#endif
-#define TABLE_SIZE 16
+#define TABLE_SIZE 32
/* slow but works */
int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
ts=1;
if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
- if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
- goto err; /* 2 */
-
- if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
- window=1;
- else if (bits >= 256)
- window=5; /* max size of window */
- else if (bits >= 128)
- window=4;
- else
- window=3;
- j=1<<(window-1);
- for (i=1; i<j; i++)
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1)
{
- BN_init(&val[i]);
- if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
- goto err;
+ if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
+ goto err; /* 2 */
+ j=1<<(window-1);
+ for (i=1; i<j; i++)
+ {
+ BN_init(&val[i]);
+ if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
+ goto err;
+ }
+ ts=i;
}
- ts=i;
-
+
start=1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
else
aa=a;
if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
- if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
-
- if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
- window=1;
- else if (bits >= 256)
- window=5; /* max size of window */
- else if (bits >= 128)
- window=4;
- else
- window=3;
- j=1<<(window-1);
- for (i=1; i<j; i++)
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1)
{
- BN_init(&(val[i]));
- if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
- goto err;
+ if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
+ j=1<<(window-1);
+ for (i=1; i<j; i++)
+ {
+ BN_init(&(val[i]));
+ if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
+ goto err;
+ }
+ ts=i;
}
- ts=i;
start=1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
BN_init(&(val[0]));
ts=1;
if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
- if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
- goto err; /* 2 */
-
- if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
- window=1;
- else if (bits >= 256)
- window=5; /* max size of window */
- else if (bits >= 128)
- window=4;
- else
- window=3;
- j=1<<(window-1);
- for (i=1; i<j; i++)
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1)
{
- BN_init(&(val[i]));
- if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
- goto err;
+ if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
+ goto err; /* 2 */
+ j=1<<(window-1);
+ for (i=1; i<j; i++)
+ {
+ BN_init(&(val[i]));
+ if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
+ goto err;
+ }
+ ts=i;
}
- ts=i;
start=1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
+/* crypto/bn/bn_exp2.c */
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
+ * All rights reserved.
+ *
+ * This package is an SSL implementation written
+ * by Eric Young (eay@cryptsoft.com).
+ * The implementation was written so as to conform with Netscapes SSL.
+ *
+ * This library is free for commercial and non-commercial use as long as
+ * the following conditions are aheared to. The following conditions
+ * apply to all code found in this distribution, be it the RC4, RSA,
+ * lhash, DES, etc., code; not just the SSL code. The SSL documentation
+ * included with this distribution is covered by the same copyright terms
+ * except that the holder is Tim Hudson (tjh@cryptsoft.com).
+ *
+ * Copyright remains Eric Young's, and as such any Copyright notices in
+ * the code are not to be removed.
+ * If this package is used in a product, Eric Young should be given attribution
+ * as the author of the parts of the library used.
+ * This can be in the form of a textual message at program startup or
+ * in documentation (online or textual) provided with the package.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ * must display the following acknowledgement:
+ * "This product includes cryptographic software written by
+ * Eric Young (eay@cryptsoft.com)"
+ * The word 'cryptographic' can be left out if the rouines from the library
+ * being used are not cryptographic related :-).
+ * 4. If you include any Windows specific code (or a derivative thereof) from
+ * the apps directory (application code) you must include an acknowledgement:
+ * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+ * The licence and distribution terms for any publically available version or
+ * derivative of this code cannot be changed. i.e. this code cannot simply be
+ * copied and put under another distribution licence
+ * [including the GNU Public Licence.]
+ */
+/* ====================================================================
+ * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ * software must display the following acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ * endorse or promote products derived from this software without
+ * prior written permission. For written permission, please contact
+ * openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ * nor may "OpenSSL" appear in their names without prior written
+ * permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ * acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
-/* I've done some timing with different table sizes.
- * The main hassle is that even with bits set at 3, this requires
- * 63 BIGNUMs to store the pre-calculated values.
