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-rw-r--r--crypto/bn/bn_exp.c1888
1 files changed, 952 insertions, 936 deletions
diff --git a/crypto/bn/bn_exp.c b/crypto/bn/bn_exp.c
index 611fa3262bed..27146c89e740 100644
--- a/crypto/bn/bn_exp.c
+++ b/crypto/bn/bn_exp.c
@@ -5,21 +5,21 @@
* 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:
@@ -34,10 +34,10 @@
* 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
+ * 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
@@ -49,7 +49,7 @@
* 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
@@ -63,7 +63,7 @@
* are met:
*
* 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
+ * 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
@@ -109,7 +109,6 @@
*
*/
-
#include "cryptlib.h"
#include "bn_lcl.h"
@@ -126,979 +125,996 @@
#endif
/* maximum precomputation table size for *variable* sliding windows */
-#define TABLE_SIZE 32
+#define TABLE_SIZE 32
/* this one works - simple but works */
int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
- {
- int i,bits,ret=0;
- BIGNUM *v,*rr;
-
- if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
- {
- /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
- BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
- return -1;
- }
-
- BN_CTX_start(ctx);
- if ((r == a) || (r == p))
- rr = BN_CTX_get(ctx);
- else
- rr = r;
- v = BN_CTX_get(ctx);
- if (rr == NULL || v == NULL) goto err;
-
- if (BN_copy(v,a) == NULL) goto err;
- bits=BN_num_bits(p);
-
- if (BN_is_odd(p))
- { if (BN_copy(rr,a) == NULL) goto err; }
- else { if (!BN_one(rr)) goto err; }
-
- for (i=1; i<bits; i++)
- {
- if (!BN_sqr(v,v,ctx)) goto err;
- if (BN_is_bit_set(p,i))
- {
- if (!BN_mul(rr,rr,v,ctx)) goto err;
- }
- }
- ret=1;
-err:
- if (r != rr) BN_copy(r,rr);
- BN_CTX_end(ctx);
- bn_check_top(r);
- return(ret);
- }
-
+{
+ int i, bits, ret = 0;
+ BIGNUM *v, *rr;
+
+ if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
+ /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
+ BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return -1;
+ }
+
+ BN_CTX_start(ctx);
+ if ((r == a) || (r == p))
+ rr = BN_CTX_get(ctx);
+ else
+ rr = r;
+ v = BN_CTX_get(ctx);
+ if (rr == NULL || v == NULL)
+ goto err;
+
+ if (BN_copy(v, a) == NULL)
+ goto err;
+ bits = BN_num_bits(p);
+
+ if (BN_is_odd(p)) {
+ if (BN_copy(rr, a) == NULL)
+ goto err;
+ } else {
+ if (!BN_one(rr))
+ goto err;
+ }
+
+ for (i = 1; i < bits; i++) {
+ if (!BN_sqr(v, v, ctx))
+ goto err;
+ if (BN_is_bit_set(p, i)) {
+ if (!BN_mul(rr, rr, v, ctx))
+ goto err;
+ }
+ }
+ if (r != rr)
+ BN_copy(r, rr);
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ bn_check_top(r);
+ return (ret);
+}
int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
- BN_CTX *ctx)
- {
- int ret;
-
- bn_check_top(a);
- bn_check_top(p);
- bn_check_top(m);
-
- /* For even modulus m = 2^k*m_odd, it might make sense to compute
- * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
- * exponentiation for the odd part), using appropriate exponent
- * reductions, and combine the results using the CRT.
- *
- * For now, we use Montgomery only if the modulus is odd; otherwise,
- * exponentiation using the reciprocal-based quick remaindering
- * algorithm is used.
- *
- * (Timing obtained with expspeed.c [computations a^p mod m
- * where a, p, m are of the same length: 256, 512, 1024, 2048,
- * 4096, 8192 bits], compared to the running time of the
- * standard algorithm:
- *
- * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
- * 55 .. 77 % [UltraSparc processor, but
- * debug-solaris-sparcv8-gcc conf.]
- *
- * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
- * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
- *
- * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
- * at 2048 and more bits, but at 512 and 1024 bits, it was
- * slower even than the standard algorithm!
- *
- * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
- * should be obtained when the new Montgomery reduction code
- * has been integrated into OpenSSL.)
- */
+ BN_CTX *ctx)
+{
+ int ret;
+
+ bn_check_top(a);
+ bn_check_top(p);
+ bn_check_top(m);
+
+ /*-
+ * For even modulus m = 2^k*m_odd, it might make sense to compute
+ * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
+ * exponentiation for the odd part), using appropriate exponent
+ * reductions, and combine the results using the CRT.
+ *
+ * For now, we use Montgomery only if the modulus is odd; otherwise,
+ * exponentiation using the reciprocal-based quick remaindering
+ * algorithm is used.
+ *
+ * (Timing obtained with expspeed.c [computations a^p mod m
+ * where a, p, m are of the same length: 256, 512, 1024, 2048,
+ * 4096, 8192 bits], compared to the running time of the
+ * standard algorithm:
+ *
+ * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
+ * 55 .. 77 % [UltraSparc processor, but
+ * debug-solaris-sparcv8-gcc conf.]
+ *
+ * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
+ * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
+ *
+ * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
+ * at 2048 and more bits, but at 512 and 1024 bits, it was
+ * slower even than the standard algorithm!
+ *
+ * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
+ * should be obtained when the new Montgomery reduction code
+ * has been integrated into OpenSSL.)
