/* crypto/bn/bn_mont.c */
-/* Copyright (C) 1995-1997 Eric Young (eay@cryptsoft.com)
+/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* [including the GNU Public Licence.]
*/
+/*
+ * 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"
-int BN_mod_mul_montgomery(r,a,b,mont,ctx)
-BIGNUM *r,*a,*b;
-BN_MONT_CTX *mont;
-BN_CTX *ctx;
+int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
+ BN_MONT_CTX *mont, BN_CTX *ctx)
{
- BIGNUM *tmp;
+ BIGNUM *tmp,*tmp2;
- tmp=ctx->bn[ctx->tos++];
+ tmp= &(ctx->bn[ctx->tos]);
+ tmp2= &(ctx->bn[ctx->tos]);
+ ctx->tos+=2;
+
+ 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)) goto err;
+ if (!BN_mul(tmp,a,b,ctx)) goto err;
}
/* reduce from aRR to aR */
if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err;
- ctx->tos--;
+ ctx->tos-=2;
return(1);
err:
return(0);
}
-#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;
+int BN_from_montgomery(BIGNUM *ret, BIGNUM *a, BN_MONT_CTX *mont,
+ BN_CTX *ctx)
{
- BIGNUM *n,*t1,*r;
- BN_ULONG *ap,*np,*rp,k,n0,v,v2;
- int al,nl,max,i,x;
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;
- t1=ctx->bn[ctx->tos];
- r=ctx->bn[ctx->tos+1];
-
- if (!BN_copy(r,a)) goto err;
- n=mont->N;
+ r= &(ctx->bn[ctx->tos]);
- if (!BN_copy(t1,a)) goto err;
- BN_mask_bits(t1,mont->ri);
+ if (!BN_copy(r,a)) goto err;
+ n= &(mont->N);
- a=t1;
+ 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;
- al=a->top;
- nl=n->top;
- if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
+ nl=n->top;
+ if ((al == 0) || (nl == 0)) { r->top=0; return(1); }
- max=(nl+al+1); /* allow for overflow (no?) XXX */
- if (bn_expand(r,(max)*BN_BITS2) == NULL) goto err;
+ 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;
- ap=a->d;
- np=n->d;
- rp=r->d;
+ r->neg=a->neg^n->neg;
+ np=n->d;
+ rp=r->d;
+ nrp= &(r->d[nl]);
- /* clear the top bytes of T */
- for (i=r->top; i<max; i++) /* memset? XXX */
- r->d[i]=0;
-/* memset(&(r->d[r->top]),0,(max-r->top)*sizeof(BN_ULONG)); */
+ /* clear the top words of T */
+#if 1
+ 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));
+#endif
- r->top=max;
- n0=mont->n0;
+ r->top=max;
+ n0=mont->n0;
- for (i=0; i<nl; i++)
- {
- /* This is were part words probably goes wrong */
- k=(rp[0]*n0)&BN_MASK2;
- v=bn_mul_add_word(rp,np,nl,k);
-
- for (x=nl; v; x++)
+#ifdef BN_COUNT
+printf("word BN_from_montgomery %d * %d\n",nl,nl);
+#endif
+ for (i=0; i<nl; i++)
{
- v2=rp[x];
- v2+=v;
- rp[x]=v2;
- v=((v2&BN_MASK2) < v)?1:0; /* ever true? XXX */
+ 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++) ;
+ }
}
- rp++;
- }
- while (r->d[r->top-1] == 0)
- r->top--;
+ bn_fix_top(r);
- BN_rshift(ret,r,mont->ri);
-
- if (BN_ucmp(ret,mont->N) >= 0)
- {
- bn_qsub(ret,ret,mont->N); /* XXX */
- }
- retn=1;
-err:
- return(retn);
- }
+ /* mont->ri will be a multiple of the word size */
+#if 0
+ BN_rshift(ret,r,mont->ri);
#else
-int BN_from_montgomery(r,a,mont,ctx)
-BIGNUM *r;
-BIGNUM *a;
-BN_MONT_CTX *mont;
-BN_CTX *ctx;
- {
- BIGNUM *t1,*t2;
+ 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];
