ed5da6d8118),
+    UINT64_C(0xd807aa98a3030242), UINT64_C(0x12835b0145706fbe), 
+    UINT64_C(0x243185be4ee4b28c), UINT64_C(0x550c7dc3d5ffb4e2),
+    UINT64_C(0x72be5d74f27b896f), UINT64_C(0x80deb1fe3b1696b1), 
+    UINT64_C(0x9bdc06a725c71235), UINT64_C(0xc19bf174cf692694),
+    UINT64_C(0xe49b69c19ef14ad2), UINT64_C(0xefbe4786384f25e3), 
+    UINT64_C(0x0fc19dc68b8cd5b5), UINT64_C(0x240ca1cc77ac9c65),
+    UINT64_C(0x2de92c6f592b0275), UINT64_C(0x4a7484aa6ea6e483), 
+    UINT64_C(0x5cb0a9dcbd41fbd4), UINT64_C(0x76f988da831153b5),
+    UINT64_C(0x983e5152ee66dfab), UINT64_C(0xa831c66d2db43210), 
+    UINT64_C(0xb00327c898fb213f), UINT64_C(0xbf597fc7beef0ee4),
+    UINT64_C(0xc6e00bf33da88fc2), UINT64_C(0xd5a79147930aa725), 
+    UINT64_C(0x06ca6351e003826f), UINT64_C(0x142929670a0e6e70),
+    UINT64_C(0x27b70a8546d22ffc), UINT64_C(0x2e1b21385c26c926), 
+    UINT64_C(0x4d2c6dfc5ac42aed), UINT64_C(0x53380d139d95b3df),
+    UINT64_C(0x650a73548baf63de), UINT64_C(0x766a0abb3c77b2a8), 
+    UINT64_C(0x81c2c92e47edaee6), UINT64_C(0x92722c851482353b),
+    UINT64_C(0xa2bfe8a14cf10364), UINT64_C(0xa81a664bbc423001),
+    UINT64_C(0xc24b8b70d0f89791), UINT64_C(0xc76c51a30654be30),
+    UINT64_C(0xd192e819d6ef5218), UINT64_C(0xd69906245565a910), 
+    UINT64_C(0xf40e35855771202a), UINT64_C(0x106aa07032bbd1b8),
+    UINT64_C(0x19a4c116b8d2d0c8), UINT64_C(0x1e376c085141ab53), 
+    UINT64_C(0x2748774cdf8eeb99), UINT64_C(0x34b0bcb5e19b48a8),
+    UINT64_C(0x391c0cb3c5c95a63), UINT64_C(0x4ed8aa4ae3418acb), 
+    UINT64_C(0x5b9cca4f7763e373), UINT64_C(0x682e6ff3d6b2b8a3),
+    UINT64_C(0x748f82ee5defb2fc), UINT64_C(0x78a5636f43172f60), 
+    UINT64_C(0x84c87814a1f0ab72), UINT64_C(0x8cc702081a6439ec),
+    UINT64_C(0x90befffa23631e28), UINT64_C(0xa4506cebde82bde9), 
+    UINT64_C(0xbef9a3f7b2c67915), UINT64_C(0xc67178f2e372532b),
+    UINT64_C(0xca273eceea26619c), UINT64_C(0xd186b8c721c0c207), 
+    UINT64_C(0xeada7dd6cde0eb1e), UINT64_C(0xf57d4f7fee6ed178),
+    UINT64_C(0x06f067aa72176fba), UINT64_C(0x0a637dc5a2c898a6), 
+    UINT64_C(0x113f9804bef90dae), UINT64_C(0x1b710b35131c471b),
+    UINT64_C(0x28db77f523047d84), UINT64_C(0x32caab7b40c72493), 
+    UINT64_C(0x3c9ebe0a15c9bebc), UINT64_C(0x431d67c49c100d4c),
+    UINT64_C(0x4cc5d4becb3e42b6), UINT64_C(0x597f299cfc657e2a), 
+    UINT64_C(0x5fcb6fab3ad6faec), UINT64_C(0x6c44198c4a475817)
+};
+
+/* Various logical functions */
+
+#define ROR64c(x, y) \
+    ( ((((x)&UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)(y)&UINT64_C(63))) | \
+      ((x)<<((uint64_t)(64-((y)&UINT64_C(63)))))) & UINT64_C(0xFFFFFFFFFFFFFFFF))
+
+#define STORE64H(x, y)                                                                     \
+   { (y)[0] = (unsigned char)(((x)>>56)&255); (y)[1] = (unsigned char)(((x)>>48)&255);     \
+     (y)[2] = (unsigned char)(((x)>>40)&255); (y)[3] = (unsigned char)(((x)>>32)&255);     \
+     (y)[4] = (unsigned char)(((x)>>24)&255); (y)[5] = (unsigned char)(((x)>>16)&255);     \
+     (y)[6] = (unsigned char)(((x)>>8)&255); (y)[7] = (unsigned char)((x)&255); }
+
+#define LOAD64H(x, y)                                                      \
+   { x = (((uint64_t)((y)[0] & 255))<<56)|(((uint64_t)((y)[1] & 255))<<48) | \
+         (((uint64_t)((y)[2] & 255))<<40)|(((uint64_t)((y)[3] & 255))<<32) | \
+         (((uint64_t)((y)[4] & 255))<<24)|(((uint64_t)((y)[5] & 255))<<16) | \
+         (((uint64_t)((y)[6] & 255))<<8)|(((uint64_t)((y)[7] & 255))); }
+
+
+#define Ch(x,y,z)       (z ^ (x & (y ^ z)))
+#define Maj(x,y,z)      (((x | y) & z) | (x & y)) 
+#define S(x, n)         ROR64c(x, n)
+#define R(x, n)         (((x) &UINT64_C(0xFFFFFFFFFFFFFFFF))>>((uint64_t)n))
+#define Sigma0(x)       (S(x, 28) ^ S(x, 34) ^ S(x, 39))
+#define Sigma1(x)       (S(x, 14) ^ S(x, 18) ^ S(x, 41))
+#define Gamma0(x)       (S(x, 1) ^ S(x, 8) ^ R(x, 7))
+#define Gamma1(x)       (S(x, 19) ^ S(x, 61) ^ R(x, 6))
+#ifndef MIN
+   #define MIN(x, y) ( ((x)<(y))?(x):(y) )
+#endif
+
+/* compress 1024-bits */
+static int sha512_compress(sha512_context *md, unsigned char *buf)
+{
+    uint64_t S[8], W[80], t0, t1;
+    int i;
+
+    /* copy state into S */
+    for (i = 0; i < 8; i++) {
+        S[i] = md->state[i];
+    }
+
+    /* copy the state into 1024-bits into W[0..15] */
+    for (i = 0; i < 16; i++) {
+        LOAD64H(W[i], buf + (8*i));
+    }
+
+    /* fill W[16..79] */
+    for (i = 16; i < 80; i++) {
+        W[i] = Gamma1(W[i - 2]) + W[i - 7] + Gamma0(W[i - 15]) + W[i - 16];
+    }        
+
+/* Compress */
+    #define RND(a,b,c,d,e,f,g,h,i) \
+    t0 = h + Sigma1(e) + Ch(e, f, g) + K[i] + W[i]; \
+    t1 = Sigma0(a) + Maj(a, b, c);\
+    d += t0; \
+    h  = t0 + t1;
+
+    for (i = 0; i < 80; i += 8) {
+       RND(S[0],S[1],S[2],S[3],S[4],S[5],S[6],S[7],i+0);
+       RND(S[7],S[0],S[1],S[2],S[3],S[4],S[5],S[6],i+1);
+       RND(S[6],S[7],S[0],S[1],S[2],S[3],S[4],S[5],i+2);
+       RND(S[5],S[6],S[7],S[0],S[1],S[2],S[3],S[4],i+3);
+       RND(S[4],S[5],S[6],S[7],S[0],S[1],S[2],S[3],i+4);
+       RND(S[3],S[4],S[5],S[6],S[7],S[0],S[1],S[2],i+5);
+       RND(S[2],S[3],S[4],S[5],S[6],S[7],S[0],S[1],i+6);
+       RND(S[1],S[2],S[3],S[4],S[5],S[6],S[7],S[0],i+7);
+   }
+
+   #undef RND
+
+
+
+    /* feedback */
+   for (i = 0; i < 8; i++) {
+        md->state[i] = md->state[i] + S[i];
+    }
+
+    return 0;
+}