+ */
#define MONT_MUL_MOD
#define MONT_EXP_WORD
#define RECP_MUL_MOD
#ifdef MONT_MUL_MOD
- /* I have finally been able to take out this pre-condition of
- * the top bit being set. It was caused by an error in BN_div
- * with negatives. There was also another problem when for a^b%m
- * a >= m. eay 07-May-97 */
-/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
-
- if (BN_is_odd(m))
- {
-# ifdef MONT_EXP_WORD
- if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
- {
- BN_ULONG A = a->d[0];
- ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
- }
- else
-# endif
- ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
- }
- else
+ /*
+ * I have finally been able to take out this pre-condition of the top bit
+ * being set. It was caused by an error in BN_div with negatives. There
+ * was also another problem when for a^b%m a >= m. eay 07-May-97
+ */
+ /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
+
+ if (BN_is_odd(m)) {
+# ifdef MONT_EXP_WORD
+ if (a->top == 1 && !a->neg
+ && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
+ BN_ULONG A = a->d[0];
+ ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
+ } else
+# endif
+ ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
+ } else
#endif
#ifdef RECP_MUL_MOD
- { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
+ {
+ ret = BN_mod_exp_recp(r, a, p, m, ctx);
+ }
#else
- { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
+ {
+ ret = BN_mod_exp_simple(r, a, p, m, ctx);
+ }
#endif
- bn_check_top(r);
- return(ret);
- }
-
+ bn_check_top(r);
+ return (ret);
+}
int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
- const BIGNUM *m, BN_CTX *ctx)
- {
- int i,j,bits,ret=0,wstart,wend,window,wvalue;
- int start=1;
- BIGNUM *aa;
- /* Table of variables obtained from 'ctx' */
- BIGNUM *val[TABLE_SIZE];
- BN_RECP_CTX recp;
-
- if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
- {
- /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
- BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
- return -1;
- }
-
- bits=BN_num_bits(p);
-
- if (bits == 0)
- {
- ret = BN_one(r);
- return ret;
- }
-
- BN_CTX_start(ctx);
- aa = BN_CTX_get(ctx);
- val[0] = BN_CTX_get(ctx);
- if(!aa || !val[0]) goto err;
-
- BN_RECP_CTX_init(&recp);
- if (m->neg)
- {
- /* ignore sign of 'm' */
- if (!BN_copy(aa, m)) goto err;
- aa->neg = 0;
- if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
- }
- else
- {
- if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
- }
-
- if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
- if (BN_is_zero(val[0]))
- {
- BN_zero(r);
- ret = 1;
- goto err;
- }
-
- window = BN_window_bits_for_exponent_size(bits);
- if (window > 1)
- {
- 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++)
- {
- if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
- !BN_mod_mul_reciprocal(val[i],val[i-1],
- aa,&recp,ctx))
- goto err;
- }
- }
-
- start=1; /* This is used to avoid multiplication etc
- * when there is only the value '1' in the
- * buffer. */
- wvalue=0; /* The 'value' of the window */
- wstart=bits-1; /* The top bit of the window */
- wend=0; /* The bottom bit of the window */
-
- if (!BN_one(r)) goto err;
-
- for (;;)
- {
- if (BN_is_bit_set(p,wstart) == 0)
- {
- if (!start)
- if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
- goto err;
- if (wstart == 0) break;
- wstart--;
- 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;
- wvalue=1;
- wend=0;
- for (i=1; i<window; i++)
- {
- if (wstart-i < 0) break;
- if (BN_is_bit_set(p,wstart-i))
- {
- wvalue<<=(i-wend);
- wvalue|=1;
- wend=i;
- }
- }
-
- /* wend is the size of the current window */
- j=wend+1;
- /* add the 'bytes above' */
- if (!start)
- for (i=0; i<j; i++)
- {
- if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
- goto err;
- }
-
- /* wvalue will be an odd number < 2^window */
- if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
- goto err;
-
- /* move the 'window' down further */
- wstart-=wend+1;
- wvalue=0;
- start=0;
- if (wstart < 0) break;
- }
- ret=1;
-err:
- BN_CTX_end(ctx);
- BN_RECP_CTX_free(&recp);
- bn_check_top(r);
- return(ret);
- }
-
+ const BIGNUM *m, BN_CTX *ctx)
+{
+ int i, j, bits, ret = 0, wstart, wend, window, wvalue;
+ int start = 1;
+ BIGNUM *aa;
+ /* Table of variables obtained from 'ctx' */
+ BIGNUM *val[TABLE_SIZE];
+ BN_RECP_CTX recp;
+
+ if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
+ /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
+ BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return -1;
+ }
+
+ bits = BN_num_bits(p);
+
+ if (bits == 0) {
+ ret = BN_one(r);
+ return ret;
+ }
+
+ BN_CTX_start(ctx);
+ aa = BN_CTX_get(ctx);
+ val[0] = BN_CTX_get(ctx);
+ if (!aa || !val[0])
+ goto err;
+
+ BN_RECP_CTX_init(&recp);
+ if (m->neg) {
+ /* ignore sign of 'm' */
+ if (!BN_copy(aa, m))
+ goto err;
+ aa->neg = 0;
+ if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
+ goto err;
+ } else {
+ if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
+ goto err;
+ }
+
+ if (!BN_nnmod(val[0], a, m, ctx))
+ goto err; /* 1 */
+ if (BN_is_zero(val[0])) {
+ BN_zero(r);
+ ret = 1;
+ goto err;
+ }
+
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1) {
+ 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++) {
+ if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
+ !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
+ goto err;
+ }
+ }
+
+ start = 1; /* This is used to avoid multiplication etc
+ * when there is only the value '1' in the
+ * buffer. */
+ wvalue = 0; /* The 'value' of the window */
+ wstart = bits - 1; /* The top bit of the window */
+ wend = 0; /* The bottom bit of the window */
+
+ if (!BN_one(r))
+ goto err;
+
+ for (;;) {
+ if (BN_is_bit_set(p, wstart) == 0) {
+ if (!start)
+ if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
+ goto err;
+ if (wstart == 0)
+ break;
+ wstart--;
+ 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;
+ wvalue = 1;
+ wend = 0;
+ for (i = 1; i < window; i++) {
+ if (wstart - i < 0)
+ break;
+ if (BN_is_bit_set(p, wstart - i)) {
+ wvalue <<= (i - wend);
+ wvalue |= 1;
+ wend = i;
+ }
+ }
+
+ /* wend is the size of the current window */
+ j = wend + 1;
+ /* add the 'bytes above' */
+ if (!start)
+ for (i = 0; i < j; i++) {
+ if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
+ goto err;
+ }
+
+ /* wvalue will be an odd number < 2^window */
+ if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
+ goto err;
+
+ /* move the 'window' down further */
+ wstart -= wend + 1;
+ wvalue = 0;
+ start = 0;
+ if (wstart < 0)
+ break;
+ }
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ BN_RECP_CTX_free(&recp);
+ bn_check_top(r);
+ return (ret);
+}
int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
- const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
- {
- int i,j,bits,ret=0,wstart,wend,window,wvalue;
