#include #include "cryptlib.h" #include "bn_lcl.h" #define SIZE 32 #define BN_MONT_CTX_set bn_mcs #define BN_from_montgomery bn_fm #define BN_mod_mul_montgomery bn_mmm #undef BN_to_montgomery #define BN_to_montgomery(r,a,mont,ctx) bn_mmm(\ r,a,(mont)->RR,(mont),ctx) main() { BIGNUM prime,a,b,r,A,B,R; BN_MONT_CTX *mont; BN_CTX *ctx; int i; ctx=BN_CTX_new(); BN_init(&prime); BN_init(&a); BN_init(&b); BN_init(&r); BN_init(&A); BN_init(&B); BN_init(&R); BN_generate_prime(&prime,SIZE,0,NULL,NULL,NULL,NULL); BN_rand(&A,SIZE,1,0); BN_rand(&B,SIZE,1,0); BN_mod(&A,&A,&prime,ctx); BN_mod(&B,&B,&prime,ctx); i=A.top; BN_mul(&R,&A,&B,ctx); BN_mask_bits(&R,i*BN_BITS2); BN_print_fp(stdout,&A); printf(" <- a\n"); BN_print_fp(stdout,&B); printf(" <- b\n"); BN_mul_high(&r,&A,&B,&R,i); BN_print_fp(stdout,&r); printf(" <- high(BA*DC)\n"); BN_mask_bits(&A,i*32); BN_mask_bits(&B,i*32); BN_mul(&R,&A,&B); BN_rshift(&R,&R,i*32); BN_print_fp(stdout,&R); printf(" <- norm BA*DC\n"); BN_sub(&R,&R,&r); BN_print_fp(stdout,&R); printf(" <- diff\n"); } #if 0 int bn_mul_high(BIGNUM *r, BIGNUM *a, BIGNUM *b, BIGNUM *low, int words) { int i; BIGNUM t1,t2,t3,h,ah,al,bh,bl,m,s0,s1; BN_init(&al); BN_init(&ah); BN_init(&bl); BN_init(&bh); BN_init(&t1); BN_init(&t2); BN_init(&t3); BN_init(&s0); BN_init(&s1); BN_init(&h); BN_init(&m); i=a->top; if (i >= words) { al.top=words; ah.top=a->top-words; ah.d= &(a->d[ah.top]); } else al.top=i; al.d=a->d; i=b->top; if (i >= words) { bl.top=words; bh.top=i-words; bh.d= &(b->d[bh.top]); } else bl.top=i; bl.d=b->d; i=low->top; if (i >= words) { s0.top=words; s1.top=i-words; s1.d= &(low->d[s1.top]); } else s0.top=i; s0.d=low->d; al.max=al.top; ah.max=ah.top; bl.max=bl.top; bh.max=bh.top; s0.max=bl.top; s1.max=bh.top; /* Calculate (al-ah)*(bh-bl) */ BN_sub(&t1,&al,&ah); BN_sub(&t2,&bh,&bl); BN_mul(&m,&t1,&t2); /* Calculate ah*bh */ BN_mul(&h,&ah,&bh); /* s0 == low(al*bl) * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl) * We know s0 and s1 so the only unknown is high(al*bl) * high(al*bl) == s1 - low(ah*bh+(al-ah)*(bh-bl)+s0) */ BN_add(&m,&m,&h); BN_add(&t2,&m,&s0); /* Quick and dirty mask off of high words */ t3.d=t2.d; t3.top=(t2.top > words)?words:t2.top; t3.neg=t2.neg; t3.max=t3.top; /* BN_print_fp(stdout,&s1); printf(" s1\n"); */ /* BN_print_fp(stdout,&t2); printf(" middle value\n"); */ /* BN_print_fp(stdout,&t3); printf(" low middle value\n"); */ BN_sub(&t1,&s1,&t3); if (t1.neg) { /*printf("neg fixup\n"); BN_print_fp(stdout,&t1); printf(" before\n"); */ BN_lshift(&t2,BN_value_one(),words*32); BN_add(&t1,&t2,&t1); BN_mask_bits(&t1,words*32); /* BN_print_fp(stdout,&t1); printf(" after\n"); */ } /* al*bl == high(al*bl)<bn[ctx->tos++]); if (a == b) { if (!BN_sqr(tmp,a,ctx)) goto err; } else { if (!BN_mul(tmp,a,b)) goto err; } /* reduce from aRR to aR */ if (!BN_from_montgomery(r,tmp,mont,ctx)) goto err; ctx->tos--; return(1); err: return(0); } int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont, BN_CTX *ctx) { BIGNUM z1; BIGNUM *t1,*t2; BN_ULONG *ap,*bp,*rp; int j,i,bl,al; BN_init(&z1); t1= &(ctx->bn[ctx->tos]); t2= &(ctx->bn[ctx->tos+1]); if (!BN_copy(t1,a)) goto err; /* can cheat */ BN_mask_bits(t1,mont->ri); if (!BN_mul(t2,t1,mont->Ni)) goto err; BN_mask_bits(t2,mont->ri); if (!BN_mul(t1,t2,mont->N)) goto err; if (!BN_add(t2,t1,a)) goto err; /* At this point, t2 has the bottom ri bits set to zero. * This means that the bottom ri bits == the 1^ri minus the bottom * ri bits of a. * This means that only the bits above 'ri' in a need to be added, * and XXXXXXXXXXXXXXXXXXXXXXXX */ BN_print_fp(stdout,t2); printf("\n"); BN_rshift(r,t2,mont->ri); if (BN_ucmp(r,mont->N) >= 0) BN_usub(r,r,mont->N); return(1); err: return(0); } int BN_MONT_CTX_set(BN_MONT_CTX *mont, BIGNUM *mod, BN_CTX *ctx) { 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 */ mont->ri=(BN_num_bits(mod)+(BN_BITS2-1))/BN_BITS2*BN_BITS2; BN_lshift(R,BN_value_one(),mont->ri); /* R */ if ((Ri=BN_mod_inverse(NULL,R,mod,ctx)) == NULL) goto err;/* Ri */ BN_lshift(Ri,Ri,mont->ri); /* R*Ri */ BN_usub(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 */ /* setup RR for conversions */ BN_lshift(mont->RR,BN_value_one(),mont->ri*2); BN_mod(mont->RR,mont->RR,mont->N,ctx); return(1); err: return(0); } #endif