+
+
+/**
+   Initialize the hash state
+   @param md   The hash state you wish to initialize
+   @return 0 if successful
+*/
+int sha512_init(sha512_context * md) {
+    if (md == NULL) return 1;
+
+    md->curlen = 0;
+    md->length = 0;
+    md->state[0] = UINT64_C(0x6a09e667f3bcc908);
+    md->state[1] = UINT64_C(0xbb67ae8584caa73b);
+    md->state[2] = UINT64_C(0x3c6ef372fe94f82b);
+    md->state[3] = UINT64_C(0xa54ff53a5f1d36f1);
+    md->state[4] = UINT64_C(0x510e527fade682d1);
+    md->state[5] = UINT64_C(0x9b05688c2b3e6c1f);
+    md->state[6] = UINT64_C(0x1f83d9abfb41bd6b);
+    md->state[7] = UINT64_C(0x5be0cd19137e2179);
+
+    return 0;
+}
+
+/**
+   Process a block of memory though the hash
+   @param md     The hash state
+   @param in     The data to hash
+   @param inlen  The length of the data (octets)
+   @return 0 if successful
+*/
+int sha512_update (sha512_context * md, const unsigned char *in, size_t inlen)               
+{                                                                                           
+    size_t n;
+    size_t i;                                                                        
+    int           err;     
+    if (md == NULL) return 1;  
+    if (in == NULL) return 1;                                                              
+    if (md->curlen > sizeof(md->buf)) {                             
+       return 1;                                                            
+    }                                                                                       
+    while (inlen > 0) {                                                                     
+        if (md->curlen == 0 && inlen >= 128) {                           
+           if ((err = sha512_compress (md, (unsigned char *)in)) != 0) {               
+              return err;                                                                   
+           }                                                                                
+           md->length += 128 * 8;                                        
+           in             += 128;                                                    
+           inlen          -= 128;                                                    
+        } else {                                                                            
+           n = MIN(inlen, (128 - md->curlen));
+
+           for (i = 0; i < n; i++) {
+            md->buf[i + md->curlen] = in[i];
+           }
+
+
+           md->curlen += n;                                                     
+           in             += n;                                                             
+           inlen          -= n;                                                             
+           if (md->curlen == 128) {                                      
+              if ((err = sha512_compress (md, md->buf)) != 0) {            
+                 return err;                                                                
+              }                                                                             
+              md->length += 8*128;                                       
+              md->curlen = 0;                                                   
+           }                                                                                
+       }                                                                                    
+    }                                                                                       
+    return 0;                                                                        
+}
+
+/**
+   Terminate the hash to get the digest
+   @param md  The hash state
+   @param out [out] The destination of the hash (64 bytes)
+   @return 0 if successful
+*/
+   int sha512_final(sha512_context * md, unsigned char *out)
+   {
+    int i;
+
+    if (md == NULL) return 1;
+    if (out == NULL) return 1;
+
+    if (md->curlen >= sizeof(md->buf)) {
+     return 1;
+ }
+
+    /* increase the length of the message */
+ md->length += md->curlen * UINT64_C(8);
+
+    /* append the '1' bit */
+ md->buf[md->curlen++] = (unsigned char)0x80;
+
+    /* if the length is currently above 112 bytes we append zeros
+     * then compress.  Then we can fall back to padding zeros and length
+     * encoding like normal.
+     */
+     if (md->curlen > 112) {
+        while (md->curlen < 128) {
+            md->buf[md->curlen++] = (unsigned char)0;
+        }
+        sha512_compress(md, md->buf);
+        md->curlen = 0;
+    }
+
+    /* pad upto 120 bytes of zeroes 
+     * note: that from 112 to 120 is the 64 MSB of the length.  We assume that you won't hash
+     * > 2^64 bits of data... :-)
+     */
+while (md->curlen < 120) {
+    md->buf[md->curlen++] = (unsigned char)0;
+}
+
+    /* store length */
+STORE64H(md->length, md->buf+120);
+sha512_compress(md, md->buf);
+
+    /* copy output */
+for (i = 0; i < 8; i++) {
+    STORE64H(md->state[i], out+(8*i));
+}
+
+return 0;
+}
+
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out)
+{
+    sha512_context ctx;
+    int ret;
+    if (ret = sha512_init(&ctx)) return ret;
+    if (ret = sha512_update(&ctx, message, message_len)) return ret;
+    if (ret = sha512_final(&ctx, out)) return ret;
+    return 0;
+}
\ No newline at end of file