- * 512 1024
- * bits=1 75.4% 79.4%
- * bits=2 61.2% 62.4%
- * bits=3 61.3% 59.3%
- * The lack of speed improvement is also a function of the pre-calculation
- * which could be removed.
- */
-#define EXP2_TABLE_BITS 2 /* 1 2 3 4 5 */
-#define EXP2_TABLE_SIZE 4 /* 2 4 8 16 32 */
+#define TABLE_SIZE 32
int BN_mod_exp2_mont(BIGNUM *rr, BIGNUM *a1, BIGNUM *p1, BIGNUM *a2,
BIGNUM *p2, BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
- int i,j,k,bits,bits1,bits2,ret=0,wstart,wend,window,xvalue,yvalue;
- int start=1,ts=0,x,y;
- BIGNUM *d,*aa1,*aa2,*r;
- BIGNUM val[EXP2_TABLE_SIZE][EXP2_TABLE_SIZE];
+ int i,j,bits,b,bits1,bits2,ret=0,wpos1,wpos2,window1,window2,wvalue1,wvalue2;
+ int r_is_one=1,ts1=0,ts2=0;
+ BIGNUM *d,*r;
+ BIGNUM *a_mod_m;
+ BIGNUM val1[TABLE_SIZE], val2[TABLE_SIZE];
BN_MONT_CTX *mont=NULL;
bn_check_top(a1);
if (!(m->d[0] & 1))
{
- BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
+ BNerr(BN_F_BN_MOD_EXP2_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
return(0);
}
bits1=BN_num_bits(p1);
BN_one(rr);
return(1);
}
+ bits=(bits1 > bits2)?bits1:bits2;
BN_CTX_start(ctx);
d = BN_CTX_get(ctx);
r = BN_CTX_get(ctx);
if (d == NULL || r == NULL) goto err;
- bits=(bits1 > bits2)?bits1:bits2;
-
- /* If this is not done, things will break in the montgomery
- * part */
-
if (in_mont != NULL)
mont=in_mont;
else
if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
}
- BN_init(&(val[0][0]));
- BN_init(&(val[1][1]));
- BN_init(&(val[0][1]));
- BN_init(&(val[1][0]));
- ts=1;
+ window1 = BN_window_bits_for_exponent_size(bits1);
+ window2 = BN_window_bits_for_exponent_size(bits2);
+
+ /*
+ * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1)
+ */
+ BN_init(&val1[0]);
+ ts1=1;
if (BN_ucmp(a1,m) >= 0)
{
- BN_mod(&(val[1][0]),a1,m,ctx);
- aa1= &(val[1][0]);
+ if (!BN_mod(&(val1[0]),a1,m,ctx))
+ goto err;
+ a_mod_m = &(val1[0]);
}
else
- aa1=a1;
+ a_mod_m = a1;
+ if (!BN_to_montgomery(&(val1[0]),a_mod_m,mont,ctx)) goto err;
+ if (window1 > 1)
+ {
+ if (!BN_mod_mul_montgomery(d,&(val1[0]),&(val1[0]),mont,ctx)) goto err;
+
+ j=1<<(window1-1);
+ for (i=1; i<j; i++)
+ {
+ BN_init(&(val1[i]));
+ if (!BN_mod_mul_montgomery(&(val1[i]),&(val1[i-1]),d,mont,ctx))
+ goto err;
+ }
+ ts1=i;
+ }
+
+
+ /*
+ * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1)
+ */
+ BN_init(&val2[0]);
+ ts2=1;
if (BN_ucmp(a2,m) >= 0)
{
- BN_mod(&(val[0][1]),a2,m,ctx);
- aa2= &(val[0][1]);
+ if (!BN_mod(&(val2[0]),a2,m,ctx))
+ goto err;
+ a_mod_m = &(val2[0]);
}
else
- aa2=a2;
- if (!BN_to_montgomery(&(val[1][0]),aa1,mont,ctx)) goto err;
- if (!BN_to_montgomery(&(val[0][1]),aa2,mont,ctx)) goto err;
- if (!BN_mod_mul_montgomery(&(val[1][1]),
- &(val[1][0]),&(val[0][1]),mont,ctx))
- goto err;
-
-#if 0
- if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
- window=1;
- else if (bits > 250)
- window=5; /* max size of window */
- else if (bits >= 120)
- window=4;
- else
- window=3;
-#else
- window=EXP2_TABLE_BITS;
-#endif
-
- k=1<<window;
- for (x=0; x<k; x++)
+ a_mod_m = a2;
