X-Git-Url: https://git.cryptolib.org/?a=blobdiff_plain;f=bigint%2Fbigint.c;h=8524daad3b66a042439307f080d024776e8f474d;hb=01b5d29136b37105c7e533bd3ec2299d31551627;hp=fb2f524cfc2fedc0227a3ee5c2903e1d64b15de9;hpb=eb09a2a6f447833e3cf73a71fc0113f84d51f41b;p=avr-crypto-lib.git diff --git a/bigint/bigint.c b/bigint/bigint.c index fb2f524..8524daa 100644 --- a/bigint/bigint.c +++ b/bigint/bigint.c @@ -1,6 +1,6 @@ /* bigint.c */ /* - This file is part of the AVR-Crypto-Lib. + This file is part of the ARM-Crypto-Lib. Copyright (C) 2008 Daniel Otte (daniel.otte@rub.de) This program is free software: you can redistribute it and/or modify @@ -26,45 +26,55 @@ */ +#define STRING2(x) #x +#define STRING(x) STRING2(x) +#define STR_LINE STRING(__LINE__) + #include "bigint.h" #include -#include "bigint_io.h" +#define DEBUG 1 + +#if DEBUG || 1 #include "cli.h" +#include "uart_i.h" +#include "bigint_io.h" +#include +#endif #ifndef MAX #define MAX(a,b) (((a)>(b))?(a):(b)) #endif #ifndef MIN - #define MIN(a,b) (((a)<(b))?(a):(b)) + #define MIN(a,b) (((a) < (b)) ? (a) : (b)) #endif -#define SET_FBS(a, v) do{(a)->info &=0xF8; (a)->info |= (v);}while(0) -#define GET_FBS(a) ((a)->info&BIGINT_FBS_MASK) +#define SET_FBS(a, v) do {(a)->info &= ~BIGINT_FBS_MASK; (a)->info |= (v);} while(0) +#define GET_FBS(a) ((a)->info & BIGINT_FBS_MASK) #define SET_NEG(a) (a)->info |= BIGINT_NEG_MASK #define SET_POS(a) (a)->info &= ~BIGINT_NEG_MASK -#define XCHG(a,b) do{(a)^=(b); (b)^=(a); (a)^=(b);}while(0) -#define XCHG_PTR(a,b) do{ a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \ - b = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b))); \ - a = (void*)(((uint16_t)(a)) ^ ((uint16_t)(b)));}while(0) +#define XCHG(a,b) do{(a) ^= (b); (b) ^= (a); (a) ^= (b);} while(0) +#define XCHG_PTR(a,b) do{ a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \ + b = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b))); \ + a = (void*)(((intptr_t)(a)) ^ ((intptr_t)(b)));} while(0) -#define GET_SIGN(a) ((a)->info&BIGINT_NEG_MASK) +#define GET_SIGN(a) ((a)->info & BIGINT_NEG_MASK) /******************************************************************************/ -void bigint_adjust(bigint_t* a){ - while(a->length_B!=0 && a->wordv[a->length_B-1]==0){ - a->length_B--; +void bigint_adjust(bigint_t *a){ + while (a->length_W != 0 && a->wordv[a->length_W - 1] == 0) { + a->length_W--; } - if(a->length_B==0){ + if (a->length_W == 0) { a->info=0; return; } - uint8_t t; - uint8_t i = 0x07; - t = a->wordv[a->length_B-1]; - while((t&0x80)==0 && i){ - t<<=1; + bigint_word_t t; + uint8_t i = BIGINT_WORD_SIZE - 1; + t = a->wordv[a->length_W - 1]; + while ((t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) == 0 && i) { + t <<= 1; i--; } SET_FBS(a, i); @@ -72,172 +82,199 @@ void bigint_adjust(bigint_t* a){ /******************************************************************************/ -void bigint_copy(bigint_t* dest, const bigint_t* src){ - memcpy(dest->wordv, src->wordv, src->length_B); - dest->length_B = src->length_B; +bigint_length_t bigint_length_b(const bigint_t *a){ + if(!a->length_W || a->length_W==0){ + return 0; + } + return (a->length_W-1) * BIGINT_WORD_SIZE + GET_FBS(a); +} + +/******************************************************************************/ + +bigint_length_t bigint_length_B(const bigint_t *a){ + return a->length_W * sizeof(bigint_word_t); +} + +/******************************************************************************/ + +int32_t bigint_get_first_set_bit(const bigint_t *a){ + if(a->length_W == 0) { + return -1; + } + return (a->length_W-1) * sizeof(bigint_word_t) * CHAR_BIT + GET_FBS(a); +} + + +/******************************************************************************/ + +int32_t bigint_get_last_set_bit(const bigint_t *a){ + uint32_t r = 0; + uint8_t b = 0; + bigint_word_t x = 1; + if (a->length_W == 0) { + return -1; + } + while (a->wordv[r] == 0 && r < a->length_W) { + ++r; + } + if (a->wordv[r] == 0) { + return (uint32_t)(-1); + } + while ((x&a->wordv[r])==0) { + ++b; + x <<= 1; + } + return r * BIGINT_WORD_SIZE + b; +} + +/******************************************************************************/ + +void bigint_copy(bigint_t *dest, const bigint_t *src){ + if(dest->wordv != src->wordv){ + memcpy(dest->wordv, src->wordv, src->length_W * sizeof(bigint_word_t)); + } + dest->length_W = src->length_W; dest->info = src->info; } /******************************************************************************/ /* this should be implemented in assembly */ -/* -void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ - uint16_t t=0, i; - if(a->length_B < b->length_B){ - XCHG_PTR(a,b); - } - for(i=0; ilength_B; ++i){ - t = a->wordv[i] + b->wordv[i] + t; - dest->wordv[i] = (uint8_t)t; - t>>=8; - } - for(; ilength_B; ++i){ - t = a->wordv[i] + t; - dest->wordv[i] = (uint8_t)t; - t>>=8; - } - dest->wordv[i++] = t; - dest->length_B = i; +void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ + bigint_length_t i; + bigint_wordplus_t t = 0LL; + if (a->length_W < b->length_W) { + XCHG_PTR(a, b); + } + for(i = 0; i < b->length_W; ++i) { + t += a->wordv[i]; + t += b->wordv[i]; + dest->wordv[i] = (bigint_word_t)t; + t >>= BIGINT_WORD_SIZE; + } + for(; i < a->length_W; ++i){ + t += a->wordv[i]; + dest->wordv[i] = (bigint_word_t)t; + t >>= BIGINT_WORD_SIZE; + } + if(t){ + dest->wordv[i++] = (bigint_word_t)t; + } + dest->length_W = i; + SET_POS(dest); bigint_adjust(dest); } -*/ + /******************************************************************************/ /* this should be implemented in assembly */ -void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){ - uint16_t i,j=0; - uint16_t t=0; - if(scale>dest->length_B) - memset(dest->wordv+dest->length_B, 0, scale-dest->length_B); - for(i=scale; ilength_B+scale; ++i,++j){ - t = a->wordv[j] + t; - if(dest->length_B>i){ - t += dest->wordv[i]; - } - dest->wordv[i] = (uint8_t)t; - t>>=8; +void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale){ + if(a->length_W == 0){ + return; } - while(t){ - if(dest->length_B>i){ - t = dest->wordv[i] + t; - } - dest->wordv[i] = (uint8_t)t; - t>>=8; - ++i; + if(scale == 0){ + bigint_add_u(dest, dest, a); + return; } - if(dest->length_B < i){ - dest->length_B = i; + bigint_t x; +#if BIGINT_WORD_SIZE == 8 + memset(dest->wordv + dest->length_W, 0, MAX(dest->length_W, a->length_W + scale) - dest->length_W); + x.wordv = dest->wordv + scale; + x.length_W = dest->length_W - scale; + if((int16_t)x.length_W < 0){ + x.length_W = 0; + x.info = 0; + } else { + x.info = dest->info; } + bigint_add_u(&x, &x, a); + dest->length_W = x.length_W + scale; + dest->info = 0; bigint_adjust(dest); +#else + bigint_t s; + bigint_length_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t); + bigint_word_t bv[a->length_W + 1]; + s.wordv = bv; + bv[0] = bv[a->length_W] = 0; + memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_W * sizeof(bigint_word_t)); + s.length_W = a->length_W + 1; + bigint_adjust(&s); + memset(dest->wordv + dest->length_W, 0, (MAX(dest->length_W, s.length_W + word_shift) - dest->length_W) * sizeof(bigint_word_t)); + x.wordv = dest->wordv + word_shift; + x.length_W = dest->length_W - word_shift; + if((int16_t)x.length_W < 0){ + x.length_W = 0; + x.info = 0; + }else{ + x.info = dest->info; + } + bigint_add_u(&x, &x, &s); + dest->length_W = x.length_W + word_shift; + dest->info = 0; + bigint_adjust(dest); +#endif } /******************************************************************************/ /* this should be implemented in assembly */ -void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ - int8_t borrow=0; +void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ + int8_t borrow = 0; int8_t r; - int16_t t; - uint16_t i, min, max; - min = MIN(a->length_B, b->length_B); - max = MAX(a->length_B, b->length_B); - r = bigint_cmp_u(a,b); - if(r==0){ - dest->length_B = 0; - dest->wordv[0] = 0; - bigint_adjust(dest); + bigint_wordplus_signed_t t = 0; + bigint_length_t i; + if(b->length_W == 0){ + bigint_copy(dest, a); + SET_POS(dest); return; } - if(b->length_B==0){ - dest->length_B = a->length_B; - memcpy(dest->wordv, a->wordv, a->length_B); - dest->info = a->info; - SET_POS(dest); + if(a->length_W == 0){ + bigint_copy(dest, b); + SET_NEG(dest); return; } - if(a->length_B==0){ - dest->length_B = b->length_B; - memcpy(dest->wordv, b->wordv, b->length_B); - dest->info = b->info; - SET_NEG(dest); - return; - } - if(r<0){ - for(i=0; iwordv[i] - b->wordv[i] - borrow; - if(t<1){ - borrow = 0; - dest->wordv[i]=(uint8_t)(-t); - }else{ - borrow = -1; - dest->wordv[i]=(uint8_t)(-t); - } - } - for(;iwordv[i] + borrow; - if(t<1){ - borrow = 0; - dest->wordv[i]=(uint8_t)t; - }else{ - borrow = -1; - dest->wordv[i]=(uint8_t)t; - } - } + r = bigint_cmp_u(a,b); + if(r == 0){ + bigint_set_zero(dest); + return; + } + if(r < 0){ + bigint_sub_u(dest, b, a); SET_NEG(dest); - dest->length_B = i; - bigint_adjust(dest); - }else{ - for(i=0; iwordv[i] - b->wordv[i] - borrow; - if(t<0){ - borrow = 1; - dest->wordv[i]=(uint8_t)t; - }else{ - borrow = 0; - dest->wordv[i]=(uint8_t)t; - } - } - for(;iwordv[i] - borrow; - if(t<0){ - borrow = 1; - dest->wordv[i]=(uint8_t)t; - }else{ - borrow = 0; - dest->wordv[i]=(uint8_t)t; - } - + return; + } + for(i = 0; i < a->length_W; ++i){ + t = a->wordv[i]; + if(i < b->length_W){ + t -= b->wordv[i]; } - SET_POS(dest); - dest->length_B = i; - bigint_adjust(dest); + t -= borrow; + dest->wordv[i] = (bigint_word_t)t; + borrow = t < 0 ? 