Add J-PAKE demo.

diff --git a/demos/jpake/Makefile b/demos/jpake/Makefile
new file mode 100644 (file)
index 0000000..09b8f03
--- /dev/null
+++ b/demos/jpake/Makefile
@@ -0,0 +1,7 @@
+LDFLAGS=-L../.. -lcrypto
+CFLAGS=-I../../include -Wall -Werror -g
+
+all: jpakedemo
+
+jpakedemo: jpakedemo.o
+       $(CC) -g -o jpakedemo jpakedemo.o $(LDFLAGS)

diff --git a/demos/jpake/jpakedemo.c b/demos/jpake/jpakedemo.c
new file mode 100644 (file)
index 0000000..a5f8587
--- /dev/null
+++ b/demos/jpake/jpakedemo.c
@@ -0,0 +1,463 @@
+#include "openssl/bn.h"
+#include "openssl/sha.h"
+#include <assert.h>
+#include <string.h>
+#include <stdlib.h>
+
+/* Copyright (C) 2008 Ben Laurie (ben@links.org) */
+
+/*
+ * Implement J-PAKE, as described in
+ * http://grouper.ieee.org/groups/1363/Research/contributions/hao-ryan-2008.pdf
+ * 
+ * With hints from http://www.cl.cam.ac.uk/~fh240/software/JPAKE2.java.
+ */
+
+static void showbn(const char *name, const BIGNUM *bn)
+    {
+    fputs(name, stdout);
+    fputs(" = ", stdout);
+    BN_print_fp(stdout, bn);
+    putc('\n', stdout);
+    }
+
+typedef struct
+    {
+    BN_CTX *ctx;  // Perhaps not the best place for this?
+    BIGNUM *p;
+    BIGNUM *q;
+    BIGNUM *g;
+    } JPakeParameters;
+
+static void JPakeParametersInit(JPakeParameters *params)
+    {
+    params->ctx = BN_CTX_new();
+
+    // For now use p, q, g from Java sample code. Later, generate them.
+    params->p = NULL;
+    BN_hex2bn(&params->p, "fd7f53811d75122952df4a9c2eece4e7f611b7523cef4400c31e3f80b6512669455d402251fb593d8d58fabfc5f5ba30f6cb9b556cd7813b801d346ff26660b76b9950a5a49f9fe8047b1022c24fbba9d7feb7c61bf83b57e7c6a8a6150f04fb83f6d3c51ec3023554135a169132f675f3ae2b61d72aeff22203199dd14801c7");
+    params->q = NULL;
+    BN_hex2bn(&params->q, "9760508f15230bccb292b982a2eb840bf0581cf5");
+    params->g = NULL;
+    BN_hex2bn(&params->g, "f7e1a085d69b3ddecbbcab5c36b857b97994afbbfa3aea82f9574c0b3d0782675159578ebad4594fe67107108180b449167123e84c281613b7cf09328cc8a6e13c167a8b547c8d28e0a3ae1e2bb3a675916ea37f0bfa213562f1fb627a01243bcca4f1bea8519089a883dfe15ae59f06928b665e807b552564014c3bfecf492a");
+
+    showbn("p", params->p);
+    showbn("q", params->q);
+    showbn("g", params->g);
+    }
+
+typedef struct
+    {
+    BIGNUM *gr;  // g^r (r random)
+    BIGNUM *b;   // b = r - x*h, h=hash(g, g^r, g^x, name)
+    } JPakeZKP;
+
+typedef struct
+    {
+    BIGNUM *gx;       // g^x
+    JPakeZKP zkpx;    // ZKP(x)
+    } JPakeStep1;
+
+typedef struct
+    {
+    BIGNUM *X;        // g^(xa + xc + xd) * xb * s
+    JPakeZKP zkpxbs;  // ZKP(xb * s)
+    } JPakeStep2;
+
+/*
+ * The user structure. In the definition, (xa, xb, xc, xd) are Alice's
+ * (x1, x2, x3, x4) or Bob's (x3, x4, x1, x2). If you see what I mean.
+ */
+typedef struct
+    {
+    const char *name;  // Must be unique
+    int base;          // 1 for Alice, 3 for Bob. Only used for printing stuff.
+    BIGNUM *secret;    // The shared secret
+    BIGNUM *key;       // The calculated (shared) key
+    BIGNUM *xa;        // Alice's x1 or Bob's x3
+    BIGNUM *xb;        // Alice's x2 or Bob's x4
+    JPakeStep1 s1c;    // Alice's g^x3, ZKP(x3) or Bob's g^x1, ZKP(x1)
+    JPakeStep1 s1d;    // Alice's g^x4, ZKP(x4) or Bob's g^x2, ZKP(x2)
+    JPakeStep2 s2;     // Alice's A, ZKP(x2 * s) or Bob's B, ZKP(x4 * s)
+    } JPakeUser;
+
+// Generate each party's random numbers. xa is in [0, q), xb is in [1, q).
