* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
+/* ====================================================================
+ * Copyright (c) 1998-2006 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).
+ *
+ */
+
+/*
+ * Details about Montgomery multiplication algorithms can be found at
+ * http://security.ece.orst.edu/publications.html, e.g.
+ * http://security.ece.orst.edu/koc/papers/j37acmon.pdf and
+ * sections 3.8 and 4.2 in http://security.ece.orst.edu/koc/papers/r01rsasw.pdf
+ */
+
+#define OPENSSL_FIPSAPI
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
-int BN_mod_mul_montgomery(r,a,b,mont,ctx)
-BIGNUM *r,*a,*b;
-BN_MONT_CTX *mont;
-BN_CTX *ctx;
+#define MONT_WORD /* use the faster word-based algorithm */
+
+#ifdef MONT_WORD
+static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont);
+#endif
+
+int BN_mod_mul_montgomery(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
+ BN_MONT_CTX *mont, BN_CTX *ctx)
{
BIGNUM *tmp;
+ int ret=0;
+#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
+ int num = mont->N.top;
- tmp=ctx->bn[ctx->tos++];
+ if (num>1 && a->top==num && b->top==num)
+ {
+ if (bn_wexpand(r,num) == NULL) return(0);
+ if (bn_mul_mont(r->d,a->d,b->d,mont->N.d,mont->n0,num))
+ {
+ r->neg = a->neg^b->neg;
+ r->top = num;
+ bn_correct_top(r);
+ return(1);
+ }
+ }
+#endif
+
+ BN_CTX_start(ctx);
+ tmp = BN_CTX_get(ctx);
+ if (tmp == NULL) goto err;
+ bn_check_top(tmp);
if (a == b)
{
if (!BN_sqr(tmp,a,ctx)) goto err;
}
else
{
- if (!BN_mul(tmp,a,b)) goto err;
+ if (!BN_mul(tmp,a,b,ctx)) goto err;
}
/* reduce from aRR to aR */
+#ifdef MONT_WORD
+ if (!BN_from_montgomery_word(r,tmp,mont)) goto err;
+#else
if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
- ctx->tos--;
- return(1);
+#endif
+ bn_check_top(r);
+ ret=1;
err:
- return(0);
+ BN_CTX_end(ctx);
+ return(ret);
}
-#define MONT_WORD
-
#ifdef MONT_WORD
-int BN_from_montgomery(ret,a,mont,ctx)
-BIGNUM *ret;
-BIGNUM *a;
-BN_MONT_CTX *mont;
-BN_CTX *ctx;
+static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
{
- BIGNUM *n,*t1,*r;
- BN_ULONG *ap,*np,*rp,n0,v;
- int al,nl,max,i,x,ri;
- int retn=0;
-
- t1=ctx->bn[ctx->tos];
- r=ctx->bn[ctx->tos+1];
-
- if (!BN_copy(r,a)) goto err;
- n=mont->N;
-
- ap=a->d;
- /* mont->ri is the size of mont->N in bits/words */
- al=ri=mont->ri/BN_BITS2;
+ BIGNUM *n;
+ BN_ULONG *ap,*np,*rp,n0,v,carry;
+ int nl,max,i;
+ n= &(mont->N);
nl=n->top;
- if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
+ if (nl == 0) { ret->top=0; return(1); }
- max=(nl+al+1); /* allow for overflow (no?) XXX */
- if (bn_wexpand(r,max) == NULL) goto err;
- if (bn_wexpand(ret,max) == NULL) goto err;
+ max=(2*nl); /* carry is stored separately */
+ if (bn_wexpand(r,max) == NULL) return(0);
- r->neg=a->neg^n->neg;
+ r->neg^=n->neg;
np=n->d;
rp=r->d;
/* clear the top words of T */
#if 1
for (i=r->top; i<max; i++) /* memset? XXX */
- r->d[i]=0;
+ rp[i]=0;
#else
- memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
+ memset(&(rp[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
#endif
r->top=max;
- n0=mont->n0;
+ n0=mont->n0[0];
- for (i=0; i<nl; i++)
+#ifdef BN_COUNT
+ fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl);
+#endif
+ for (carry=0, i=0; i<nl; i++, rp++)
{
-#if 0
- int x1,x2;
-
- if (i+4 > nl)
- {
- x2=nl;
- x1=0;
- }