- int start=1;
- BIGNUM *d,*r;
- const BIGNUM *aa;
- /* Table of variables obtained from 'ctx' */
- BIGNUM *val[TABLE_SIZE];
- BN_MONT_CTX *mont=NULL;
-
- if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
- {
- return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
- }
-
- bn_check_top(a);
- bn_check_top(p);
- bn_check_top(m);
-
- if (!BN_is_odd(m))
- {
- BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
- return(0);
- }
- bits=BN_num_bits(p);
- if (bits == 0)
- {
- ret = BN_one(rr);
- return ret;
- }
-
- BN_CTX_start(ctx);
- d = BN_CTX_get(ctx);
- r = BN_CTX_get(ctx);
- val[0] = BN_CTX_get(ctx);
- if (!d || !r || !val[0]) goto err;
-
- /* If this is not done, things will break in the montgomery
- * part */
-
- if (in_mont != NULL)
- mont=in_mont;
- else
- {
- if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
- if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
- }
-
- if (a->neg || BN_ucmp(a,m) >= 0)
- {
- if (!BN_nnmod(val[0],a,m,ctx))
- goto err;
- aa= val[0];
- }
- else
- aa=a;
- if (BN_is_zero(aa))
- {
- BN_zero(rr);
- ret = 1;
- goto err;
- }
- if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
-
- window = BN_window_bits_for_exponent_size(bits);
- if (window > 1)
- {
- 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++)
- {
- if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
- !BN_mod_mul_montgomery(val[i],val[i-1],
- d,mont,ctx))
- goto err;
- }
- }
-
- start=1; /* This is used to avoid multiplication etc
- * when there is only the value '1' in the
- * buffer. */
- wvalue=0; /* The '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 (;;)
- {
- if (BN_is_bit_set(p,wstart) == 0)
- {
- if (!start)
- {
- if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
- goto err;
- }
- if (wstart == 0) break;
- wstart--;
- 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;
- wvalue=1;
- wend=0;
- for (i=1; i<window; i++)
- {
- if (wstart-i < 0) break;
- if (BN_is_bit_set(p,wstart-i))
- {
- wvalue<<=(i-wend);
- wvalue|=1;
- wend=i;
- }
- }
-
- /* wend is the size of the current window */
- j=wend+1;
- /* add the 'bytes above' */
- if (!start)
- for (i=0; i<j; i++)
- {
- if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
- goto err;
- }
-
- /* wvalue will be an odd number < 2^window */
- if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
- goto err;
-
- /* move the 'window' down further */
- wstart-=wend+1;
- wvalue=0;
- start=0;
- if (wstart < 0) break;
- }
- if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
- ret=1;
-err:
- if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
- BN_CTX_end(ctx);
- bn_check_top(rr);
- return(ret);
- }
-
-
-/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
- * so that accessing any of these table values shows the same access pattern as far
- * as cache lines are concerned. The following functions are used to transfer a BIGNUM
- * from/to that table. */
-
-static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top, unsigned char *buf, int idx, int width)
- {
- size_t i, j;
-
- if (top > b->top)
- top = b->top; /* this works because 'buf' is explicitly zeroed */
- for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
- {
- buf[j] = ((unsigned char*)b->d)[i];
- }
-
- return 1;
- }
-
-static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
- {
- size_t i, j;
-
- if (bn_wexpand(b, top) == NULL)
- return 0;
-
- for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
- {
- ((unsigned char*)b->d)[i] = buf[j];
- }
-
- b->top = top;
- bn_correct_top(b);
- return 1;
- }
-
-/* Given a pointer value, compute the next address that is a cache line multiple. */
-#define MOD_EXP_CTIME_ALIGN(x_) \
- ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
+ const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
+{
+ int i, j, bits, ret = 0, wstart, wend, window, wvalue;
+ int start = 1;
+ BIGNUM *d, *r;
+ const BIGNUM *aa;
+ /* Table of variables obtained from 'ctx' */
+ BIGNUM *val[TABLE_SIZE];
+ BN_MONT_CTX *mont = NULL;
+
+ if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
+ return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
+ }
+
+ bn_check_top(a);
+ bn_check_top(p);
+ bn_check_top(m);
+
+ if (!BN_is_odd(m)) {
+ BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return (0);
+ }
+ bits = BN_num_bits(p);
+ if (bits == 0) {
+ ret = BN_one(rr);
+ return ret;
+ }
+
+ BN_CTX_start(ctx);
+ d = BN_CTX_get(ctx);
+ r = BN_CTX_get(ctx);
+ val[0] = BN_CTX_get(ctx);
+ if (!d || !r || !val[0])
+ goto err;
+
+ /*
+ * If this is not done, things will break in the montgomery part
+ */
+
+ if (in_mont != NULL)
+ mont = in_mont;
+ else {
+ if ((mont = BN_MONT_CTX_new()) == NULL)
+ goto err;
+ if (!BN_MONT_CTX_set(mont, m, ctx))
+ goto err;
+ }
+
+ if (a->neg || BN_ucmp(a, m) >= 0) {
+ if (!BN_nnmod(val[0], a, m, ctx))
+ goto err;
+ aa = val[0];
+ } else
+ aa = a;
+ if (BN_is_zero(aa)) {
+ BN_zero(rr);
+ ret = 1;
+ goto err;
+ }
+ if (!BN_to_montgomery(val[0], aa, mont, ctx))
+ goto err; /* 1 */
+
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1) {
+ 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++) {
+ if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
+ !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
+ goto err;
+ }
+ }
+
+ start = 1; /* This is used to avoid multiplication etc
+ * when there is only the value '1' in the
+ * buffer. */
+ wvalue = 0; /* The '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 (;;) {
+ if (BN_is_bit_set(p, wstart) == 0) {
+ if (!start) {
+ if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
+ goto err;
+ }
+ if (wstart == 0)
+ break;
+ wstart--;
+ 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;
+ wvalue = 1;
+ wend = 0;
+ for (i = 1; i < window; i++) {
+ if (wstart - i < 0)
+ break;
+ if (BN_is_bit_set(p, wstart - i)) {
+ wvalue <<= (i - wend);
+ wvalue |= 1;
+ wend = i;
+ }
+ }
+
+ /* wend is the size of the current window */
+ j = wend + 1;
+ /* add the 'bytes above' */
+ if (!start)
+ for (i = 0; i < j; i++) {
+ if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
+ goto err;
+ }
+
+ /* wvalue will be an odd number < 2^window */
+ if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
+ goto err;
+
+ /* move the 'window' down further */
+ wstart -= wend + 1;
+ wvalue = 0;
+ start = 0;
+ if (wstart < 0)
+ break;
+ }
+ if (!BN_from_montgomery(rr, r, mont, ctx))
+ goto err;
+ ret = 1;
+ err:
+ if ((in_mont == NULL) && (mont != NULL))
+ BN_MONT_CTX_free(mont);
+ BN_CTX_end(ctx);
+ bn_check_top(rr);
+ return (ret);
+}
+
+/*
+ * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
+ * layout so that accessing any of these table values shows the same access
+ * pattern as far as cache lines are concerned. The following functions are
+ * used to transfer a BIGNUM from/to that table.