+static void genrand(JPakeUser *user, const JPakeParameters *params)
+    {
+    BIGNUM *qm1;
+
+    // xa in [0, q)
+    user->xa = BN_new();
+    BN_rand_range(user->xa, params->q);
+
+    // q-1
+    qm1 = BN_new();
+    BN_copy(qm1, params->q);
+    BN_sub_word(qm1, 1);
+
+    // ... and xb in [0, q-1)
+    user->xb = BN_new();
+    BN_rand_range(user->xb, qm1);
+    // [1, q)
+    BN_add_word(user->xb, 1);
+
+    // cleanup
+    BN_free(qm1);
+
+    // Show
+    printf("x%d", user->base);
+    showbn("", user->xa);
+    printf("x%d", user->base+1);
+    showbn("", user->xb);
+    }
+
+static void hashlength(SHA_CTX *sha, size_t l)
+    {
+    unsigned char b[2];
+
+    assert(l <= 0xffff);
+    b[0] = l >> 8;
+    b[1] = l&0xff;
+    SHA1_Update(sha, b, 2);
+    }
+
+static void hashstring(SHA_CTX *sha, const char *string)
+    {
+    size_t l = strlen(string);
+
+    hashlength(sha, l);
+    SHA1_Update(sha, string, l);
+    }
+
+static void hashbn(SHA_CTX *sha, const BIGNUM *bn)
+    {
+    size_t l = BN_num_bytes(bn);
+    unsigned char *bin = alloca(l);
+
+    hashlength(sha, l);
+    BN_bn2bin(bn, bin);
+    SHA1_Update(sha, bin, l);
+    }
+
+// h=hash(g, g^r, g^x, name)
+static void zkpHash(BIGNUM *h, const JPakeZKP *zkp, const BIGNUM *gx,
+                   const JPakeUser *from, const JPakeParameters *params)
+    {
+    unsigned char md[SHA_DIGEST_LENGTH];
+    SHA_CTX sha;
+
+    // XXX: hash should not allow moving of the boundaries - Java code
+    // is flawed in this respect. Length encoding seems simplest.
+    SHA1_Init(&sha);
+    hashbn(&sha, params->g);
+    hashbn(&sha, zkp->gr);
+    hashbn(&sha, gx);
+    hashstring(&sha, from->name);
+    SHA1_Final(md, &sha);
+    BN_bin2bn(md, SHA_DIGEST_LENGTH, h);
+    }
+
+// Prove knowledge of x
+// Note that we don't send g^x because, as it happens, we've always
+// sent it elsewhere. Also note that because of that, we could avoid calculating it here, but we don't, for clarity... 
+static void CreateZKP(JPakeZKP *zkp, const BIGNUM *x, const JPakeUser *us,
+                     const BIGNUM *zkpg, const JPakeParameters *params,
+                     int n, const char *suffix)
+    {
+    BIGNUM *r = BN_new();
+    BIGNUM *gx = BN_new();
+    BIGNUM *h = BN_new();
+    BIGNUM *t = BN_new();
+
+    // r in [0,q)
+    // XXX: Java chooses r in [0, 2^160) - i.e. distribution not uniform
+    BN_rand_range(r, params->q);
+    // g^r
+    zkp->gr = BN_new();
+    BN_mod_exp(zkp->gr, zkpg, r, params->p, params->ctx);
+    // g^x
+    BN_mod_exp(gx, zkpg, x, params->p, params->ctx);
+
+    // h=hash...
