* 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
* 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(BIGNUM *r, BIGNUM *a, BIGNUM *b,
+#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,*tmp2;
+ BIGNUM *tmp;
+ int ret=0;
+#if defined(OPENSSL_BN_ASM_MONT) && defined(MONT_WORD)
+ int num = mont->N.top;
+
+ 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
- tmp= &(ctx->bn[ctx->tos]);
- tmp2= &(ctx->bn[ctx->tos]);
- ctx->tos+=2;
+ BN_CTX_start(ctx);
+ tmp = BN_CTX_get(ctx);
+ if (tmp == NULL) goto err;
bn_check_top(tmp);
- bn_check_top(tmp2);
-
if (a == b)
{
-#if 0
- bn_wexpand(tmp,a->top*2);
- bn_wexpand(tmp2,a->top*4);
- bn_sqr_recursive(tmp->d,a->d,a->top,tmp2->d);
- tmp->top=a->top*2;
- if (tmp->d[tmp->top-1] == 0)
- tmp->top--;
-#else
if (!BN_sqr(tmp,a,ctx)) goto err;
-#endif
}
else
{
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-=2;
- return(1);
+#endif
+ bn_check_top(r);
+ ret=1;
err:
- return(0);
+ BN_CTX_end(ctx);
+ return(ret);
}
-int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
- BN_CTX *ctx)
+#ifdef MONT_WORD
+static int BN_from_montgomery_word(BIGNUM *ret, BIGNUM *r, BN_MONT_CTX *mont)
{
- int retn=0;
-#ifdef BN_RECURSION_MONT
- if (mont->use_word)
-#endif
- {
- BIGNUM *n,*r;
- BN_ULONG *ap,*np,*rp,n0,v,*nrp;
- int al,nl,max,i,x,ri;
+ BIGNUM *n;
+ BN_ULONG *ap,*np,*rp,n0,v,carry;
+ int nl,max,i;
- r= &(ctx->bn[ctx->tos]);
+ n= &(mont->N);
+ nl=n->top;
+ if (nl == 0) { ret->top=0; return(1); }
- if (!BN_copy(r,a)) goto err;
- n= &(mont->N);
+ max=(2*nl); /* carry is stored separately */
+ if (bn_wexpand(r,max) == NULL) return(0);
- ap=a->d;
- /* mont->ri is the size of mont->N in bits (rounded up
- to the word size) */
- al=ri=mont->ri/BN_BITS2;
+ r->neg^=n->neg;
+ np=n->d;
+ rp=r->d;
- nl=n->top;
- if ((al == 0) || (nl == 0)) { r->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;
-
- r->neg=a->neg^n->neg;
- np=n->d;
- rp=r->d;
- nrp= &(r->d[nl]);
-
- /* clear the top words of T */
+ /* clear the top words of T */
#if 1
- for (i=r->top; i<max; i++) /* memset? XXX */
- r->d[i]=0;
+ for (i=r->top; i<max; i++) /* memset? XXX */
+ 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;
+ r->top=max;
+ n0=mont->n0[0];
#ifdef BN_COUNT
-printf("word BN_from_montgomery %d * %d\n",nl,nl);
+ fprintf(stderr,"word BN_from_montgomery_word %d * %d\n",nl,nl);
#endif
- for (i=0; i<nl; i++)
- {
- v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
- nrp++;
- rp++;
- if (((nrp[-1]+=v)&BN_MASK2) >= v)
- continue;
- else
- {
- if (((++nrp[0])&BN_MASK2) != 0) continue;
- if (((++nrp[1])&BN_MASK2) != 0) continue;
- for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
- }
- }
- bn_fix_top(r);
-
- /* mont->ri will be a multiple of the word size */
-#if 0
- BN_rshift(ret,r,mont->ri);
+ for (carry=0, i=0; i<nl; i++, rp++)
+ {
+#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
- x=ri;
- rp=ret->d;
- ap= &(r->d[x]);
- if (r->top < x)
- al=0;
- else
- al=r->top-x;
- ret->top=al;
- al-=4;
- for (i=0; i<al; i+=4)
- {
- BN_ULONG t1,t2,t3,t4;
-
- t1=ap[i+0];
- t2=ap[i+1];
- t3=ap[i+2];
- t4=ap[i+3];
- rp[i+0]=t1;
- rp[i+1]=t2;
- rp[i+2]=t3;
- rp[i+3]=t4;
- }
- al+=4;
- for (; i<al; i++)
- rp[i]=ap[i];
+ v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
#endif
-
- if (BN_ucmp(ret, &(mont->N)) >= 0)
- {
- BN_usub(ret,ret,&(mont->N)); /* XXX */
- }
- retn=1;
+ v = (v+carry+rp[nl])&BN_MASK2;
+ carry |= (v != rp[nl]);
+ carry &= (v <= rp[nl]);
+ rp[nl]=v;
}
-#ifdef BN_RECURSION_MONT
- else /* bignum version */
- {
- BIGNUM *t1,*t2;
- t1=&(ctx->bn[ctx->tos]);
- t2=&(ctx->bn[ctx->tos+1]);
- ctx->tos+=2;
+ if (bn_wexpand(ret,nl) == NULL) return(0);
+ ret->top=nl;
+ ret->neg=r->neg;
- if (!BN_copy(t1,a)) goto err;
- BN_mask_bits(t1,mont->ri);
+ rp=ret->d;
+ ap=&(r->d[nl]);
- if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