diff --git a/src/ed25519/sha512.h b/src/ed25519/sha512.h
new file mode 100644 (file)
index 0000000..e56b00e
--- /dev/null
+++ b/src/ed25519/sha512.h
@@ -0,0 +1,21 @@
+#ifndef SHA512_H
+#define SHA512_H
+
+#include <stddef.h>
+
+#include "fixedint.h"
+
+/* state */
+typedef struct sha512_context_ {
+    uint64_t  length, state[8];
+    size_t curlen;
+    unsigned char buf[128];
+} sha512_context;
+
+
+int sha512_init(sha512_context * md);
+int sha512_final(sha512_context * md, unsigned char *out);
+int sha512_update(sha512_context * md, const unsigned char *in, size_t inlen);
+int sha512(const unsigned char *message, size_t message_len, unsigned char *out);
+
+#endif
\ No newline at end of file

diff --git a/src/ed25519/sign.c b/src/ed25519/sign.c
new file mode 100644 (file)
index 0000000..199a839
--- /dev/null
+++ b/src/ed25519/sign.c
@@ -0,0 +1,31 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+
+void ed25519_sign(unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key, const unsigned char *private_key) {
+    sha512_context hash;
+    unsigned char hram[64];
+    unsigned char r[64];
+    ge_p3 R;
+
+
+    sha512_init(&hash);
+    sha512_update(&hash, private_key + 32, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, r);
+
+    sc_reduce(r);
+    ge_scalarmult_base(&R, r);
+    ge_p3_tobytes(signature, &R);
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, hram);
+
+    sc_reduce(hram);
+    sc_muladd(signature + 32, hram, private_key, r);
+}