+    zkpHash(h, zkp, gx, us, params);
+    
+    // b = r - x*h
+    BN_mod_mul(t, x, h, params->q, params->ctx);
+    zkp->b = BN_new();
+    BN_mod_sub(zkp->b, r, t, params->q, params->ctx);
+
+    // show
+    printf("  ZKP(x%d%s)\n", n, suffix);
+    showbn("   zkpg", zkpg);
+    showbn("    g^x", gx);
+    showbn("    g^r", zkp->gr);
+    showbn("      b", zkp->b);
+
+    // cleanup
+    BN_free(t);
+    BN_free(h);
+    BN_free(gx);
+    BN_free(r);
+    }
+
+static int VerifyZKP(const JPakeZKP *zkp, BIGNUM *x, const JPakeUser *them,
+                    const BIGNUM *zkpg, const JPakeParameters *params,
+                    int n, const char *suffix)
+    {
+    BIGNUM *h = BN_new();
+    BIGNUM *t1 = BN_new();
+    BIGNUM *t2 = BN_new();
+    BIGNUM *t3 = BN_new();
+    int ret = 0;
+
+    zkpHash(h, zkp, x, them, params);
+
+    // t1 = g^b
+    BN_mod_exp(t1, zkpg, zkp->b, params->p, params->ctx);
+    // t2 = (g^x)^h = g^{hx}
+    BN_mod_exp(t2, x, h, params->p, params->ctx);
+    // t3 = t1 * t2 = g^{hx} * g^b = g^{hx+b} = g^r (allegedly)
+    BN_mod_mul(t3, t1, t2, params->p, params->ctx);
+
+    printf("  ZKP(x%d%s)\n", n, suffix);
+    showbn("    zkpg", zkpg);
+    showbn("    g^r'", t3);
+
+    // verify t3 == g^r
+    if(BN_cmp(t3, zkp->gr) == 0)
+       ret = 1;
+
+    // cleanup
+    BN_free(t3);
+    BN_free(t2);
+    BN_free(t1);
+    BN_free(h);
+
+    if(ret)
+       puts("    OK");
+    else
+       puts("    FAIL");
+
+    return ret;
+    }    
+
+static void sendstep1_substep(JPakeStep1 *s1, const BIGNUM *x,
+                             const JPakeUser *us,
+                             const JPakeParameters *params, int n)
+    {
+    s1->gx = BN_new();
+    BN_mod_exp(s1->gx, params->g, x, params->p, params->ctx);
+    printf("  g^{x%d}", n);
+    showbn("", s1->gx);
+
+    CreateZKP(&s1->zkpx, x, us, params->g, params, n, "");
+    }
+
+static void sendstep1(const JPakeUser *us, JPakeUser *them,
+                     const JPakeParameters *params)
+    {
+    printf("\n%s sends %s:\n\n", us->name, them->name);
+
+    // from's g^xa (which becomes to's g^xc) and ZKP(xa)
+    sendstep1_substep(&them->s1c, us->xa, us, params, us->base);
+    // from's g^xb (which becomes to's g^xd) and ZKP(xb)
+    sendstep1_substep(&them->s1d, us->xb, us, params, us->base+1);
+    }
+
+static int verifystep1(const JPakeUser *us, const JPakeUser *them,
+                      const JPakeParameters *params)
+    {
+    printf("\n%s verifies %s:\n\n", us->name, them->name);
+
+    // verify their ZKP(xc)
+    if(!VerifyZKP(&us->s1c.zkpx, us->s1c.gx, them, params->g, params,
+                 them->base, ""))
+       return 0;
+
+    // verify their ZKP(xd)
+    if(!VerifyZKP(&us->s1d.zkpx, us->s1d.gx, them, params->g, params,
+                 them->base+1, ""))
+       return 0;
+
+    // g^xd != 1
+    printf("  g^{x%d} != 1: ", them->base+1);
+    if(BN_is_one(us->s1d.gx))
+       {
+       puts("FAIL");
+       return 0;
+       }
+    puts("OK");
+
+    return 1;
+    }
+
+static void sendstep2(const JPakeUser *us, JPakeUser *them,
+                     const JPakeParameters *params)
+    {
+    BIGNUM *t1 = BN_new();
+    BIGNUM *t2 = BN_new();
+
+    printf("\n%s sends %s:\n\n", us->name, them->name);
+
+    // X = g^{(xa + xc + xd) * xb * s}
+    // t1 = g^xa
+    BN_mod_exp(t1, params->g, us->xa, params->p, params->ctx);
+    // t2 = t1 * g^{xc} = g^{xa} * g^{xc} = g^{xa + xc}
+    BN_mod_mul(t2, t1, us->s1c.gx, params->p, params->ctx);
+    // t1 = t2 * g^{xd} = g^{xa + xc + xd}
+    BN_mod_mul(t1, t2, us->s1d.gx, params->p, params->ctx);
+    // t2 = xb * s
+    BN_mod_mul(t2, us->xb, us->secret, params->q, params->ctx);
+    // X = t1^{t2} = t1^{xb * s} = g^{(xa + xc + xd) * xb * s}
+    them->s2.X = BN_new();
+    BN_mod_exp(them->s2.X, t1, t2, params->p, params->ctx);
+
+    // Show
+    printf("  g^{(x%d + x%d + x%d) * x%d * s)", us->base, them->base,
+          them->base+1, us->base+1);
+    showbn("", them->s2.X);