- BN_mask_bits(t2,mont->ri);
+#define BRANCH_FREE 1
+#if BRANCH_FREE
+ {
+ BN_ULONG *nrp;
+ size_t m;
- if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
- if (!BN_add(t2,a,t1)) goto err;
- BN_rshift(ret,t2,mont->ri);
+ 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)
- BN_usub(ret,ret,&mont->N);
- ctx->tos-=2;
- retn=1;
+ for (i=0,nl-=4; i<nl; i+=4)
+ {
+ 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;
}
+ for (nl+=4; i<nl; i++)
+ rp[i]=nrp[i], ap[i]=0;
+ }
+#else
+ 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)
+ {
+ int retn=0;
+#ifdef MONT_WORD
+ BIGNUM *t;
+
+ 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;
+ BN_mask_bits(t1,mont->ri);
+
+ if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
+ BN_mask_bits(t2,mont->ri);
+
+ if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
+ if (!BN_add(t2,a,t1)) goto err;
+ if (!BN_rshift(ret,t2,mont->ri)) goto err;
+
+ 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);
}
{
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);
BN_MONT_CTX_init(ret);
void BN_MONT_CTX_init(BN_MONT_CTX *ctx)
{
- ctx->use_word=0;
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;
}
BN_free(&(mont->N));
BN_free(&(mont->Ni));
if (mont->flags & BN_FLG_MALLOCED)
- Free(mont);
+ OPENSSL_free(mont);
}
int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
{
- BIGNUM Ri,*R;
+ int ret = 0;
+ BIGNUM *Ri,*R;
- BN_init(&Ri);
+ BN_CTX_start(ctx);
+ if((Ri = BN_CTX_get(ctx)) == NULL) goto err;
R= &(mont->RR); /* grab RR as a temp */
- BN_copy(&(mont->N),mod); /* Set N */
+ if (!BN_copy(&(mont->N),mod)) goto err; /* Set N */
+ mont->N.neg = 0;
-#ifdef BN_RECURSION_MONT
- /* the word-based algorithm is faster */
- if (mont->N.top > BN_MONT_CTX_SET_SIZE_WORD)
-#endif
+#ifdef MONT_WORD
{
BIGNUM tmod;
BN_ULONG buf[2];
- mont->use_word=1;
+ 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);
- BN_set_bit(R,BN_BITS2); /* R = 2^ri */
+ 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
+ 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.d=buf;
- tmod.top=1;
- tmod.max=2;
- tmod.neg=mod->neg;
+ tmod.top = buf[0] != 0 ? 1 : 0;
/* Ri = R^-1 mod N*/
- if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
+ if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
goto err;
- BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */
- if (!BN_is_zero(&Ri))
- BN_sub_word(&Ri,1);
+ 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 */
- BN_set_word(&Ri,BN_MASK2); /* Ri-- (mod word size) */
- BN_div(&Ri,NULL,&Ri,&tmod,ctx); /* Ni = (R*Ri-1)/N,
- * keep only list significant word: */
- mont->n0=Ri.d[0];
- BN_free(&Ri);
+ {
+ 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
}
-#ifdef BN_RECURSION_MONT
- else
+#else /* !MONT_WORD */
{ /* bignum version */
- mont->use_word=0;
- mont->ri=BN_num_bits(mod);
+ mont->ri=BN_num_bits(&mont->N);
BN_zero(R);
- BN_set_bit(R,mont->ri); /* R = 2^ri */
- /* Ri = R^-1 mod N*/
- if ((BN_mod_inverse(&Ri,R,mod,ctx)) == NULL)
+ 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;
- BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */
- BN_sub_word(&Ri,1);
+ if (!BN_lshift(Ri,Ri,mont->ri)) goto err; /* R*Ri */
+ if (!BN_sub_word(Ri,1)) goto err;
/* Ni = (R*Ri-1) / N */
- BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
- BN_free(&Ri);
+ if (!BN_div(&(mont->Ni),NULL,Ri,&mont->N,ctx)) goto err;
}
#endif
/* setup RR for conversions */
BN_zero(&(mont->RR));
- BN_set_bit(&(mont->RR),mont->ri*2);
- BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
+ 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);
- BN_copy(&(to->RR),&(from->RR));
- BN_copy(&(to->N),&(from->N));
- BN_copy(&(to->Ni),&(from->Ni));
- to->use_word=from->use_word;
+ 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=from->n0;
+ 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;
+ }