+ */
-/* This variant of BN_mod_exp_mont() uses fixed windows and the special
- * precomputation memory layout to limit data-dependency to a minimum
- * to protect secret exponents (cf. the hyper-threading timing attacks
- * pointed out by Colin Percival,
- * http://www.daemonology.net/hyperthreading-considered-harmful/)
+static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
+ unsigned char *buf, int idx,
+ int width)
+{
+ size_t i, j;
+
+ if (top > b->top)
+ top = b->top; /* this works because 'buf' is explicitly
+ * zeroed */
+ for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
+ buf[j] = ((unsigned char *)b->d)[i];
+ }
+
+ return 1;
+}
+
+static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
+ unsigned char *buf, int idx,
+ int width)
+{
+ size_t i, j;
+
+ if (bn_wexpand(b, top) == NULL)
+ return 0;
+
+ for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
+ ((unsigned char *)b->d)[i] = buf[j];
+ }
+
+ b->top = top;
+ bn_correct_top(b);
+ return 1;
+}
+
+/*
+ * Given a pointer value, compute the next address that is a cache line
+ * multiple.
+ */
+#define MOD_EXP_CTIME_ALIGN(x_) \
+ ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
+
+/*
+ * This variant of BN_mod_exp_mont() uses fixed windows and the special
+ * precomputation memory layout to limit data-dependency to a minimum to
+ * protect secret exponents (cf. the hyper-threading timing attacks pointed
+ * out by Colin Percival,
+ * http://www.daemong-consideredperthreading-considered-harmful/)
*/
int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
- const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
- {
- int i,bits,ret=0,window,wvalue;
- int top;
- BN_MONT_CTX *mont=NULL;
-
- int numPowers;
- unsigned char *powerbufFree=NULL;
- int powerbufLen = 0;
- unsigned char *powerbuf=NULL;
- BIGNUM tmp, am;
-
- bn_check_top(a);
- bn_check_top(p);
- bn_check_top(m);
-
- top = m->top;
-
- if (!(m->d[0] & 1))
- {
- BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
- return(0);
- }
- bits=BN_num_bits(p);
- if (bits == 0)
- {
- ret = BN_one(rr);
- return ret;
- }
-
- BN_CTX_start(ctx);
-
- /* Allocate a montgomery context if it was not supplied by the caller.
- * If this is not done, things will break in the montgomery part.
- */
- if (in_mont != NULL)
- mont=in_mont;
- else
- {
- if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
- if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
- }
-
- /* Get the window size to use with size of p. */
- window = BN_window_bits_for_ctime_exponent_size(bits);
+ const BIGNUM *m, BN_CTX *ctx,
+ BN_MONT_CTX *in_mont)
+{
+ int i, bits, ret = 0, window, wvalue;
+ int top;
+ BN_MONT_CTX *mont = NULL;
+
+ int numPowers;
+ unsigned char *powerbufFree = NULL;
+ int powerbufLen = 0;
+ unsigned char *powerbuf = NULL;
+ BIGNUM tmp, am;
+
+ bn_check_top(a);
+ bn_check_top(p);
+ bn_check_top(m);
+
+ top = m->top;
+
+ if (!(m->d[0] & 1)) {
+ BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return (0);
+ }
+ bits = BN_num_bits(p);
+ if (bits == 0) {
+ ret = BN_one(rr);
+ return ret;
+ }
+
+ BN_CTX_start(ctx);
+
+ /*
+ * Allocate a montgomery context if it was not supplied by the caller. If
+ * this is not done, things will break in the montgomery part.
+ */
+ if (in_mont != NULL)
+ mont = in_mont;
+ else {
+ if ((mont = BN_MONT_CTX_new()) == NULL)
+ goto err;
+ if (!BN_MONT_CTX_set(mont, m, ctx))
+ goto err;
+ }
+
+ /* Get the window size to use with size of p. */
+ window = BN_window_bits_for_ctime_exponent_size(bits);
#if defined(OPENSSL_BN_ASM_MONT5)
- if (window==6 && bits<=1024) window=5; /* ~5% improvement of 2048-bit RSA sign */
+ if (window == 6 && bits <= 1024)
+ window = 5; /* ~5% improvement of 2048-bit RSA sign */
#endif
- /* Allocate a buffer large enough to hold all of the pre-computed
- * powers of am, am itself and tmp.
- */
- numPowers = 1 << window;
- powerbufLen = sizeof(m->d[0])*(top*numPowers +
- ((2*top)>numPowers?(2*top):numPowers));
+ /*
+ * Allocate a buffer large enough to hold all of the pre-computed powers
+ * of am, am itself and tmp.