1 : 0; } + SET_POS(dest); + dest->length_W = i; + bigint_adjust(dest); } /******************************************************************************/ -int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){ - if(a->length_B > b->length_B){ +int8_t bigint_cmp_u(const bigint_t *a, const bigint_t *b){ + if(a->length_W > b->length_W){ return 1; } - if(a->length_B < b->length_B){ + if(a->length_W < b->length_W){ return -1; } - if(GET_FBS(a) > GET_FBS(b)){ - return 1; - } - if(GET_FBS(a) < GET_FBS(b)){ - return -1; - } - if(a->length_B==0){ + if(a->length_W == 0){ return 0; } - uint16_t i; - i = a->length_B-1; + bigint_length_t i; + i = a->length_W - 1; do{ - if(a->wordv[i]!=b->wordv[i]){ - if(a->wordv[i]>b->wordv[i]){ + if(a->wordv[i] != b->wordv[i]){ + if(a->wordv[i] > b->wordv[i]){ return 1; }else{ return -1; @@ -249,7 +286,7 @@ int8_t bigint_cmp_u(const bigint_t* a, const bigint_t* b){ /******************************************************************************/ -void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ +void bigint_add_s(bigint_t *dest, const bigint_t *a, const bigint_t *b){ uint8_t s; s = GET_SIGN(a)?2:0; s |= GET_SIGN(b)?1:0; @@ -275,7 +312,7 @@ void bigint_add_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ /******************************************************************************/ -void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ +void bigint_sub_s(bigint_t *dest, const bigint_t *a, const bigint_t *b){ uint8_t s; s = GET_SIGN(a)?2:0; s |= GET_SIGN(b)?1:0; @@ -302,8 +339,11 @@ void bigint_sub_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ /******************************************************************************/ -int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){ +int8_t bigint_cmp_s(const bigint_t *a, const bigint_t *b){ uint8_t s; + if(a->length_W==0 && b->length_W==0){ + return 0; + } s = GET_SIGN(a)?2:0; s |= GET_SIGN(b)?1:0; switch(s){ @@ -327,83 +367,88 @@ int8_t bigint_cmp_s(const bigint_t* a, const bigint_t* b){ /******************************************************************************/ -void bigint_shiftleft(bigint_t* a, uint16_t shift){ - uint16_t byteshift; - uint16_t i; +void bigint_shiftleft(bigint_t *a, bigint_length_t shift){ + bigint_length_t byteshift, words_to_shift; + int16_t i; uint8_t bitshift; - uint16_t t=0; - byteshift = (shift+3)/8; - bitshift = shift&7; - memmove(a->wordv+byteshift, a->wordv, a->length_B); - memset(a->wordv, 0, byteshift); - if(bitshift!=0){ - if(bitshift<=4){ /* shift to the left */ - for(i=byteshift; ilength_B+byteshift; ++i){ - t |= (a->wordv[i])<wordv[i] = (uint8_t)t; - t >>= 8; - } - a->wordv[i] = (uint8_t)t; - }else{ /* shift to the right */ - bitshift = 8 - bitshift; - for(i=a->length_B+byteshift-1; i>byteshift; --i){ - t |= (a->wordv[i])<<(8-bitshift); - a->wordv[i] = (uint8_t)(t>>8); - t <<= 8; - } - t |= (a->wordv[i])<<(8-bitshift); - a->wordv[i] = (uint8_t)(t>>8); - } + bigint_word_t *p; + bigint_wordplus_t t = 0; + if (a->length_W == 0 || shift == 0) { + return; } - a->length_B += byteshift+1; - bigint_adjust(a); + byteshift = shift / 8; + bitshift = shift & 7; + if (byteshift % sizeof(bigint_word_t)) { + a->wordv[a->length_W + byteshift / sizeof(bigint_t)] = 0; + } + if (byteshift) { + memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t)); + memset(a->wordv, 0, byteshift); + } + if (bitshift == 0) { + a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t); + bigint_adjust(a); + return; + } + p = &a->wordv[byteshift / sizeof(bigint_word_t)]; + words_to_shift = a->length_W + (byteshift % sizeof(bigint_word_t) ? 1 : 0); + for (i = 0; i < words_to_shift; ++i) { + t |= ((bigint_wordplus_t)p[i]) << bitshift; + p[i] = (bigint_word_t)t; + t >>= BIGINT_WORD_SIZE; + } + if (t) { + p[i] = (bigint_word_t)t; + a->length_W += 1; + } + a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t); + bigint_adjust(a); } /******************************************************************************/ -void bigint_shiftright(bigint_t* a, uint16_t shift){ - uint16_t byteshift; - uint16_t i; +void bigint_shiftright(bigint_t *a, bigint_length_t shift){ + bigint_length_t byteshift; + bigint_length_t i; uint8_t bitshift; - uint16_t t=0; - byteshift = shift/8; - bitshift = shift&7; - if(byteshift >= a->length_B){ /* we would shift out more than we have */ - a->length_B=0; - a->wordv[0] = 0; - SET_FBS(a, 0); - return; + bigint_wordplus_t t = 0; + byteshift = shift / 8; + bitshift = shift & 7; + + if (a->length_W == 0) { + return; } - if(byteshift == a->length_B-1 && bitshift>GET_FBS(a)){ - a->length_B=0; - a->wordv[0] = 0; - SET_FBS(a, 0); + + if(bigint_get_first_set_bit(a) < shift){ /* we would shift out more than we have */ + bigint_set_zero(a); return; } + if(byteshift){ - memmove(a->wordv, a->wordv+byteshift, a->length_B-byteshift); - memset(a->wordv+a->length_B-byteshift, 0, byteshift); + memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift); + memset((uint8_t*)&a->wordv[a->length_W] - byteshift, 0, byteshift); + a->length_W -= byteshift / sizeof(bigint_word_t); } - if(bitshift!