- else
- {
- x2=i+4;
- x1=nl-x2;
- }
- v=bn_mul_add_words(&(rp[x1]),&(np[x1]),x2,(rp[x1]*n0)&BN_MASK2);
+#ifdef __TANDEM
+ {
+ long long t1;
+ long long t2;
+ long long t3;
+ t1 = rp[0] * (n0 & 0177777);
+ t2 = 037777600000l;
+ t2 = n0 & t2;
+ t3 = rp[0] & 0177777;
+ t2 = (t3 * t2) & BN_MASK2;
+ t1 = t1 + t2;
+ v=bn_mul_add_words(rp,np,nl,(BN_ULONG) t1);
+ }
#else
v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
#endif
-
- if (((rp[nl]+=v)&BN_MASK2) < v)
- {
- for (x=(nl+1); (((++rp[x])&BN_MASK2) == 0); x++)
- ;
- }
- rp++;
+ v = (v+carry+rp[nl])&BN_MASK2;
+ carry |= (v != rp[nl]);
+ carry &= (v <= rp[nl]);
+ rp[nl]=v;
}
- while (r->d[r->top-1] == 0)
- r->top--;
- /* mont->ri will be a multiple of the word size */
-#if 0
- BN_rshift(ret,r,mont->ri);
-#else
- ap=r->d;
+ if (bn_wexpand(ret,nl) == NULL) return(0);
+ ret->top=nl;
+ ret->neg=r->neg;
+
rp=ret->d;
- x=ri;
- al=r->top-x;
- for (i=0; i<al; i++)
- {
- rp[i]=ap[i+x];
- }
- ret->top=al;
-#endif
+ ap=&(r->d[nl]);
+
+#define BRANCH_FREE 1
+#if BRANCH_FREE
+ {
+ BN_ULONG *nrp;
+ size_t m;
+
+ v=bn_sub_words(rp,ap,np,nl)-carry;
+ /* if subtraction result is real, then
+ * trick unconditional memcpy below to perform in-place
+ * "refresh" instead of actual copy. */
+ m=(0-(size_t)v);
+ nrp=(BN_ULONG *)(((PTR_SIZE_INT)rp&~m)|((PTR_SIZE_INT)ap&m));
- if (BN_ucmp(ret,mont->N) >= 0)
+ for (i=0,nl-=4; i<nl; i+=4)
{
- bn_qsub(ret,ret,mont->N); /* XXX */
+ BN_ULONG t1,t2,t3,t4;
+
+ t1=nrp[i+0];
+ t2=nrp[i+1];
+ t3=nrp[i+2]; ap[i+0]=0;
+ t4=nrp[i+3]; ap[i+1]=0;
+ rp[i+0]=t1; ap[i+2]=0;
+ rp[i+1]=t2; ap[i+3]=0;
+ rp[i+2]=t3;
+ rp[i+3]=t4;
}
- retn=1;
-err:
- return(retn);
+ for (nl+=4; i<nl; i++)
+ rp[i]=nrp[i], ap[i]=0;
}
#else
-int BN_from_montgomery(r,a,mont,ctx)
-BIGNUM *r;
-BIGNUM *a;
-BN_MONT_CTX *mont;
-BN_CTX *ctx;
+ if (bn_sub_words (rp,ap,np,nl)-carry)
+ memcpy(rp,ap,nl*sizeof(BN_ULONG));
+#endif
+ bn_correct_top(r);
+ bn_correct_top(ret);
+ bn_check_top(ret);
+
+ return(1);
+ }
+#endif /* MONT_WORD */
+
+int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
+ BN_CTX *ctx)
{
- BIGNUM *t1,*t2;
+ int retn=0;
+#ifdef MONT_WORD
+ BIGNUM *t;
- t1=ctx->bn[ctx->tos];
- t2=ctx->bn[ctx->tos+1];
+ BN_CTX_start(ctx);
+ if ((t = BN_CTX_get(ctx)) && BN_copy(t,a))
+ retn = BN_from_montgomery_word(ret,t,mont);
+ BN_CTX_end(ctx);
+#else /* !MONT_WORD */
+ BIGNUM *t1,*t2;
+ BN_CTX_start(ctx);
+ t1 = BN_CTX_get(ctx);
+ t2 = BN_CTX_get(ctx);
+ if (t1 == NULL || t2 == NULL) goto err;
+
if (!BN_copy(t1,a)) goto err;
- /* can cheat */
BN_mask_bits(t1,mont->ri);
- if (!BN_mul(t2,t1,mont->Ni)) goto err;
+ if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
BN_mask_bits(t2,mont->ri);
- if (!BN_mul(t1,t2,mont->N)) goto err;
+ if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
if (!BN_add(t2,a,t1)) goto err;
- BN_rshift(r,t2,mont->ri);
-
- if (BN_ucmp(r,mont->N) >= 0)
- bn_qsub(r,r,mont->N);
+ if (!BN_rshift(ret,t2,mont->ri)) goto err;
- return(1);
-err:
- return(0);
+ if (BN_ucmp(ret, &(mont->N)) >= 0)
+ {
+ if (!BN_usub(ret,ret,&(mont->N))) goto err;
+ }
+ retn=1;
+ bn_check_top(ret);
+ err:
+ BN_CTX_end(ctx);
+#endif /* MONT_WORD */
+ return(retn);
}
-#endif
-BN_MONT_CTX *BN_MONT_CTX_new()
+BN_MONT_CTX *BN_MONT_CTX_new(void)
{
BN_MONT_CTX *ret;
- if ((ret=(BN_MONT_CTX *)Malloc(sizeof(BN_MONT_CTX))) == NULL)
