*/
/*
- * Details about Montgomery multiplication algorithms can be found at:
- * http://www.ece.orst.edu/ISL/Publications.html
- * http://www.ece.orst.edu/ISL/Koc/papers/j37acmon.pdf
+ * 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
*/
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
-#define MONT_WORD
+#define MONT_WORD /* use the faster word-based algorithm */
-int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
+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;
- 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
{
}
/* reduce from aRR to aR */
if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
- ctx->tos-=2;
- return(1);
+ 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,
+int BN_from_montgomery(BIGNUM *ret, const BIGNUM *a, BN_MONT_CTX *mont,
BN_CTX *ctx)
{
-#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;
- int retn=0;
+ int retn=0;
- r= &(ctx->bn[ctx->tos]);
+#ifdef MONT_WORD
+ BIGNUM *n,*r;
+ BN_ULONG *ap,*np,*rp,n0,v,*nrp;
+ int al,nl,max,i,x,ri;
- if (!BN_copy(r,a)) goto err1;
- n= &(mont->N);
+ BN_CTX_start(ctx);
+ if ((r = BN_CTX_get(ctx)) == NULL) goto err;
- ap=a->d;
- /* mont->ri is the size of mont->N in bits/words */
- al=ri=mont->ri/BN_BITS2;
+ if (!BN_copy(r,a)) goto err;
+ n= &(mont->N);
- nl=n->top;
- if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
+ 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;
+
+ 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 err1;
- if (bn_wexpand(ret,max) == NULL) goto err1;
+ 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]);
+ 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 */
+ r->d[i]=0;
#else
- memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
+ memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG));
#endif
- r->top=max;
- n0=mont->n0;
+ r->top=max;
+ n0=mont->n0;
#ifdef BN_COUNT
-printf("word BN_from_montgomery %d * %d\n",nl,nl);
+ fprintf(stderr,"word BN_from_montgomery %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 (i=0; i<nl; i++)
+ {
+#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)
+ nrp++;
+ rp++;
+ if (((nrp[-1]+=v)&BN_MASK2) >= v)
+ continue;
+ else
{
- BN_usub(ret,ret,&(mont->N)); /* XXX */
+ if (((++nrp[0])&BN_MASK2) != 0) continue;
+ if (((++nrp[1])&BN_MASK2) != 0) continue;
+ for (x=2; (((++nrp[x])&BN_MASK2) == 0); x++) ;
}
- retn=1;
-err1:
- return(retn);
}
-#ifdef BN_RECURSION_MONT
- else /* bignum version */
+ bn_correct_top(r);
+
+ /* mont->ri will be a multiple of the word size */
+#if 0
+ BN_rshift(ret,r,mont->ri);
+#else
+ ret->neg = r->neg;
+ 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)
{
- BIGNUM *t1,*t2,*t3;
- int j,i;
-
-#ifdef BN_COUNT
-printf("number BN_from_montgomery\n");
-#endif
-
- t1= &(ctx->bn[ctx->tos]);
- t2= &(ctx->bn[ctx->tos+1]);
- t3= &(ctx->bn[ctx->tos+2]);
-
- i=mont->Ni.top;
- bn_wexpand(ret,i); /* perhaps only i*2 */
- bn_wexpand(t1,i*4); /* perhaps only i*2 */
- bn_wexpand(t2,i*2); /* perhaps only i */
-
- bn_mul_low_recursive(t2->d,a->d,mont->Ni.d,i,t1->d);
-
- BN_zero(t3);
- BN_set_bit(t3,mont->N.top*BN_BITS2);
- bn_sub_words(t3->d,t3->d,a->d,i);
- bn_mul_high(ret->d,t2->d,mont->N.d,t3->d,i,t1->d);
-
- /* hmm... if a is between i and 2*i, things are bad */
- if (a->top > i)