+ */
+ numPowers = 1 << window;
+ powerbufLen = sizeof(m->d[0]) * (top * numPowers +
+ ((2 * top) >
+ numPowers ? (2 * top) : numPowers));
#ifdef alloca
- if (powerbufLen < 3072)
- powerbufFree = alloca(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
- else
+ if (powerbufLen < 3072)
+ powerbufFree =
+ alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
+ else
#endif
- if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
- goto err;
-
- powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
- memset(powerbuf, 0, powerbufLen);
+ if ((powerbufFree =
+ (unsigned char *)OPENSSL_malloc(powerbufLen +
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
+ == NULL)
+ goto err;
+
+ powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
+ memset(powerbuf, 0, powerbufLen);
#ifdef alloca
- if (powerbufLen < 3072)
- powerbufFree = NULL;
+ if (powerbufLen < 3072)
+ powerbufFree = NULL;
#endif
- /* lay down tmp and am right after powers table */
- tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0])*top*numPowers);
- am.d = tmp.d + top;
- tmp.top = am.top = 0;
- tmp.dmax = am.dmax = top;
- tmp.neg = am.neg = 0;
- tmp.flags = am.flags = BN_FLG_STATIC_DATA;
+ /* lay down tmp and am right after powers table */
+ tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
+ am.d = tmp.d + top;
+ tmp.top = am.top = 0;
+ tmp.dmax = am.dmax = top;
+ tmp.neg = am.neg = 0;
+ tmp.flags = am.flags = BN_FLG_STATIC_DATA;
- /* prepare a^0 in Montgomery domain */
+ /* prepare a^0 in Montgomery domain */
#if 1
- if (!BN_to_montgomery(&tmp,BN_value_one(),mont,ctx)) goto err;
+ if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
+ goto err;
#else
- tmp.d[0] = (0-m->d[0])&BN_MASK2; /* 2^(top*BN_BITS2) - m */
- for (i=1;i<top;i++)
- tmp.d[i] = (~m->d[i])&BN_MASK2;
- tmp.top = top;
+ tmp.d[0] = (0 - m->d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */
+ for (i = 1; i < top; i++)
+ tmp.d[i] = (~m->d[i]) & BN_MASK2;
+ tmp.top = top;
#endif
- /* prepare a^1 in Montgomery domain */
- if (a->neg || BN_ucmp(a,m) >= 0)
- {
- if (!BN_mod(&am,a,m,ctx)) goto err;
- if (!BN_to_montgomery(&am,&am,mont,ctx)) goto err;
- }
- else if (!BN_to_montgomery(&am,a,mont,ctx)) goto err;
+ /* prepare a^1 in Montgomery domain */
+ if (a->neg || BN_ucmp(a, m) >= 0) {
+ if (!BN_mod(&am, a, m, ctx))
+ goto err;
+ if (!BN_to_montgomery(&am, &am, mont, ctx))
+ goto err;
+ } else if (!BN_to_montgomery(&am, a, mont, ctx))
+ goto err;
#if defined(OPENSSL_BN_ASM_MONT5)
- /* This optimization uses ideas from http://eprint.iacr.org/2011/239,
- * specifically optimization of cache-timing attack countermeasures
- * and pre-computation optimization. */
-
- /* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
- * 512-bit RSA is hardly relevant, we omit it to spare size... */
- if (window==5 && top>1)
- {
- void bn_mul_mont_gather5(BN_ULONG *rp,const BN_ULONG *ap,
- const void *table,const BN_ULONG *np,
- const BN_ULONG *n0,int num,int power);
- void bn_scatter5(const BN_ULONG *inp,size_t num,
- void *table,size_t power);
- void bn_gather5(BN_ULONG *out,size_t num,
- void *table,size_t power);
-
- BN_ULONG *np=mont->N.d, *n0=mont->n0;
-
- /* BN_to_montgomery can contaminate words above .top
- * [in BN_DEBUG[_DEBUG] build]... */
- for (i=am.top; i<top; i++) am.d[i]=0;
- for (i=tmp.top; i<top; i++) tmp.d[i]=0;
-
- bn_scatter5(tmp.d,top,powerbuf,0);
- bn_scatter5(am.d,am.top,powerbuf,1);
- bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
- bn_scatter5(tmp.d,top,powerbuf,2);
-
-#if 0
- for (i=3; i<32; i++)
- {
- /* Calculate a^i = a^(i-1) * a */
- bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
- bn_scatter5(tmp.d,top,powerbuf,i);
- }
-#else
- /* same as above, but uses squaring for 1/2 of operations */
- for (i=4; i<32; i*=2)
- {
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_scatter5(tmp.d,top,powerbuf,i);
- }
- for (i=3; i<8; i+=2)
- {
- int j;
- bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
- bn_scatter5(tmp.d,top,powerbuf,i);
- for (j=2*i; j<32; j*=2)
- {
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_scatter5(tmp.d,top,powerbuf,j);
- }
- }
- for (; i<16; i+=2)
- {
- bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
- bn_scatter5(tmp.d,top,powerbuf,i);
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_scatter5(tmp.d,top,powerbuf,2*i);
- }
- for (; i<32; i+=2)
- {
- bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
- bn_scatter5(tmp.d,top,powerbuf,i);
- }
-#endif
- bits--;
- for (wvalue=0, i=bits%5; i>=0; i--,bits--)
- wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
- bn_gather5(tmp.d,top,powerbuf,wvalue);
-
- /* Scan the exponent one window at a time starting from the most
- * significant bits.
- */
- while (bits >= 0)
- {
- for (wvalue=0, i=0; i<5; i++,bits--)
- wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
-
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
- bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
- }
-
- tmp.top=top;
- bn_correct_top(&tmp);
- }
- else
+ if (window == 5 && top > 1) {
+ /*
+ * This optimization uses ideas from http://eprint.iacr.org/2011/239,
+ * specifically optimization of cache-timing attack countermeasures
+ * and pre-computation optimization.
+ */
+
+ /*
+ * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
+ * 512-bit RSA is hardly relevant, we omit it to spare size...