diff --git a/src/ed25519/verify.c b/src/ed25519/verify.c
new file mode 100644 (file)
index 0000000..32f988e
--- /dev/null
+++ b/src/ed25519/verify.c
@@ -0,0 +1,77 @@
+#include "ed25519.h"
+#include "sha512.h"
+#include "ge.h"
+#include "sc.h"
+
+static int consttime_equal(const unsigned char *x, const unsigned char *y) {
+    unsigned char r = 0;
+
+    r = x[0] ^ y[0];
+    #define F(i) r |= x[i] ^ y[i]
+    F(1);
+    F(2);
+    F(3);
+    F(4);
+    F(5);
+    F(6);
+    F(7);
+    F(8);
+    F(9);
+    F(10);
+    F(11);
+    F(12);
+    F(13);
+    F(14);
+    F(15);
+    F(16);
+    F(17);
+    F(18);
+    F(19);
+    F(20);
+    F(21);
+    F(22);
+    F(23);
+    F(24);
+    F(25);
+    F(26);
+    F(27);
+    F(28);
+    F(29);
+    F(30);
+    F(31);
+    #undef F
+
+    return !r;
+}
+
+int ed25519_verify(const unsigned char *signature, const unsigned char *message, size_t message_len, const unsigned char *public_key) {
+    unsigned char h[64];
+    unsigned char checker[32];
+    sha512_context hash;
+    ge_p3 A;
+    ge_p2 R;
+
+    if (signature[63] & 224) {
+        return 0;
+    }
+
+    if (ge_frombytes_negate_vartime(&A, public_key) != 0) {
+        return 0;
+    }
+
+    sha512_init(&hash);
+    sha512_update(&hash, signature, 32);
+    sha512_update(&hash, public_key, 32);
+    sha512_update(&hash, message, message_len);
+    sha512_final(&hash, h);
+    
+    sc_reduce(h);
+    ge_double_scalarmult_vartime(&R, h, &A, signature + 32);
+    ge_tobytes(checker, &R);
+
+    if (!consttime_equal(checker, signature)) {
+        return 0;
+    }
+
+    return 1;
+}