=0){ + + + if(bitshift != 0 && a->length_W){ /* shift to the right */ - for(i=a->length_B-byteshift-1; i>0; --i){ - t |= (a->wordv[i])<<(8-bitshift); - a->wordv[i] = (uint8_t)(t>>8); - t <<= 8; - } - t |= (a->wordv[0])<<(8-bitshift); - a->wordv[0] = (uint8_t)(t>>8); + i = a->length_W - 1; + do{ + t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - bitshift); + a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE); + t <<= BIGINT_WORD_SIZE; + }while(i--); } - a->length_B -= byteshift; bigint_adjust(a); } /******************************************************************************/ -void bigint_xor(bigint_t* dest, const bigint_t* a){ - uint16_t i; - for(i=0; ilength_B; ++i){ +void bigint_xor(bigint_t *dest, const bigint_t *a){ + bigint_length_t i; + for(i=0; ilength_W; ++i){ dest->wordv[i] ^= a->wordv[i]; } bigint_adjust(dest); @@ -411,102 +456,116 @@ void bigint_xor(bigint_t* dest, const bigint_t* a){ /******************************************************************************/ -void bigint_set_zero(bigint_t* a){ - a->length_B=0; +void bigint_set_zero(bigint_t *a){ + a->length_W=0; } /******************************************************************************/ /* using the Karatsuba-Algorithm */ /* x*y = (xh*yh)*b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + yh*yl */ -void bigint_mul_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ - if(a->length_B==0 || b->length_B==0){ +void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ + if(a->length_W == 0 || b->length_W == 0){ bigint_set_zero(dest); - depth -= 1; return; } - if(a->length_B==1 || b->length_B==1){ - if(a->length_B!=1){ + if(dest == a || dest == b){ + bigint_t d; + bigint_word_t d_b[a->length_W + b->length_W]; + d.wordv = d_b; + bigint_mul_u(&d, a, b); + bigint_copy(dest, &d); + return; + } + if(a->length_W == 1 || b->length_W == 1){ + if(a->length_W != 1){ XCHG_PTR(a,b); } - uint16_t i, t=0; - uint8_t x = a->wordv[0]; - for(i=0; ilength_B; ++i){ - t += b->wordv[i]*x; - dest->wordv[i] = (uint8_t)t; - t>>=8; + bigint_wordplus_t t = 0; + bigint_length_t i; + bigint_word_t x = a->wordv[0]; + for(i=0; i < b->length_W; ++i){ + t += ((bigint_wordplus_t)b->wordv[i]) * ((bigint_wordplus_t)x); + dest->wordv[i] = (bigint_word_t)t; + t >>= BIGINT_WORD_SIZE; + } + dest->length_W = i; + if(t){ + dest->wordv[i] = (bigint_word_t)t; + dest->length_W += 1; } - dest->wordv[i] = (uint8_t)t; - dest->length_B=i+1; + dest->info = 0; bigint_adjust(dest); return; } - if(a->length_B<=4 && b->length_B<=4){ + if(a->length_W * sizeof(bigint_word_t) <= 4 && b->length_W * sizeof(bigint_word_t) <= 4){ uint32_t p=0, q=0; uint64_t r; - memcpy(&p, a->wordv, a->length_B); - memcpy(&q, b->wordv, b->length_B); - r = (uint64_t)p*(uint64_t)q; - memcpy(dest->wordv, &r, a->length_B+b->length_B); - dest->length_B = a->length_B+b->length_B; + memcpy(&p, a->wordv, a->length_W*sizeof(bigint_word_t)); + memcpy(&q, b->wordv, b->length_W*sizeof(bigint_word_t)); + r = (uint64_t)p * (uint64_t)q; + memcpy(dest->wordv, &r, (dest->length_W = a->length_W + b->length_W)*sizeof(bigint_word_t)); bigint_adjust(dest); return; } - bigint_set_zero(dest); /* split a in xh & xl; split b in yh & yl */ - uint16_t n; - n=(MAX(a->length_B, b->length_B)+1)/2; + const bigint_length_t n = (MAX(a->length_W, b->length_W)+1)/2; bigint_t xl, xh, yl, yh; xl.wordv = a->wordv; yl.wordv = b->wordv; - if(a->length_B<=n){ - xh.info=0; - xh.length_B = 0; - xl.length_B = a->length_B; - xl.info = 0; + if(a->length_W<=n){ + bigint_set_zero(&xh); + xl.length_W = a->length_W; + xl.info = a->info; }else{ - xl.length_B=n; + xl.length_W=n; xl.info = 0; bigint_adjust(&xl); - xh.wordv = a->wordv+n; - xh.length_B = a->length_B-n; - xh.info = 0; - } - if(b->length_B<=n){ - yh.info=0; - yh.length_B = 0; - yl.length_B = b->length_B; + xh.wordv = &(a->wordv[n]); + xh.length_W = a->length_W-n; + xh.info = a->info; + } + if(b->length_W<=n){ + bigint_set_zero(&yh); + yl.length_W = b->length_W; yl.info = b->info; }else{ - yl.length_B=n; + yl.length_W=n; yl.info = 0; bigint_adjust(&yl); - yh.wordv = b->wordv+n; - yh.length_B = b->length_B-n; - yh.info = 0; + yh.wordv = &(b->wordv[n]); + yh.length_W = b->length_W-n; + yh.info = b->info; } /* now we have split up a and b */ - uint8_t tmp_b[2*n+2], m_b[2*(n+1)]; + /* remember we want to do: + * x*y = (xh * b**n + xl) * (yh * b**n + yl) + * = (xh * yh) * b**2n + xh * b**n * yl + yh * b**n * xl + xl * yl + * = (xh * yh) * b**2n + (xh * yl + yh * xl) * b**n + xl *yl + * // xh * yl + yh * xl = (xh + yh) * (xl + yl) - xh * yh - xl * yl + * x*y = (xh * yh) * b**2n + ((xh+xl)*(yh+yl) - xh*yh - xl*yl)*b**n + xl*yl + * 5 9 2 4 3 7 5 6 1 8 1 + */ + bigint_word_t tmp_b[2 * n + 2], m_b[2 * (n + 1)]; bigint_t tmp, tmp2, m; - /* calculate h=xh*yh; l=xl*yl; sx=xh+xl; sy=yh+yl */ tmp.wordv = tmp_b; - tmp2.wordv = tmp_b+n+1; + tmp2.wordv = &(tmp_b[n + 1]); m.wordv = m_b; - bigint_mul_u(dest, &xl, &yl); /* dest <= xl*yl */ - bigint_add_u(&tmp2, &xh, &xl); /* tmp2 <= xh+xl */ - bigint_add_u(&tmp, &yh, &yl); /* tmp <= yh+yl */ - bigint_mul_u(&m, &tmp2, &tmp); /* m <= tmp*tmp */ - bigint_mul_u(&tmp, &xh, &yh); /* h <= xh*yh */ - bigint_sub_u(&m, &m, dest); /* m <= m-dest */ - bigint_sub_u(&m, &m, &tmp); /* m <= m-h */ - bigint_add_scale_u(dest, &m, n); - bigint_add_scale_u(dest, &tmp, 2*n); + bigint_mul_u(dest, &xl, &yl); /* 1: dest <= xl*yl */ + bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh+xl */ + bigint_add_u(&tmp, &yh, &yl); /* 3: tmp <= yh+yl */ + bigint_mul_u(&m, &tmp2, &tmp); /* 4: m <= tmp2*tmp */ + bigint_mul_u(&tmp, &xh, &yh); /* 5: tmp <= xh*yh */ + bigint_sub_u(&m, &m, dest); /* 6: m <= m-dest */ + bigint_sub_u(&m, &m, &tmp); /* 7: m <= m-tmp */ + bigint_add_scale_u(dest, &m, n * sizeof(bigint_word_t)); /* 8: dest <= dest+m**n*/ + bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t)); /* 9: dest <= dest+tmp**(2*n) */ } /******************************************************************************/ -void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ +void bigint_mul_s(bigint_t *dest, const bigint_t *a, const bigint_t *b){ uint8_t s; s = GET_SIGN(a)?2:0; s |= GET_SIGN(b)?1:0; @@ -533,38 +592,708 @@ void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ } /******************************************************************************/ +#if OLD_SQUARE + +#if DEBUG_SQUARE +unsigned square_depth = 0; +#endif /* square */ /* (xh*b^n+xl)^2 = xh^2*b^2n + 2*xh*xl*b^n + xl^2 */ -void bigint_square(bigint_t* dest, const bigint_t* a){ - if(a->length_B<=4){ - uint64_t r=0; - memcpy(&r, a->wordv, a->length_B); - r = r*r; - memcpy(dest->wordv, &r, 2*a->length_B); +void bigint_square(bigint_t *dest, const bigint_t *a){ + if(a->length_W * sizeof(bigint_word_t) <= 4){ + uint64_t r = 0; + memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t)); + r = r * r; + memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t)); SET_POS(dest); - dest->length_B=2*a->length_B; + dest->length_W = 2 * a->length_W; bigint_adjust(dest); return; } - uint16_t n; - n=(a->length_B+1)/2; + + if(dest->wordv == a->wordv){ + bigint_t d; + bigint_word_t d_b[a->length_W*2]; + d.wordv = d_b; + bigint_square(&d, a); + bigint_copy(dest, &d); + return; + } + bigint_fast_square(dest, a); + return; +#if DEBUG_SQUARE + square_depth += 1; +#endif + + bigint_length_t n; + n=(a->length_W+1)/2; bigint_t xh, xl, tmp; /* x-high, x-low, temp */ - uint8_t buffer[2*n+1]; + bigint_word_t buffer[2*n+1]; xl.wordv = a->wordv; - xl.length_B = n; - xh.wordv = a->wordv+n; - xh.length_B = a->length_B-n; + xl.length_W = n; + xl.info = 0; + xh.wordv = &(a->wordv[n]); + xh.length_W = a->length_W-n; + xh.info = a->info; + bigint_adjust(&xl); tmp.wordv = buffer; +/* (xh * b**n + xl)**2 = xh**2 * b**2n + 2 * xh * xl * b**n + xl**2 */ +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl); + cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh); + } +#endif bigint_square(dest, &xl); - bigint_square(&tmp, &xh); - bigint_add_scale_u(dest, &tmp, 2*n); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest); + } +#endif + bigint_square(&tmp, &xh); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp); + } +#endif + bigint_add_scale_u(dest, &tmp, 2 * n * sizeof(bigint_word_t)); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest); + } +#endif bigint_mul_u(&tmp, &xl, &xh); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp); + } +#endif bigint_shiftleft(&tmp, 1); - bigint_add_scale_u(dest, &tmp, n); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp); + } +#endif + bigint_add_scale_u(dest, &tmp, n * sizeof(bigint_word_t)); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest); + cli_putstr("\r\n"); + } + square_depth -= 1; +#endif +} + +#endif + +/******************************************************************************/ + +void bigint_square(bigint_t *dest, const bigint_t *a) { + union __attribute__((packed)) { + bigint_word_t u[2]; + bigint_wordplus_t uv; + } acc; + bigint_word_t q, c1, c2; + bigint_length_t i, j; + if(a->length_W * sizeof(bigint_word_t) <= 4){ + uint64_t r = 0; + memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t)); + r = r * r; + memcpy(dest->wordv, &r, 2 * a->length_W * sizeof(bigint_word_t)); + SET_POS(dest); + dest->length_W = 2 * a->length_W; + bigint_adjust(dest); + return; + } + + if(dest->wordv == a->wordv){ + bigint_t d; + bigint_word_t d_b[a->length_W * 2]; + d.wordv = d_b; + bigint_square(&d, a); + bigint_copy(dest, &d); + return; + } + + memset(dest->wordv, 0, a->length_W * 2 * sizeof(bigint_word_t)); + + for (i = 0; i < a->length_W; ++i) { + acc.uv = (bigint_wordplus_t)a->wordv[i] * (bigint_wordplus_t)a->wordv[i] + (bigint_wordplus_t)dest->wordv[2 * i]; + dest->wordv[2 * i] = acc.u[0]; + c1 = acc.u[1]; + c2 = 0; + for (j = i + 1; j < a->length_W; ++j) { + acc.uv = (bigint_wordplus_t)a->wordv[i] * (bigint_wordplus_t)a->wordv[j]; + q = acc.u[1] >> (BIGINT_WORD_SIZE - 1); + acc.uv <<= 1; + acc.uv += dest->wordv[i + j]; + q += (acc.uv < dest->wordv[i + j]); + acc.uv += c1; + q += (acc.uv < c1); + dest->wordv[i + j] = acc.u[0]; + c1 = (bigint_wordplus_t)acc.u[1] + c2; + c2 = q + (c1 < c2); + } + dest->wordv[i + a->length_W] += c1; + if (i < a->length_W - 1) { + dest->wordv[i + a->length_W + 1] = c2 + (dest->wordv[i + a->length_W] < c1); + } + } + dest->info = 0; + dest->length_W = 2 * a->length_W; + bigint_adjust(dest); +} + +/******************************************************************************/ + +void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale){ + bigint_t tmp, x; + bigint_word_t tmp_b[b->length_W + 1]; + const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE; + + if (a->length_W < b->length_W + word_shift) { +#if DEBUG + cli_putstr("\r\nDBG: *bang*\r\n"); +#endif + bigint_set_zero(a); + return; + } + tmp.wordv = tmp_b; + bigint_copy(&tmp, b); + bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE); + + x.info = a->info; + x.wordv = &(a->wordv[word_shift]); + x.length_W = a->length_W - word_shift; + + bigint_sub_u(&x, &x, &tmp); + bigint_adjust(a); + return; } +/******************************************************************************/ + +void bigint_reduce(bigint_t *a, const bigint_t *r){ + uint8_t rfbs = GET_FBS(r); + if (r->length_W == 0 || a->length_W == 0) { + return; + } + + if (bigint_length_b(a) + 3 > bigint_length_b(r)) { + if ((r->length_W * sizeof(bigint_word_t) <= 4) && (a->length_W * sizeof(bigint_word_t) <= 4)) { + uint32_t p = 0, q = 0; + memcpy(&p, a->wordv, a->length_W * sizeof(bigint_word_t)); + memcpy(&q, r->wordv, r->length_W * sizeof(bigint_word_t)); + p %= q; + memcpy(a->wordv, &p, a->length_W * sizeof(bigint_word_t)); + a->length_W = r->length_W; + bigint_adjust(a); + return; + } + unsigned shift; + while (a->length_W > r->length_W) { + shift = (a->length_W - r->length_W) * CHAR_BIT * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1; + bigint_sub_u_bitscale(a, r, shift); + } + while ((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)) { + shift = GET_FBS(a) - rfbs - 1; + bigint_sub_u_bitscale(a, r, shift); + } + } + while (bigint_cmp_u(a, r) >= 0) { + bigint_sub_u(a, a, r); + } + bigint_adjust(a); +} + +/******************************************************************************/ + +/* calculate dest = a**exp % r */ +/* using square&multiply */ +void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){ + if(a->length_W == 0){ + bigint_set_zero(dest); + return; + } + + bigint_t res, base; + bigint_word_t t, base_w[MAX(a->length_W, r->length_W)], res_w[r->length_W * 2]; + bigint_length_t i; + uint8_t j; + res.wordv = res_w; + base.wordv = base_w; + bigint_copy(&base, a); + bigint_reduce(&base, r); + res.wordv[0] = 1; + res.length_W = 1; + res.info = 0; + bigint_adjust(&res); + if(exp->length_W == 0){ + bigint_copy(dest, &res); + return; + } + bigint_copy(&res, &base); + uint8_t flag = 0; + t = exp->wordv[exp->length_W - 1]; + for (i = exp->length_W; i > 0; --i) { + t = exp->wordv[i - 1]; + for (j = BIGINT_WORD_SIZE; j > 0; --j) { + if (!flag) { + if (t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))) { + flag = 1; + } + } else { + bigint_square(&res, &res); + bigint_reduce(&res, r); + if(t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))){ + bigint_mul_u(&res, &res, &base); + bigint_reduce(&res, r); + } + } + t <<= 1; + } + } + + SET_POS(&res); + bigint_copy(dest, &res); +} + +/******************************************************************************/ +/* gcd <-- gcd(x,y) a*x+b*y=gcd */ +void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, const