+ */
+ void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
+ const void *table, const BN_ULONG *np,
+ const BN_ULONG *n0, int num, int power);
+ void bn_scatter5(const BN_ULONG *inp, size_t num,
+ void *table, size_t power);
+ void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
+
+ BN_ULONG *np = mont->N.d, *n0 = mont->n0;
+
+ /*
+ * BN_to_montgomery can contaminate words above .top [in
+ * BN_DEBUG[_DEBUG] build]...
+ */
+ for (i = am.top; i < top; i++)
+ am.d[i] = 0;
+ for (i = tmp.top; i < top; i++)
+ tmp.d[i] = 0;
+
+ bn_scatter5(tmp.d, top, powerbuf, 0);
+ bn_scatter5(am.d, am.top, powerbuf, 1);
+ bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, 2);
+
+# if 0
+ for (i = 3; i < 32; i++) {
+ /* Calculate a^i = a^(i-1) * a */
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ }
+# else
+ /* same as above, but uses squaring for 1/2 of operations */
+ for (i = 4; i < 32; i *= 2) {
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ }
+ for (i = 3; i < 8; i += 2) {
+ int j;
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ for (j = 2 * i; j < 32; j *= 2) {
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, j);
+ }
+ }
+ for (; i < 16; i += 2) {
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_scatter5(tmp.d, top, powerbuf, 2 * i);
+ }
+ for (; i < 32; i += 2) {
+ bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
+ bn_scatter5(tmp.d, top, powerbuf, i);
+ }
+# endif
+ bits--;
+ for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ bn_gather5(tmp.d, top, powerbuf, wvalue);
+
+ /*
+ * Scan the exponent one window at a time starting from the most
+ * significant bits.
+ */
+ while (bits >= 0) {
+ for (wvalue = 0, i = 0; i < 5; i++, bits--)
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
+ bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
+ }
+
+ tmp.top = top;
+ bn_correct_top(&tmp);
+ } else
#endif
- {
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers)) goto err;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers)) goto err;
-
- /* If the window size is greater than 1, then calculate
- * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
- * (even powers could instead be computed as (a^(i/2))^2
- * to use the slight performance advantage of sqr over mul).
- */
- if (window > 1)
- {
- if (!BN_mod_mul_montgomery(&tmp,&am,&am,mont,ctx)) goto err;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2, numPowers)) goto err;
- for (i=3; i<numPowers; i++)
- {
- /* Calculate a^i = a^(i-1) * a */
- if (!BN_mod_mul_montgomery(&tmp,&am,&tmp,mont,ctx))
- goto err;
- if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i, numPowers)) goto err;
- }
- }
-
- bits--;
- for (wvalue=0, i=bits%window; i>=0; i--,bits--)
- wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
- if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp,top,powerbuf,wvalue,numPowers)) goto err;
-
- /* Scan the exponent one window at a time starting from the most
- * significant bits.
- */
- while (bits >= 0)
- {
- wvalue=0; /* The 'value' of the window */
-
- /* Scan the window, squaring the result as we go */
- for (i=0; i<window; i++,bits--)
- {
- if (!BN_mod_mul_montgomery(&tmp,&tmp,&tmp,mont,ctx)) goto err;
- wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
- }
-
- /* Fetch the appropriate pre-computed value from the pre-buf */
- if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue, numPowers)) goto err;
-
- /* Multiply the result into the intermediate result */
- if (!BN_mod_mul_montgomery(&tmp,&tmp,&am,mont,ctx)) goto err;
- }
- }
-
- /* Convert the final result from montgomery to standard format */
- if (!BN_from_montgomery(rr,&tmp,mont,ctx)) goto err;
- ret=1;
-err:
- if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
- if (powerbuf!=NULL)
- {
- OPENSSL_cleanse(powerbuf,powerbufLen);
- if (powerbufFree) OPENSSL_free(powerbufFree);
- }
- BN_CTX_end(ctx);
- return(ret);
- }
+ {
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers))
+ goto err;
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers))
+ goto err;
+
+ /*
+ * If the window size is greater than 1, then calculate
+ * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
+ * powers could instead be computed as (a^(i/2))^2 to use the slight
+ * performance advantage of sqr over mul).
+ */
+ if (window > 1) {
+ if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
+ goto err;
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF
+ (&tmp, top, powerbuf, 2, numPowers))
+ goto err;
+ for (i = 3; i < numPowers; i++) {
+ /* Calculate a^i = a^(i-1) * a */
+ if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
+ goto err;
+ if (!MOD_EXP_CTIME_COPY_TO_PREBUF
+ (&tmp, top, powerbuf, i, numPowers))
+ goto err;
+ }
+ }
+
+ bits--;
+ for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
+ (&tmp, top, powerbuf, wvalue, numPowers))
+ goto err;
+
+ /*
+ * Scan the exponent one window at a time starting from the most
+ * significant bits.
+ */
+ while (bits >= 0) {
+ wvalue = 0; /* The 'value' of the window */
+
+ /* Scan the window, squaring the result as we go */
+ for (i = 0; i < window; i++, bits--) {
+ if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
+ goto err;
+ wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
+ }
+
+ /*
+ * Fetch the appropriate pre-computed value from the pre-buf
+ */
+ if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
+ (&am, top, powerbuf, wvalue, numPowers))
+ goto err;
+
+ /* Multiply the result into the intermediate result */
+ if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
+ goto err;
+ }
+ }
+
+ /* Convert the final result from montgomery to standard format */
+ if (!BN_from_montgomery(rr, &tmp, mont, ctx))
+ goto err;
+ ret = 1;
+ err:
+ if ((in_mont == NULL) && (mont != NULL))
+ BN_MONT_CTX_free(mont);
+ if (powerbuf != NULL) {
+ OPENSSL_cleanse(powerbuf, powerbufLen);
+ if (powerbufFree)
+ OPENSSL_free(powerbufFree);
+ }
+ BN_CTX_end(ctx);
+ return (ret);
+}
int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
- {
- BN_MONT_CTX *mont = NULL;
- int b, bits, ret=0;
- int r_is_one;
- BN_ULONG w, next_w;
- BIGNUM *d, *r, *t;
- BIGNUM *swap_tmp;
+{
+ BN_MONT_CTX *mont = NULL;
+ int b, bits, ret = 0;
+ int r_is_one;
+ BN_ULONG w, next_w;
+ BIGNUM *d, *r, *t;
+ BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
- (BN_mul_word(r, (w)) && \
- (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
- (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
- /* BN_MOD_MUL_WORD is only used with 'w' large,
- * so the BN_ucmp test is probably more overhead
- * than always using BN_mod (which uses BN_copy if
- * a similar test returns true). */
- /* We can use BN_mod and do not need BN_nnmod because our
- * accumulator is never negative (the result of BN_mod does
- * not depend on the sign of the modulus).