diff --git a/src/sptps_keypair.c b/src/sptps_keypair.c
new file mode 100644 (file)
index 0000000..63f396a
--- /dev/null
+++ b/src/sptps_keypair.c
@@ -0,0 +1,100 @@
+/*
+    sptps_test.c -- Simple Peer-to-Peer Security test program
+    Copyright (C) 2011-2013 Guus Sliepen <guus@tinc-vpn.org>,
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+*/
+
+#include "system.h"
+
+#include <getopt.h>
+
+#include "crypto.h"
+#include "ecdsagen.h"
+#include "utils.h"
+
+static char *program_name;
+
+static void usage() {
+       fprintf(stderr, "Usage: %s [options] private_key_file public_key_file\n\n", program_name);
+       fprintf(stderr, "Valid options are:\n"
+                       "  --help  Display this help and exit.\n"
+                       "\n");
+       fprintf(stderr, "Report bugs to tinc@tinc-vpn.org.\n");
+}
+
+static struct option const long_options[] = {
+       {"help", no_argument, NULL, 1},
+       {NULL, 0, NULL, 0}
+};
+
+int main(int argc, char *argv[]) {
+       program_name = argv[0];
+       int r;
+       int option_index = 0;
+
+       while((r = getopt_long(argc, argv, "", long_options, &option_index)) != EOF) {
+               switch (r) {
+                       case 0:   /* long option */
+                               break;
+
+                       case '?': /* wrong options */
+                               usage();
+                               return 1;
+
+                       case 1: /* help */
+                               usage();
+                               return 0;
+
+                       default:
+                               break;
+               }
+       }
+
+       argc -= optind - 1;
+       argv += optind - 1;
+
+       if(argc != 3) {
+               fprintf(stderr, "Wrong number of arguments.\n");
+               usage();
+               return 1;
+       }
+
+       crypto_init();
+
+       ecdsa_t *key = ecdsa_generate();
+       if(!key)
+               return 1;
+       
+       FILE *fp = fopen(argv[1], "w");
+       if(fp) {
+               ecdsa_write_pem_private_key(key, fp);
+               fclose(fp);
+       } else {
+               fprintf(stderr, "Could not open '%s' for writing: %s\n", strerror(errno));
+               return 1;
+       }
+
+       fp = fopen(argv[2], "w");
+       if(fp) {
+               ecdsa_write_pem_public_key(key, fp);
+               fclose(fp);
+       } else {
+               fprintf(stderr, "Could not open '%s' for writing: %s\n", strerror(errno));
+               return 1;
+       }
+
+       return 0;
+}

diff --git a/src/sptps_speed.c b/src/sptps_speed.c
index 268e6c9bf0ce388af2cc269b635d6db1f10131fb..d9776b7ef2714086fe2397c67c1832b8b7fcdd86 100644 (file)
--- a/src/sptps_speed.c
+++ b/src/sptps_speed.c
@@ -82,6 +82,10 @@ int main(int argc, char *argv[]) {
 
        crypto_init();
 
+       randomize(buf1, sizeof buf1);
+       randomize(buf2, sizeof buf2);
+       randomize(buf3, sizeof buf3);
+
        // Key generation
 
        fprintf(stderr, "Generating keys for %lg seconds: ", duration);

diff --git a/test/sptps-basic.test b/test/sptps-basic.test
index 2abb99c0f6a010a366585eae59d8f6e2669bd4d0..644a31e0b1f0b216baa7b4dd03f484b64111aaed 100755 (executable)
--- a/test/sptps-basic.test
+++ b/test/sptps-basic.test
@@ -6,12 +6,8 @@
 
 mkdir -p $d1
 
-openssl ecparam -genkey -name secp521r1 -noout -out $d1/server.priv
-openssl ecparam -genkey -name secp521r1 -noout -out $d1/client.priv
-yes '' | openssl req -new -pubkey -key $d1/server.priv -noout -out $d1/server.pub
-echo
-yes '' | openssl req -new -pubkey -key $d1/client.priv -noout -out $d1/client.pub
-echo
+$sptps_keypair $d1/server.priv $d1/server.pub
+$sptps_keypair $d1/client.priv $d1/client.pub
 
 # Test transfer of a simple file.
 

diff --git a/test/testlib.sh b/test/testlib.sh
index 39a2bf4e14468cb7f60b563dfea32957f2c557d7..31033352c4137d19c474755294c5826af807d6de 100644 (file)
--- a/test/testlib.sh
+++ b/test/testlib.sh
@@ -5,6 +5,7 @@
 tincd=../src/tincd
 tinc=../src/tinc
 sptps_test=../src/sptps_test
+sptps_keypair=../src/sptps_keypair
 
 # Test directories