bigint_t *y){ + bigint_length_t i = 0; + if(x->length_W == 0 || y->length_W == 0){ + if(gcd){ + bigint_set_zero(gcd); + } + if(a){ + bigint_set_zero(a); + } + if(b){ + bigint_set_zero(b); + } + return; + } + if(x->length_W == 1 && x->wordv[0] == 1){ + if(gcd){ + gcd->length_W = 1; + gcd->wordv[0] = 1; + gcd->info = 0; + } + if(a){ + a->length_W = 1; + a->wordv[0] = 1; + SET_POS(a); + bigint_adjust(a); + } + if(b){ + bigint_set_zero(b); + } + return; + } + if(y->length_W == 1 && y->wordv[0] == 1){ + if(gcd){ + gcd->length_W = 1; + gcd->wordv[0] = 1; + gcd->info = 0; + } + if(b){ + b->length_W = 1; + b->wordv[0] = 1; + SET_POS(b); + bigint_adjust(b); + } + if(a){ + bigint_set_zero(a); + } + return; + } + + while(x->wordv[i] == 0 && y->wordv[i] == 0){ + ++i; + } + bigint_word_t g_b[i + 2], x_b[x->length_W - i], y_b[y->length_W - i]; + bigint_word_t u_b[x->length_W - i], v_b[y->length_W - i]; + bigint_word_t a_b[y->length_W + 2], c_b[y->length_W + 2]; + bigint_word_t b_b[x->length_W + 2], d_b[x->length_W + 2]; + bigint_t g, x_, y_, u, v, a_, b_, c_, d_; + + g.wordv = g_b; + x_.wordv = x_b; + y_.wordv = y_b; + memset(g_b, 0, i * sizeof(bigint_word_t)); + g_b[i] = 1; + g.length_W = i + 1; + g.info = 0; + x_.info = y_.info = 0; + x_.length_W = x->length_W - i; + y_.length_W = y->length_W - i; + memcpy(x_.wordv, x->wordv + i, x_.length_W * sizeof(bigint_word_t)); + memcpy(y_.wordv, y->wordv + i, y_.length_W * sizeof(bigint_word_t)); + for(i = 0; (x_.wordv[0] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0; ++i){ + } + + bigint_adjust(&x_); + bigint_adjust(&y_); + + if(i){ + bigint_shiftleft(&g, i); + bigint_shiftright(&x_, i); + bigint_shiftright(&y_, i); + } + + u.wordv = u_b; + v.wordv = v_b; + a_.wordv = a_b; + b_.wordv = b_b; + c_.wordv = c_b; + d_.wordv = d_b; + + bigint_copy(&u, &x_); + bigint_copy(&v, &y_); + a_.wordv[0] = 1; + a_.length_W = 1; + a_.info = 0; + d_.wordv[0] = 1; + d_.length_W = 1; + d_.info = 0; + bigint_set_zero(&b_); + bigint_set_zero(&c_); + do { + while ((u.wordv[0] & 1) == 0) { + bigint_shiftright(&u, 1); + if((a_.wordv[0] & 1) || (b_.wordv[0] & 1)){ + bigint_add_s(&a_, &a_, &y_); + bigint_sub_s(&b_, &b_, &x_); + } + bigint_shiftright(&a_, 1); + bigint_shiftright(&b_, 1); + } + while ((v.wordv[0] & 1) == 0) { + bigint_shiftright(&v, 1); + if((c_.wordv[0] & 1) || (d_.wordv[0] & 1)){ + bigint_add_s(&c_, &c_, &y_); + bigint_sub_s(&d_, &d_, &x_); + } + bigint_shiftright(&c_, 1); + bigint_shiftright(&d_, 1); + } + if(bigint_cmp_u(&u, &v) >= 0){ + bigint_sub_u(&u, &u, &v); + bigint_sub_s(&a_, &a_, &c_); + bigint_sub_s(&b_, &b_, &d_); + }else{ + bigint_sub_u(&v, &v, &u); + bigint_sub_s(&c_, &c_, &a_); + bigint_sub_s(&d_, &d_, &b_); + } + } while(u.length_W); + if(gcd){ + bigint_mul_s(gcd, &v, &g); + } + if(a){ + bigint_copy(a, &c_); + } + if(b){ + bigint_copy(b, &d_); + } +} + +/******************************************************************************/ + +void bigint_inverse(bigint_t *dest, const bigint_t *a, const bigint_t *m){ + bigint_gcdext(NULL, dest, NULL, a, m); + while(dest->info&BIGINT_NEG_MASK){ + bigint_add_s(dest, dest, m); + } +} + +/******************************************************************************/ + +void bigint_changeendianess(bigint_t *a){ + uint8_t t, *p, *q; + p = (uint8_t*)(a->wordv); + q = p + a->length_W * sizeof(bigint_word_t) - 1; + while(plength_W; ++i){ + c1 = ((bigint_wordplus_t)(a->wordv[i])) * ((bigint_wordplus_t)b); + c1 += c0; + a->wordv[i] = (bigint_word_t)c1; + c0 = c1 >> BIGINT_WORD_SIZE; + } + if(c0){ + a->wordv[a->length_W] = (bigint_word_t)c0; + a->length_W += 1; + } + bigint_adjust(a); +} + +/******************************************************************************/ +#if 1 + +void bigint_clip(bigint_t *dest, bigint_length_t length_W){ + if(dest->length_W > length_W){ + dest->length_W = length_W; + } + bigint_adjust(dest); +} +/******************************************************************************/ + +/* + * m_ = m * m'[0] + * dest = (a * b) % m (?) + */ + +void bigint_mont_mul(bigint_t *dest, const bigint_t *a, const bigint_t *b, const bigint_t *m, const bigint_t *m_){ + const bigint_length_t s = MAX(MAX(a->length_W, b->length_W), m->length_W); + bigint_t u, t; + bigint_word_t u_w[s + 2], t_w[s + 2]; + bigint_length_t i; + + if (a->length_W == 0 || b->length_W == 0) { + bigint_set_zero(dest); + return; + } + u.wordv = u_w; + u.info = 0; + u.length_W = 0; + t.wordv = t_w; + for (i = 0; i < a->length_W; ++i) { + bigint_copy(&t, b); + bigint_mul_word_u(&t, a->wordv[i]); + bigint_add_u(&u, &u, &t); + bigint_copy(&t, m_); + if (u.length_W != 0) { + bigint_mul_word_u(&t, u.wordv[0]); + bigint_add_u(&u, &u, &t); + } + bigint_shiftright(&u, BIGINT_WORD_SIZE); + } + for (; i < s; ++i) { + bigint_copy(&t, m_); + if (u.length_W != 0) { + bigint_mul_word_u(&t, u.wordv[0]); + bigint_add_u(&u, &u, &t); + } + bigint_shiftright(&u, BIGINT_WORD_SIZE); + } + bigint_reduce(&u, m); + bigint_copy(dest, &u); +} + +/******************************************************************************/ + +void bigint_mont_red(bigint_t *dest, const bigint_t *a, const bigint_t *m, const bigint_t *m_){ + bigint_t u, t; + bigint_length_t i, s = MAX(a->length_W, m->length_W); + bigint_word_t u_w[s + 2], t_w[s + 2]; + + t.wordv = t_w; + u.wordv = u_w; + if (a->length_W == 0) { + bigint_set_zero(dest); + return; + } + bigint_copy(&u, a); + for (i = 0; i < m->length_W; ++i) { + bigint_copy(&t, m_); + if (u.length_W != 0) { + bigint_mul_word_u(&t, u.wordv[0]); + bigint_add_u(&u, &u, &t); + } + bigint_shiftright(&u, BIGINT_WORD_SIZE); + } + bigint_reduce(&u, m); + bigint_copy(dest, &u); +} + +/******************************************************************************/ +/* + * m_ = m * (- m0^-1 (mod 2^W)) + */ +void bigint_mont_gen_m_(bigint_t* dest, const bigint_t* m){ + bigint_word_t x_w[2], m_w_0[1]; + bigint_t x, m_0; +#if 0 + printf("\nm = "); + bigint_print_hex(m); + uart0_flush(); +#endif + if (m->length_W == 0) { + bigint_set_zero(dest); + return; + } + if ((m->wordv[0] & 1) == 0) { + printf_P(PSTR("ERROR: m must not be even, m = ")); + bigint_print_hex(m); + putchar('\n'); + uart0_flush(); + return; + } + x.wordv = x_w; + x.info = 0; + x.length_W = 2; + x_w[0] = 0; + x_w[1] = 1; + m_0.wordv = m_w_0; + m_0.info = 0; + m_0.length_W = 1; + m_0.wordv[0] = m->wordv[0]; + bigint_adjust(&x); + bigint_adjust(&m_0); +#if 0 + printf("\nm0 = "); + bigint_print_hex(&m_0); + printf("\nx = "); + bigint_print_hex(&x); + uart0_flush(); +#endif + bigint_inverse(dest, &m_0, &x); +#if 0 + printf("\nm0^-1 = "); + bigint_print_hex(dest); + uart0_flush(); +#endif + bigint_sub_s(&x, &x, dest); +#if 0 + printf("\n-m0^-1 = "); + bigint_print_hex(&x); + uart0_flush(); +#endif + bigint_copy(dest, m); + bigint_mul_word_u(dest, x.wordv[0]); +} + +/******************************************************************************/ + +/* + * dest = a * R mod m + */ +void bigint_mont_trans(bigint_t *dest, const bigint_t *a, const bigint_t *m){ + bigint_t t; + bigint_word_t t_w[a->length_W + m->length_W]; + + t.wordv = t_w; + memset(t_w, 0, m->length_W * sizeof(bigint_word_t)); + memcpy(&t_w[m->length_W], a->wordv, a->length_W * sizeof(bigint_word_t)); + t.info = a->info; + t.length_W = a->length_W + m->length_W; + bigint_reduce(&t, m); + bigint_copy(dest, &t); +} + +/******************************************************************************/ + +/* calculate dest = a**exp % r */ +/* using square&multiply */ +void bigint_expmod_u_mont_accel(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r, const bigint_t *m_){ + if(r->length_W == 0) { + return; + } + + bigint_length_t s = r->length_W; + bigint_t res, ax; + bigint_word_t t, res_w[r->length_W * 2], ax_w[MAX(s, a->length_W)]; + bigint_length_t i; + uint8_t j; + + res.wordv = res_w; + ax.wordv = ax_w; + + res.wordv[0] = 1; + res.length_W = 1; + res.info = 0; + bigint_adjust(&res); + if (exp->length_W == 0) { + bigint_copy(dest, &res); + return; + } + bigint_copy(&ax, a); + bigint_reduce(&ax, r); + bigint_mont_trans(&ax, &ax, r); + bigint_mont_trans(&res, &res, r); + uint8_t flag = 0; + t = exp->wordv[exp->length_W - 1]; + for (i = exp->length_W; i > 0; --i) { + t = exp->wordv[i - 1]; + for(j = BIGINT_WORD_SIZE; j > 0; --j){ + if (!flag) { + if(t & (((bigint_wordplus_t)1) << (BIGINT_WORD_SIZE - 1))){ + flag = 1; + } + } + if (flag) { + bigint_square(&res, &res); + bigint_mont_red(&res, &res, r, m_); + if (t & (((bigint_wordplus_t)1) << (BIGINT_WORD_SIZE - 1))) { + bigint_mont_mul(&res, &res, &ax, r, m_); + } + } + t <<= 1; + } + } + SET_POS(&res); + bigint_mont_red(dest, &res, r, m_); +} + +/******************************************************************************/ + +void bigint_expmod_u_mont_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){ + if(r->length_W == 0) { + return; + } + if(a->length_W == 0) { + bigint_set_zero(dest); + return; + } + bigint_t m_; + bigint_word_t m_w_[r->length_W + 1]; + m_.wordv = m_w_; + bigint_mont_gen_m_(&m_, r); + bigint_expmod_u_mont_accel(dest, a, exp, r,&m_); +} + +/******************************************************************************/ + +#endif + +void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){ + if (r->wordv[0] & 1) { + bigint_expmod_u_mont_sam(dest, a, exp, r); + } else { + bigint_expmod_u_sam(dest, a, exp, r); + } +} + + + + + + + + + +