- */
+ (BN_mul_word(r, (w)) && \
+ (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
+ (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
+ /*
+ * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
+ * probably more overhead than always using BN_mod (which uses BN_copy if
+ * a similar test returns true).
+ */
+ /*
+ * We can use BN_mod and do not need BN_nnmod because our accumulator is
+ * never negative (the result of BN_mod does not depend on the sign of
+ * the modulus).
+ */
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
- (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
-
- if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
- {
- /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
- BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
- return -1;
- }
-
- bn_check_top(p);
- bn_check_top(m);
-
- if (!BN_is_odd(m))
- {
- BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
- return(0);
- }
- if (m->top == 1)
- a %= m->d[0]; /* make sure that 'a' is reduced */
-
- bits = BN_num_bits(p);
- if (bits == 0)
- {
- /* x**0 mod 1 is still zero. */
- if (BN_is_one(m))
- {
- ret = 1;
- BN_zero(rr);
- }
- else
- ret = BN_one(rr);
- return ret;
- }
- if (a == 0)
- {
- BN_zero(rr);
- ret = 1;
- return ret;
- }
-
- BN_CTX_start(ctx);
- d = BN_CTX_get(ctx);
- r = BN_CTX_get(ctx);
- t = BN_CTX_get(ctx);
- if (d == NULL || r == NULL || t == NULL) goto err;
-
- if (in_mont != NULL)
- mont=in_mont;
- else
- {
- if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
- if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
- }
-
- r_is_one = 1; /* except for Montgomery factor */
-
- /* bits-1 >= 0 */
-
- /* The result is accumulated in the product r*w. */
- w = a; /* bit 'bits-1' of 'p' is always set */
- for (b = bits-2; b >= 0; b--)
- {
- /* First, square r*w. */
- next_w = w*w;
- if ((next_w/w) != w) /* overflow */
- {
- if (r_is_one)
- {
- if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
- r_is_one = 0;
- }
- else
- {
- if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
- }
- next_w = 1;
- }
- w = next_w;
- if (!r_is_one)
- {
- if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
- }
-
- /* Second, multiply r*w by 'a' if exponent bit is set. */
- if (BN_is_bit_set(p, b))
- {
- next_w = w*a;
- if ((next_w/a) != w) /* overflow */
- {
- if (r_is_one)
- {
- if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
- r_is_one = 0;
- }
- else
- {
- if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
- }
- next_w = a;
- }
- w = next_w;
- }
- }
-
- /* Finally, set r:=r*w. */
- if (w != 1)
- {
- if (r_is_one)
- {
- if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
- r_is_one = 0;
- }
- else
- {
- if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
- }
- }
-
- if (r_is_one) /* can happen only if a == 1*/
- {
- if (!BN_one(rr)) goto err;
- }
- else
- {
- if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
- }
- ret = 1;
-err:
- if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
- BN_CTX_end(ctx);
- bn_check_top(rr);
- return(ret);
- }
-
+ (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
+
+ if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
+ /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
+ BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return -1;
+ }
+
+ bn_check_top(p);
+ bn_check_top(m);
+
+ if (!BN_is_odd(m)) {
+ BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
+ return (0);
+ }
+ if (m->top == 1)
+ a %= m->d[0]; /* make sure that 'a' is reduced */
+
+ bits = BN_num_bits(p);
+ if (bits == 0) {
+ /* x**0 mod 1 is still zero. */
+ if (BN_is_one(m)) {
+ ret = 1;
+ BN_zero(rr);
+ } else
+ ret = BN_one(rr);
+ return ret;
+ }
+ if (a == 0) {
+ BN_zero(rr);
+ ret = 1;
+ return ret;
+ }
+
+ BN_CTX_start(ctx);
+ d = BN_CTX_get(ctx);
+ r = BN_CTX_get(ctx);
+ t = BN_CTX_get(ctx);
+ if (d == NULL || r == NULL || t == NULL)
+ goto err;
+
+ if (in_mont != NULL)
+ mont = in_mont;
+ else {
+ if ((mont = BN_MONT_CTX_new()) == NULL)
+ goto err;
+ if (!BN_MONT_CTX_set(mont, m, ctx))
+ goto err;
+ }
+
+ r_is_one = 1; /* except for Montgomery factor */
+
+ /* bits-1 >= 0 */
+
+ /* The result is accumulated in the product r*w. */
+ w = a; /* bit 'bits-1' of 'p' is always set */
+ for (b = bits - 2; b >= 0; b--) {
+ /* First, square r*w. */
+ next_w = w * w;
+ if ((next_w / w) != w) { /* overflow */
+ if (r_is_one) {
+ if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
+ goto err;
+ r_is_one = 0;
+ } else {
+ if (!BN_MOD_MUL_WORD(r, w, m))
+ goto err;
+ }
+ next_w = 1;
+ }
+ w = next_w;
+ if (!r_is_one) {
+ if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
+ goto err;
+ }
+
+ /* Second, multiply r*w by 'a' if exponent bit is set. */
+ if (BN_is_bit_set(p, b)) {
+ next_w = w * a;
+ if ((next_w / a) != w) { /* overflow */
+ if (r_is_one) {
+ if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
+ goto err;
+ r_is_one = 0;
+ } else {
+ if (!BN_MOD_MUL_WORD(r, w, m))
+ goto err;
+ }
+ next_w = a;
+ }
+ w = next_w;
+ }
+ }
+