+ if (!BN_to_montgomery(&(val2[0]),a_mod_m,mont,ctx)) goto err;
+ if (window2 > 1)
{
- if (x >= 2)
- {
- BN_init(&(val[x][0]));
- BN_init(&(val[x][1]));
- if (!BN_mod_mul_montgomery(&(val[x][0]),
- &(val[1][0]),&(val[x-1][0]),mont,ctx)) goto err;
- if (!BN_mod_mul_montgomery(&(val[x][1]),
- &(val[1][0]),&(val[x-1][1]),mont,ctx)) goto err;
- }
- for (y=2; y<k; y++)
+ if (!BN_mod_mul_montgomery(d,&(val2[0]),&(val2[0]),mont,ctx)) goto err;
+
+ j=1<<(window2-1);
+ for (i=1; i<j; i++)
{
- BN_init(&(val[x][y]));
- if (!BN_mod_mul_montgomery(&(val[x][y]),
- &(val[x][y-1]),&(val[0][1]),mont,ctx))
+ BN_init(&(val2[i]));
+ if (!BN_mod_mul_montgomery(&(val2[i]),&(val2[i-1]),d,mont,ctx))
goto err;
}
+ ts2=i;
}
- ts=k;
-
- start=1; /* This is used to avoid multiplication etc
- * when there is only the value '1' in the
- * buffer. */
- xvalue=0; /* The 'x value' of the window */
- yvalue=0; /* The 'y value' of the window */
- wstart=bits-1; /* The top bit of the window */
- wend=0; /* The bottom bit of the window */
-
- if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
- for (;;)
+
+
+ /* Now compute the power product, using independent windows. */
+ r_is_one=1;
+ wvalue1=0; /* The 'value' of the first window */
+ wvalue2=0; /* The 'value' of the second window */
+ wpos1=0; /* If wvalue1 > 0, the bottom bit of the first window */
+ wpos2=0; /* If wvalue2 > 0, the bottom bit of the second window */
+
+ if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
+ for (b=bits-1; b>=0; b--)
{
- xvalue=BN_is_bit_set(p1,wstart);
- yvalue=BN_is_bit_set(p2,wstart);
- if (!(xvalue || yvalue))
+ if (!r_is_one)
{
- if (!start)
+ if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
+ goto err;
+ }
+
+ if (!wvalue1)
+ if (BN_is_bit_set(p1, b))
{
- if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
- goto err;
+ /* consider bits b-window1+1 .. b for this window */
+ i = b-window1+1;
+ while (!BN_is_bit_set(p1, i))
+ i++;
+ wpos1 = i;
+ wvalue1 = 1;
+ for (i = b-1; i >= wpos1; i--)
+ {
+ wvalue1 <<= 1;
+ if (BN_is_bit_set(p1, i))
+ wvalue1++;
+ }
}
- wstart--;
- if (wstart < 0) break;
- continue;
- }
- /* We now have wstart on a 'set' bit, we now need to work out
- * how bit a window to do. To do this we need to scan
- * forward until the last set bit before the end of the
- * window */
- j=wstart;
- /* xvalue=BN_is_bit_set(p1,wstart); already set */
- /* yvalue=BN_is_bit_set(p1,wstart); already set */
- wend=0;
- for (i=1; i<window; i++)
- {
- if (wstart-i < 0) break;
- xvalue+=xvalue;
- xvalue|=BN_is_bit_set(p1,wstart-i);
- yvalue+=yvalue;
- yvalue|=BN_is_bit_set(p2,wstart-i);
- }
-
- /* i is the size of the current window */
- /* add the 'bytes above' */
- if (!start)
- for (j=0; j<i; j++)
+
+ if (!wvalue2)
+ if (BN_is_bit_set(p2, b))
{
- if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
- goto err;
+ /* consider bits b-window2+1 .. b for this window */
+ i = b-window2+1;
+ while (!BN_is_bit_set(p2, i))
+ i++;
+ wpos2 = i;
+ wvalue2 = 1;
+ for (i = b-1; i >= wpos2; i--)
+ {
+ wvalue2 <<= 1;
+ if (BN_is_bit_set(p2, i))