+ if ((ret=(BN_MONT_CTX *)OPENSSL_malloc(sizeof(BN_MONT_CTX))) == NULL)
return(NULL);
- ret->ri=0;
- ret->RR=BN_new();
- ret->N=BN_new();
- ret->Ni=NULL;
- if ((ret->RR == NULL) || (ret->N == NULL))
- {
- BN_MONT_CTX_free(ret);
- return(NULL);
- }
+
+ BN_MONT_CTX_init(ret);
+ ret->flags=BN_FLG_MALLOCED;
return(ret);
}
-void BN_MONT_CTX_free(mont)
-BN_MONT_CTX *mont;
+void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
{
- if (mont->RR != NULL) BN_free(mont->RR);
- if (mont->N != NULL) BN_free(mont->N);
- if (mont->Ni != NULL) BN_free(mont->Ni);
- Free(mont);
+ ctx->ri=0;
+ BN_init(&(ctx->RR));
+ BN_init(&(ctx->N));
+ BN_init(&(ctx->Ni));
+ ctx->n0[0] = ctx->n0[1] = 0;
+ ctx->flags=0;
}
-int BN_MONT_CTX_set(mont,mod,ctx)
-BN_MONT_CTX *mont;
-BIGNUM *mod;
-BN_CTX *ctx;
+void BN_MONT_CTX_free(BN_MONT_CTX *mont)
{
- BIGNUM *Ri=NULL,*R=NULL;
+ if(mont == NULL)
+ return;
+
+ BN_free(&(mont->RR));
+ BN_free(&(mont->N));
+ BN_free(&(mont->Ni));
+ if (mont->flags & BN_FLG_MALLOCED)
+ OPENSSL_free(mont);
+ }
- if (mont->RR == NULL) mont->RR=BN_new();
- if (mont->N == NULL) mont->N=BN_new();
+int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
+ {
+ int ret = 0;
+ BIGNUM *Ri,*R;
- R=mont->RR; /* grab RR as a temp */
- BN_copy(mont->N,mod); /* Set N */
+ BN_CTX_start(ctx);
+ if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
+ R= &(mont->RR); /* grab RR as a temp */
+ if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
+ mont->N.neg = 0;
#ifdef MONT_WORD
-{
- BIGNUM tmod;
- BN_ULONG buf[2];
- /* int z; */
-
- mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
- BN_lshift(R,BN_value_one(),BN_BITS2); /* R */
- /* I was bad, this modification of a passed variable was
- * breaking the multithreaded stuff :-(
- * z=mod->top;
- * mod->top=1; */
-
- buf[0]=mod->d[0];
- buf[1]=0;
- tmod.d=buf;
- tmod.top=1;
- tmod.max=mod->max;
- tmod.neg=mod->neg;
-
- if ((Ri=BN_mod_inverse(R,&tmod,ctx)) == NULL) goto err; /* Ri */
- BN_lshift(Ri,Ri,BN_BITS2); /* R*Ri */
- bn_qsub(Ri,Ri,BN_value_one()); /* R*Ri - 1 */
- BN_div(Ri,NULL,Ri,&tmod,ctx);
- mont->n0=Ri->d[0];
- BN_free(Ri);
- /* mod->top=z; */
-}
+ {
+ BIGNUM tmod;
+ BN_ULONG buf[2];
+
+ BN_init(&tmod);
+ tmod.d=buf;
+ tmod.dmax=2;
+ tmod.neg=0;
+
+ mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
+
+#if defined(OPENSSL_BN_ASM_MONT) && (BN_BITS2<=32)
+ /* Only certain BN_BITS2<=32 platforms actually make use of
+ * n0[1], and we could use the #else case (with a shorter R
+ * value) for the others. However, currently only the assembler
+ * files do know which is which. */
+
+ BN_zero(R);
+ if (!(BN_set_bit(R,2*BN_BITS2))) goto err;
+
+ tmod.top=0;
+ if ((buf[0] = mod->d[0])) tmod.top=1;
+ if ((buf[1] = mod->top>1 ? mod->d[1] : 0)) tmod.top=2;
+
+ if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
+ goto err;
+ if (!BN_lshift(Ri,Ri,2*BN_BITS2)) goto err; /* R*Ri */
+ if (!BN_is_zero(Ri))
+ {
+ if (!BN_sub_word(Ri,1)) goto err;
+ }
+ else /* if N mod word size == 1 */
+ {
+ if (bn_expand(Ri,(int)sizeof(BN_ULONG)*2) == NULL)
+ goto err;
+ /* Ri-- (mod double word size) */
+ Ri->neg=0;
+ Ri->d[0]=BN_MASK2;
+ Ri->d[1]=BN_MASK2;
+ Ri->top=2;
+ }
+ if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
+ /* Ni = (R*Ri-1)/N,
+ * keep only couple of least significant words: */
+ mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
+ mont->n0[1] = (Ri->top > 1) ? Ri->d[1] : 0;
#else
- mont->ri=BN_num_bits(mod);
- BN_lshift(R,BN_value_one(),mont->ri); /* R */
- if ((Ri=BN_mod_inverse(R,mod,ctx)) == NULL) goto err; /* Ri */
- BN_lshift(Ri,Ri,mont->ri); /* R*Ri */
- bn_qsub(Ri,Ri,BN_value_one()); /* R*Ri - 1 */
- BN_div(Ri,NULL,Ri,mod,ctx);
- if (mont->Ni != NULL) BN_free(mont->Ni);
- mont->Ni=Ri; /* Ni=(R*Ri-1)/N */
+ BN_zero(R);
+ if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
+
+ buf[0]=mod->d[0]; /* tmod = N mod word size */
+ buf[1]=0;
+ tmod.top = buf[0] != 0 ? 1 : 0;
+ /* Ri = R^-1 mod N*/
+ if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
+ goto err;
+ if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
+ if (!BN_is_zero(Ri))
+ {
+ if (!BN_sub_word(Ri,1)) goto err;
+ }
+ else /* if N mod word size == 1 */
+ {
+ if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
+ }
+ if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
+ /* Ni = (R*Ri-1)/N,
+ * keep only least significant word: */
+ mont->n0[0] = (Ri->top > 0) ? Ri->d[0] : 0;
+ mont->n0[1] = 0;
+#endif
+ }
+#else /* !MONT_WORD */
+ { /* bignum version */
+ mont->ri=BN_num_bits(&mont->N);
+ BN_zero(R);
+ if (!BN_set_bit(R,mont->ri)) goto err; /* R = 2^ri */
+ /* Ri = R^-1 mod N*/
+ if ((BN_mod_inverse(Ri,R,&mont->N,ctx)) == NULL)
+ goto err;
+ if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
+ if (!BN_sub_word(Ri,1)) goto err;
+ /* Ni = (R*Ri-1) / N */
+ if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
+ }
#endif
/* setup RR for conversions */
- BN_lshift(mont->RR,BN_value_one(),mont->ri*2);
- BN_mod(mont->RR,mont->RR,mont->N,ctx);
+ BN_zero(&(mont->RR));
+ if (!BN_set_bit(&(mont->RR),mont->ri*2)) goto err;
+ if (!BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx)) goto err;
- return(1);
+ ret = 1;
err:
- return(0);
+ BN_CTX_end(ctx);
+ return ret;
}
+BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from)
+ {
+ if (to == from) return(to);
+
+ if (!BN_copy(&(to->RR),&(from->RR))) return NULL;
+ if (!BN_copy(&(to->N),&(from->N))) return NULL;
+ if (!BN_copy(&(to->Ni),&(from->Ni))) return NULL;
+ to->ri=from->ri;
+ to->n0[0]=from->n0[0];
+ to->n0[1]=from->n0[1];
+ return(to);
+ }
+
+BN_MONT_CTX *BN_MONT_CTX_set_locked(BN_MONT_CTX **pmont, int lock,
+ const BIGNUM *mod, BN_CTX *ctx)
+ {
+ BN_MONT_CTX *ret;
+
+ CRYPTO_r_lock(lock);
+ ret = *pmont;
+ CRYPTO_r_unlock(lock);
+ if (ret)
+ return ret;
+
+ /* We don't want to serialise globally while doing our lazy-init math in
+ * BN_MONT_CTX_set. That punishes threads that are doing independent
+ * things. Instead, punish the case where more than one thread tries to
+ * lazy-init the same 'pmont', by having each do the lazy-init math work
+ * independently and only use the one from the thread that wins the race
+ * (the losers throw away the work they've done). */
+ ret = BN_MONT_CTX_new();
+ if (!ret)
+ return NULL;
+ if (!BN_MONT_CTX_set(ret, mod, ctx))
+ {
+ BN_MONT_CTX_free(ret);
+ return NULL;
+ }
+
+ /* The locked compare-and-set, after the local work is done. */
+ CRYPTO_w_lock(lock);
+ if (*pmont)
+ {
+ BN_MONT_CTX_free(ret);
+ ret = *pmont;
+ }
+ else
+ *pmont = ret;
+ CRYPTO_w_unlock(lock);
+ return ret;
+ }
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