+ /* Finally, set r:=r*w. */
+ if (w != 1) {
+ if (r_is_one) {
+ if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
+ goto err;
+ r_is_one = 0;
+ } else {
+ if (!BN_MOD_MUL_WORD(r, w, m))
+ goto err;
+ }
+ }
+
+ if (r_is_one) { /* can happen only if a == 1 */
+ if (!BN_one(rr))
+ goto err;
+ } else {
+ if (!BN_from_montgomery(rr, r, mont, ctx))
+ goto err;
+ }
+ ret = 1;
+ err:
+ if ((in_mont == NULL) && (mont != NULL))
+ BN_MONT_CTX_free(mont);
+ BN_CTX_end(ctx);
+ bn_check_top(rr);
+ return (ret);
+}
/* The old fallback, simple version :-) */
int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
- const BIGNUM *m, BN_CTX *ctx)
- {
- int i,j,bits,ret=0,wstart,wend,window,wvalue;
- int start=1;
- BIGNUM *d;
- /* Table of variables obtained from 'ctx' */
- BIGNUM *val[TABLE_SIZE];
-
- if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
- {
- /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
- BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
- return -1;
- }
-
- bits=BN_num_bits(p);
-
- if (bits == 0)
- {
- ret = BN_one(r);
- return ret;
- }
-
- BN_CTX_start(ctx);
- d = BN_CTX_get(ctx);
- val[0] = BN_CTX_get(ctx);
- if(!d || !val[0]) goto err;
-
- if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
- if (BN_is_zero(val[0]))
- {
- BN_zero(r);
- ret = 1;
- goto err;
- }
-
- window = BN_window_bits_for_exponent_size(bits);
- if (window > 1)
- {
- if (!BN_mod_mul(d,val[0],val[0],m,ctx))
- goto err; /* 2 */
- j=1<<(window-1);
- for (i=1; i<j; i++)
- {
- if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
- !BN_mod_mul(val[i],val[i-1],d,m,ctx))
- goto err;
- }
- }
-
- start=1; /* This is used to avoid multiplication etc
- * when there is only the value '1' in the
- * buffer. */
- wvalue=0; /* The 'value' of the window */
- wstart=bits-1; /* The top bit of the window */
- wend=0; /* The bottom bit of the window */
-
- if (!BN_one(r)) goto err;
-
- for (;;)
- {
- if (BN_is_bit_set(p,wstart) == 0)
- {
- if (!start)
- if (!BN_mod_mul(r,r,r,m,ctx))
- goto err;
- if (wstart == 0) break;
- wstart--;
- 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;
- wvalue=1;
- wend=0;
- for (i=1; i<window; i++)
- {
- if (wstart-i < 0) break;
- if (BN_is_bit_set(p,wstart-i))
- {
- wvalue<<=(i-wend);
- wvalue|=1;
- wend=i;
- }
- }
-
- /* wend is the size of the current window */
- j=wend+1;
- /* add the 'bytes above' */
- if (!start)
- for (i=0; i<j; i++)
- {
- if (!BN_mod_mul(r,r,r,m,ctx))
- goto err;
- }
-
- /* wvalue will be an odd number < 2^window */
- if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
- goto err;
-
- /* move the 'window' down further */
- wstart-=wend+1;
- wvalue=0;
- start=0;
- if (wstart < 0) break;
- }
- ret=1;
-err:
- BN_CTX_end(ctx);
- bn_check_top(r);
- return(ret);
- }
+ const BIGNUM *m, BN_CTX *ctx)
+{
+ int i, j, bits, ret = 0, wstart, wend, window, wvalue;
+ int start = 1;
+ BIGNUM *d;
+ /* Table of variables obtained from 'ctx' */
+ BIGNUM *val[TABLE_SIZE];
+
+ if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
+ /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
+ BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
+ return -1;
+ }
+
+ bits = BN_num_bits(p);
+
+ if (bits == 0) {
+ ret = BN_one(r);
+ return ret;
+ }
+
+ BN_CTX_start(ctx);
+ d = BN_CTX_get(ctx);
+ val[0] = BN_CTX_get(ctx);
+ if (!d || !val[0])
+ goto err;
+
+ if (!BN_nnmod(val[0], a, m, ctx))
+ goto err; /* 1 */
+ if (BN_is_zero(val[0])) {
+ BN_zero(r);
+ ret = 1;
+ goto err;
+ }
+
+ window = BN_window_bits_for_exponent_size(bits);
+ if (window > 1) {
+ if (!BN_mod_mul(d, val[0], val[0], m, ctx))
+ goto err; /* 2 */
+ j = 1 << (window - 1);
+ for (i = 1; i < j; i++) {
+ if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
+ !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
+ goto err;
+ }
+ }
+
+ start = 1; /* This is used to avoid multiplication etc
+ * when there is only the value '1' in the
+ * buffer. */
+ wvalue = 0; /* The 'value' of the window */
+ wstart = bits - 1; /* The top bit of the window */
+ wend = 0; /* The bottom bit of the window */
+
+ if (!BN_one(r))
+ goto err;
+
+ for (;;) {
+ if (BN_is_bit_set(p, wstart) == 0) {
+ if (!start)
+ if (!BN_mod_mul(r, r, r, m, ctx))
+ goto err;
+ if (wstart == 0)
+ break;
+ wstart--;
+ 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;
+ wvalue = 1;
+ wend = 0;
+ for (i = 1; i < window; i++) {
+ if (wstart - i < 0)
+ break;
+ if (BN_is_bit_set(p, wstart - i)) {
+ wvalue <<= (i - wend);
+ wvalue |= 1;
+ wend = i;
+ }
+ }
+
+ /* wend is the size of the current window */
+ j = wend + 1;
+ /* add the 'bytes above' */
+ if (!start)
+ for (i = 0; i < j; i++) {
+ if (!BN_mod_mul(r, r, r, m, ctx))
+ goto err;
+ }
+
+ /* wvalue will be an odd number < 2^window */
+ if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
+ goto err;
+
+ /* move the 'window' down further */
+ wstart -= wend + 1;
+ wvalue = 0;
+ start = 0;
+ if (wstart < 0)
+ break;
+ }
+ ret = 1;
+ err:
+ BN_CTX_end(ctx);
+ bn_check_top(r);
+ return (ret);
+}