- {
- j=(int)(bn_add_words(ret->d,ret->d,&(a->d[i]),i));
- if (j) /* overflow */
- bn_sub_words(ret->d,ret->d,mont->N.d,i);
- }
- ret->top=i;
- bn_fix_top(ret);
- if (a->d[0])
- BN_add_word(ret,1); /* Always? */
- else /* Very very rare */
- {
- for (i=1; i<mont->N.top-1; i++)
- {
- if (a->d[i])
- {
- BN_add_word(ret,1); /* Always? */
- break;
- }
- }
- }
-
- if (BN_ucmp(ret,&(mont->N)) >= 0)
- BN_usub(ret,ret,&(mont->N));
-
- return(1);
+ 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];
#endif
+#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;
+#endif /* MONT_WORD */
+
+ 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);
+ return(retn);
}
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);
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_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 */
+ mont->N.neg = 0;
-#ifdef BN_RECURSION_MONT
- if (mont->N.top < BN_MONT_CTX_SET_SIZE_WORD)
-#endif
+#ifdef MONT_WORD
{
BIGNUM tmod;
BN_ULONG buf[2];
- mont->use_word=1;
-
mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
BN_zero(R);
- BN_set_bit(R,BN_BITS2);
- /* I was bad, this modification of a passed variable was
- * breaking the multithreaded stuff :-(
- * z=mod->top;
- * mod->top=1; */
+ if (!(BN_set_bit(R,BN_BITS2))) goto err; /* R */
- buf[0]=mod->d[0];
+ buf[0]=mod->d[0]; /* tmod = N mod word size */
buf[1]=0;
tmod.d=buf;
tmod.top=1;
- tmod.max=mod->max;
- tmod.neg=mod->neg;
-
- if ((BN_mod_inverse(&Ri,R,&tmod,ctx)) == NULL)
+ tmod.dmax=2;
+ tmod.neg=0;
+ /* Ri = R^-1 mod N*/
+ if ((BN_mod_inverse(Ri,R,&tmod,ctx)) == NULL)
goto err;
- BN_lshift(&Ri,&Ri,BN_BITS2); /* R*Ri */
- if (!BN_is_zero(&Ri))
+ if (!BN_lshift(Ri,Ri,BN_BITS2)) goto err; /* R*Ri */
+ if (!BN_is_zero(Ri))
{
-#if 1
- BN_sub_word(&Ri,1);
-#else
- BN_usub(&Ri,&Ri,BN_value_one()); /* R*Ri - 1 */
-#endif
+ if (!BN_sub_word(Ri,1)) goto err;
}
- else
+ else /* if N mod word size == 1 */
{
- /* This is not common..., 1 in BN_MASK2,
- * It happens when buf[0] was == 1. So for 8 bit,
- * this is 1/256, 16bit, 1 in 2^16 etc.
- */
- BN_set_word(&Ri,BN_MASK2);
+ if (!BN_set_word(Ri,BN_MASK2)) goto err; /* Ri-- (mod word size) */
}
- BN_div(&Ri,NULL,&Ri,&tmod,ctx);
- mont->n0=Ri.d[0];
- BN_free(&Ri);
- /* mod->top=z; */
+ if (!BN_div(Ri,NULL,Ri,&tmod,ctx)) goto err;
+ /* Ni = (R*Ri-1)/N,
+ * keep only least significant word: */
+ mont->n0 = (Ri->top > 0) ? Ri->d[0] : 0;
}
-#ifdef BN_RECURSION_MONT
- else
- {
- mont->use_word=0;
- mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2;
-#if 1
+#else /* !MONT_WORD */
+ { /* bignum version */
+ mont->ri=BN_num_bits(&mont->N);
BN_zero(R);
- BN_set_bit(R,mont->ri);
-#else
- BN_lshift(R,BN_value_one(),mont->ri); /* R */
-#endif
- 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 */
-#if 1
- BN_sub_word(&Ri,1);
-#else
- BN_usub(&Ri,&Ri,BN_value_one()); /* R*Ri - 1 */
-#endif
- BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
- BN_free(&Ri);
+ 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 */
-#if 1
BN_zero(&(mont->RR));
- BN_set_bit(&(mont->RR),mont->ri*2);
-#else
- BN_lshift(mont->RR,BN_value_one(),mont->ri*2);
-#endif
- 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;
return(to);
projects / openssl.git / blobdiff