+#endif
- t1=ctx->bn[ctx->tos];
- t2=ctx->bn[ctx->tos+1];
+ if (BN_ucmp(ret, &(mont->N)) >= 0)
+ {
+ BN_usub(ret,ret,&(mont->N)); /* XXX */
+ }
+ retn=1;
+ }
+#ifdef BN_RECURSION_MONT
+ else /* bignum version */
+ {
+ BIGNUM *t1,*t2;
- if (!BN_copy(t1,a)) goto err;
- /* can cheat */
- BN_mask_bits(t1,mont->ri);
+ t1=&(ctx->bn[ctx->tos]);
+ t2=&(ctx->bn[ctx->tos+1]);
+ ctx->tos+=2;
- if (!BN_mul(t2,t1,mont->Ni)) goto err;
- BN_mask_bits(t2,mont->ri);
+ if (!BN_copy(t1,a)) goto err;
+ BN_mask_bits(t1,mont->ri);
- if (!BN_mul(t1,t2,mont->N)) goto err;
- if (!BN_add(t2,a,t1)) goto err;
- BN_rshift(r,t2,mont->ri);
+ if (!BN_mul(t2,t1,&mont->Ni,ctx)) goto err;
+ BN_mask_bits(t2,mont->ri);
- if (BN_ucmp(r,mont->N) >= 0)
- bn_qsub(r,r,mont->N);
+ if (!BN_mul(t1,t2,&mont->N,ctx)) goto err;
+ if (!BN_add(t2,a,t1)) goto err;
+ BN_rshift(ret,t2,mont->ri);
- return(1);
-err:
- return(0);
- }
+ if (BN_ucmp(ret,&mont->N) >= 0)
+ BN_usub(ret,ret,&mont->N);
+ ctx->tos-=2;
+ retn=1;
+ }
#endif
+ err:
+ return(retn);
+ }
-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)
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->use_word=0;
+ ctx->ri=0;
+ BN_init(&(ctx->RR));
+ BN_init(&(ctx->N));
+ BN_init(&(ctx->Ni));
+ 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->RR == NULL) mont->RR=BN_new();
- if (mont->N == NULL) mont->N=BN_new();
-
- R=mont->RR; /* grab RR as a temp */
- BN_copy(mont->N,mod); /* Set N */
-
-#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; */
-}
-#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 */
+ if(mont == NULL)
+ return;
+
+ BN_free(&(mont->RR));
+ BN_free(&(mont->N));
+ BN_free(&(mont->Ni));
+ if (mont->flags & BN_FLG_MALLOCED)
+ Free(mont);
+ }
+
+int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *mod, BN_CTX *ctx)
+ {
+ BIGNUM Ri,*R;
+
+ BN_init(&Ri);
+ R= &(mont->RR); /* grab RR as a temp */
+ BN_copy(&(mont->N),mod); /* Set N */
+
+#ifdef BN_RECURSION_MONT
+ /* the word-based algorithm is faster */
+ if (mont->N.top > BN_MONT_CTX_SET_SIZE_WORD)
+#endif
+ {
+ 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); /* R = 2^ri */
+
+ 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;
+ /* 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))
+ BN_sub_word(&Ri,1);
+ 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 */
+ mont->n0=Ri.d[0];
+ BN_free(&Ri);
+ }
+#ifdef BN_RECURSION_MONT
+ else
+ { /* bignum version */
+ mont->use_word=0;
+ mont->ri=BN_num_bits(mod);
+ 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)
+ goto err;
+ BN_lshift(&Ri,&Ri,mont->ri); /* R*Ri */
+ BN_sub_word(&Ri,1);
+ /* Ni = (R*Ri-1) / N */
+ BN_div(&(mont->Ni),NULL,&Ri,mod,ctx);
+ BN_free(&Ri);
+ }
#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));
+ BN_set_bit(&(mont->RR),mont->ri*2);
+ BN_mod(&(mont->RR),&(mont->RR),&(mont->N),ctx);
return(1);
err:
return(0);
}
+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;
+ to->ri=from->ri;
+ to->n0=from->n0;
+ return(to);
+ }
+
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