+ wvalue2++;
+ }
}
+
+ if (wvalue1 && b == wpos1)
+ {
+ /* wvalue1 is odd and < 2^window1 */
+ if (!BN_mod_mul_montgomery(r,r,&(val1[wvalue1>>1]),mont,ctx))
+ goto err;
+ wvalue1 = 0;
+ r_is_one = 0;
+ }
- /* wvalue will be an odd number < 2^window */
- if (xvalue || yvalue)
+ if (wvalue2 && b == wpos2)
{
- if (!BN_mod_mul_montgomery(r,r,&(val[xvalue][yvalue]),
- mont,ctx)) goto err;
+ /* wvalue2 is odd and < 2^window2 */
+ if (!BN_mod_mul_montgomery(r,r,&(val2[wvalue2>>1]),mont,ctx))
+ goto err;
+ wvalue2 = 0;
+ r_is_one = 0;
}
-
- /* move the 'window' down further */
- wstart-=i;
- start=0;
- if (wstart < 0) break;
}
BN_from_montgomery(rr,r,mont,ctx);
ret=1;
err:
if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
BN_CTX_end(ctx);
- for (i=0; i<ts; i++)
- {
- for (j=0; j<ts; j++)
- {
- BN_clear_free(&(val[i][j]));
- }
- }
+ for (i=0; i<ts1; i++)
+ BN_clear_free(&(val1[i]));
+ for (i=0; i<ts2; i++)
+ BN_clear_free(&(val2[i]));
return(ret);
}
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
+/* ====================================================================
+ * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ * software must display the following acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ * endorse or promote products derived from this software without
+ * prior written permission. For written permission, please contact
+ * openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ * nor may "OpenSSL" appear in their names without prior written
+ * permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ * acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
#ifndef HEADER_BN_LCL_H
#define HEADER_BN_LCL_H
extern "C" {
#endif
+
+/*
+ * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
+ *
+ *
+ * For window size 'w' (w >= 2) and a random 'b' bits exponent,
+ * the number of multiplications is a constant plus on average
+ *
+ * 2^(w-1) + (b-w)/(w+1);
+ *
+ * here 2^(w-1) is for precomputing the table (we actually need
+ * entries only for windows that have the lowest bit set), and
+ * (b-w)/(w+1) is an approximation for the expected number of
+ * w-bit windows, not counting the first one.
+ *
+ * Thus we should use
+ *
+ * w >= 6 if b > 671
+ * w = 5 if 671 > b > 239
+ * w = 4 if 239 > b > 79
+ * w = 3 if 79 > b > 23
+ * w <= 2 if 23 > b
+ *
+ * (with draws in between). Very small exponents are often selected
+ * with low Hamming weight, so we use w = 1 for b <= 23.
+ */
+#if 1
+#define BN_window_bits_for_exponent_size(b) \
+ ((b) > 671 ? 6 : \
+ (b) > 239 ? 5 : \
+ (b) > 79 ? 4 : \
+ (b) > 23 ? 3 : 1)
+#else
+/* Old SSLeay/OpenSSL table.
+ * Maximum window size was 5, so this table differs for b==1024;
+ * but it coincides for other interesting values (b==160, b==512).
+ */
+#define BN_window_bits_for_exponent_size(b) \
+ ((b) > 255 ? 5 : \
+ (b) > 127 ? 4 : \
+ (b) > 17 ? 3 : 1)
+#endif
+
+
+
/* Pentium pro 16,16,16,32,64 */
/* Alpha 16,16,16,16.64 */
#define BN_MULL_SIZE_NORMAL (16) /* 32 */
projects / oweals / openssl.git / commitdiff