+
+    // ZKP(xb * s)
+    // XXX: this is kinda funky, because we're using
+    //
+    // g' = g^{xa + xc + xd}
+    //
+    // as the generator, which means B is g'^{xb * s}
+    CreateZKP(&them->s2.zkpxbs, t2, us, t1, params, us->base+1, " * s");
+
+    // cleanup
+    BN_free(t1);
+    BN_free(t2);
+    }
+
+static int verifystep2(const JPakeUser *us, const JPakeUser *them,
+                      const JPakeParameters *params)
+    {
+    BIGNUM *t1 = BN_new();
+    BIGNUM *t2 = BN_new();
+    int ret = 0;
+
+    printf("\n%s verifies %s:\n\n", us->name, them->name);
+
+    // g' = g^{xc + xa + xb} [from our POV]
+    // t1 = xa + xb
+    BN_mod_add(t1, us->xa, us->xb, params->q, params->ctx);
+    // t2 = g^{t1} = g^{xa+xb}
+    BN_mod_exp(t2, params->g, t1, params->p, params->ctx);
+    // t1 = g^{xc} * t2 = g^{xc + xa + xb}
+    BN_mod_mul(t1, us->s1c.gx, t2, params->p, params->ctx);
+
+    if(VerifyZKP(&us->s2.zkpxbs, us->s2.X, them, t1, params, them->base+1,
+                 " * s"))
+       ret = 1;
+
+    // cleanup
+    BN_free(t2);
+    BN_free(t1);
+
+    return ret;
+    }
+
+static void computekey(JPakeUser *us, const JPakeParameters *params)
+    {
+    BIGNUM *t1 = BN_new();
+    BIGNUM *t2 = BN_new();
+    BIGNUM *t3 = BN_new();
+
+    printf("\n%s calculates the shared key:\n\n", us->name);
+
+    // K = (X/g^{xb * xd * s})^{xb}
+    //   = (g^{(xc + xa + xb) * xd * s - xb * xd *s})^{xb}
+    //   = (g^{(xa + xc) * xd * s})^{xb}
+    //   = g^{(xa + xc) * xb * xd * s}
+    // [which is the same regardless of who calculates it]
+
+    // t1 = (g^{xd})^{xb} = g^{xb * xd}
+    BN_mod_exp(t1, us->s1d.gx, us->xb, params->p, params->ctx);
+    // t2 = -s = q-s
+    BN_sub(t2, params->q, us->secret);
+    // t3 = t1^t2 = g^{-xb * xd * s}
+    BN_mod_exp(t3, t1, t2, params->p, params->ctx);
+    // t1 = X * t3 = X/g^{xb * xd * s}
+    BN_mod_mul(t1, us->s2.X, t3, params->p, params->ctx);
+    // K = t1^{xb}
+    us->key = BN_new();
+    BN_mod_exp(us->key, t1, us->xb, params->p, params->ctx);
+
+    // show
+    showbn("  K", us->key);
+
+    // cleanup
+    BN_free(t3);
+    BN_free(t2);
+    BN_free(t1);
+    }
+
+int main(int argc, char **argv)
+    {
+    JPakeParameters params;
+    JPakeUser alice, bob;
+
+    alice.name = "Alice";
+    alice.base = 1;
+    bob.name = "Bob";
+    bob.base = 3;
+
+    JPakeParametersInit(&params);
+
+    // Shared secret
+    alice.secret = BN_new();
+    BN_rand(alice.secret, 32, -1, 0);
+    bob.secret = alice.secret;
+    showbn("secret", alice.secret);
+
+    assert(BN_cmp(alice.secret, params.q) < 0);
+
+    // Alice's x1, x2
+    genrand(&alice, &params);
+
+    // Bob's x3, x4
+    genrand(&bob, &params);
+
+    // Now send stuff to each other...
+    sendstep1(&alice, &bob, &params);
+    sendstep1(&bob, &alice, &params);
+
+    // And verify what each other sent
+    if(!verifystep1(&alice, &bob, &params))
+       return 1;
+    if(!verifystep1(&bob, &alice, &params))
+       return 2;
+
+    // Second send
+    sendstep2(&alice, &bob, &params);
+    sendstep2(&bob, &alice, &params);
+
+    // And second verify
+    if(!verifystep2(&alice, &bob, &params))
+       return 3;
+    if(!verifystep2(&bob, &alice, &params))
+       return 4;
+
+    // Compute common key
+    computekey(&alice, &params);
+    computekey(&bob, &params);
+
+    // Confirm the common key is identical
+    // XXX: if the two secrets are not the same, everything works up
+    // to this point, so the only way to detect a failure is by the
+    // difference in the calculated keys.
+    // Since we're all the same code, just compare them directly. In a
+    // real system, Alice sends Bob H(H(K)), Bob checks it, then sends
+    // back H(K), which Alice checks, or something equivalent.
+    puts("\nAlice and Bob check keys are the same:");
+    if(BN_cmp(alice.key, bob.key) == 0)
+       puts("  OK");
+    else
+       {
+       puts("  FAIL");
+       return 5;
+       }
+
+    return 0;
+    }