X-Git-Url: https://git.cryptolib.org/?p=avr-crypto-lib.git;a=blobdiff_plain;f=bigint%2Fbigint.c;h=676f149eb9d542cd27cd6caf703e2651fe04115a;hp=7dd841b22a867c79be8d47c0e2983163dcf5ffad;hb=4b5da1dc27a791b5c448274a3db09cd035b33493;hpb=ca25e57ca6a74d6e26cad823d45fcc4604689fa1 diff --git a/bigint/bigint.c b/bigint/bigint.c index 7dd841b..676f149 100644 --- a/bigint/bigint.c +++ b/bigint/bigint.c @@ -1,7 +1,7 @@ /* bigint.c */ /* - This file is part of the AVR-Crypto-Lib. - Copyright (C) 2008 Daniel Otte (daniel.otte@rub.de) + This file is part of the ARM-Crypto-Lib. + Copyright (C) 2006-2015 Daniel Otte (bg@nerilex.org) This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by @@ -26,45 +26,78 @@ */ +#define STRING2(x) #x +#define STRING(x) STRING2(x) +#define STR_LINE STRING(__LINE__) + #include "bigint.h" #include +#include -#include "bigint_io.h" +#define PREFERE_HEAP_SPACE 1 + +#if PREFERE_HEAP_SPACE +#include + +#define ALLOC_BIGINT_WORDS(var,words) \ + bigint_word_t *(var) = malloc((words) * sizeof(bigint_word_t)); \ + if (!(var)) { \ + puts_P(PSTR("\n\nDBG: OOM ERROR (in arithmeics)!\n")); \ + uart0_flush(); \ + for(;;) \ + ; \ + } + +#define FREE(x) free(x) + +#else + +#define ALLOC_BIGINT_WORDS(var,words) bigint_word_t var[words] +#define FREE(x) + +#endif + +#define DEBUG 1 + +#if DEBUG #include "cli.h" +#include "uart_i.h" +#include "bigint_io.h" +#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); @@ -72,145 +105,199 @@ 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); - return; - } - if(b->length_B==0){ - dest->length_B = a->length_B; - memcpy(dest->wordv, a->wordv, a->length_B); - dest->info = a->info; + bigint_wordplus_signed_t t = 0; + bigint_length_t i; + if(b->length_W == 0){ + bigint_copy(dest, a); SET_POS(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(a->length_W == 0){ + bigint_copy(dest, b); + SET_NEG(dest); + return; } - if(r<0){ + 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); - }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(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; @@ -222,7 +309,7 @@ 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; @@ -248,7 +335,7 @@ 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; @@ -275,9 +362,9 @@ 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_B==0 && b->length_B==0){ + if(a->length_W==0 && b->length_W==0){ return 0; } s = GET_SIGN(a)?2:0; @@ -303,78 +390,122 @@ 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; - 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; - byteshift++; - }else{ /* shift to the right */ - for(i=a->length_B+byteshift-1; i>byteshift-1; --i){ - t |= (a->wordv[i])<<(bitshift); - a->wordv[i] = (uint8_t)(t>>8); - t <<= 8; - } - t |= (a->wordv[i])<<(bitshift); - a->wordv[i] = (uint8_t)(t>>8); - } - } - a->length_B += byteshift; - bigint_adjust(a); +void bigint_shiftleft_bits(bigint_t *a, uint8_t shift) { + bigint_length_t i; + bigint_wordplus_t t = 0; + + for (i = 0; i < a->length_W; ++i) { + t |= ((bigint_wordplus_t)a->wordv[i]) << shift; + a->wordv[i] = (bigint_word_t)t; + t >>= BIGINT_WORD_SIZE; + } + if (t) { + a->wordv[a->length_W++] = (bigint_word_t)t; + } + bigint_adjust(a); } /******************************************************************************/ -void bigint_shiftright(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; 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 */ - bigint_set_zero(a); + + if (a->length_W == 0 || shift == 0) { return; } - if(byteshift == a->length_B-1 && bitshift>GET_FBS(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); + a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t); + } + + if (bitshift == 0) { + bigint_adjust(a); + } else { + bigint_shiftleft_bits(a, bitshift); + } +} + +/******************************************************************************/ + +void bigint_shiftright_bits(bigint_t *a, uint8_t shift){ + bigint_length_t i; + bigint_wordplus_t t = 0; + + i = a->length_W; + while (i--) { + t |= ((bigint_wordplus_t)(a->wordv[i])) << (BIGINT_WORD_SIZE - shift); + a->wordv[i] = (bigint_word_t)(t >> BIGINT_WORD_SIZE); + t <<= BIGINT_WORD_SIZE; + } + + bigint_adjust(a); +} + +/******************************************************************************/ + +void bigint_shiftright_1bit(bigint_t *a){ + bigint_length_t i; + bigint_word_t t1 = 0, t2; + + i = a->length_W; + while (i--) { + t2 = a->wordv[i] & 1; + a->wordv[i] >>= 1; + a->wordv[i] |= t1; + t1 = t2 << (BIGINT_WORD_SIZE - 1); + } + bigint_adjust(a); +} + +/******************************************************************************/ + +void bigint_shiftright_1word(bigint_t *a){ + if (a->length_W == 0) { + return; + } + memmove(a->wordv, &a->wordv[1], (a->length_W - 1) * sizeof(bigint_word_t)); + a->length_W--; +} + +/******************************************************************************/ + +void bigint_shiftright(bigint_t *a, bigint_length_t shift){ + bigint_length_t byteshift = shift / 8; + uint8_t bitshift = shift & 7; + + if (a->length_W == 0) { + return; + } + + 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); - } - if(bitshift!=0){ - /* 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); + 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); + bigint_adjust(a); + } + + if(bitshift != 0){ + bigint_shiftright_bits(a, bitshift); } - 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); @@ -382,108 +513,119 @@ 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(dest==a || dest==b){ +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); + return; + } + if (dest == a || dest == b) { bigint_t d; - uint8_t d_b[a->length_B+b->length_B]; + 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_B==0 || b->length_B==0){ - bigint_set_zero(dest); - return; - } - if(a->length_B==1 || b->length_B==1){ - if(a->length_B!=1){ + 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){ - uint32_t p=0, q=0; + 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; - }else{ - xl.length_B=n; + if (a->length_W <= n) { + bigint_set_zero(&xh); + xl.length_W = a->length_W; + xl.info = a->info; + } else { + 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; + } else { + 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 + */ + ALLOC_BIGINT_WORDS(tmp_w, 2 * n + 2); + ALLOC_BIGINT_WORDS(m_w, 2 * n + 2); bigint_t tmp, tmp2, m; - tmp.wordv = tmp_b; - 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 <= tmp2*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); + tmp.wordv = tmp_w; + tmp2.wordv = &(tmp_w[n + 1]); + m.wordv = m_w; + + 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) */ + FREE(m_w); + FREE(tmp_w); } /******************************************************************************/ -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; @@ -511,113 +653,123 @@ void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ /******************************************************************************/ -/* 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); - SET_POS(dest); - dest->length_B=2*a->length_B; - bigint_adjust(dest); - return; - } - if(dest==a){ - bigint_t d; - uint8_t d_b[a->length_B*2]; - d.wordv = d_b; - bigint_square(&d, a); - bigint_copy(dest, &d); - return; - } - uint16_t n; - n=(a->length_B+1)/2; - bigint_t xh, xl, tmp; /* x-high, x-low, temp */ - uint8_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; - tmp.wordv = buffer; - bigint_square(dest, &xl); - bigint_square(&tmp, &xh); - bigint_add_scale_u(dest, &tmp, 2*n); - bigint_mul_u(&tmp, &xl, &xh); - bigint_shiftleft(&tmp, 1); - bigint_add_scale_u(dest, &tmp, n); +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; + ALLOC_BIGINT_WORDS(d_w, a->length_W * 2); + d.wordv = d_w; + bigint_square(&d, a); + bigint_copy(dest, &d); + FREE(d_w); + 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, uint16_t bitscale){ - bigint_t tmp; - uint8_t tmp_b[b->length_B+1]; - uint16_t i,j,byteshift=bitscale/8; - uint8_t borrow=0; - int16_t t; +void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale){ + bigint_t tmp, x; + const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE; - if(a->length_B < b->length_B+byteshift){ - cli_putstr_P(PSTR("\r\nERROR: bigint_sub_u_bitscale result negative")); + 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; + ALLOC_BIGINT_WORDS(tmp_w, b->length_W + 1); + tmp.wordv = tmp_w; bigint_copy(&tmp, b); - bigint_shiftleft(&tmp, bitscale&7); - - for(j=0,i=byteshift; iwordv[i] - tmp.wordv[j] - borrow; - a->wordv[i] = (uint8_t)t; - if(t<0){ - borrow = 1; - }else{ - borrow = 0; - } - } - while(borrow){ - if(i+1 > a->length_B){ - cli_putstr_P(PSTR("\r\nERROR: bigint_sub_u_bitscale result negative (2) shift=")); - cli_hexdump_rev(&bitscale, 2); - bigint_set_zero(a); - return; - } - a->wordv[i] -= borrow; - if(a->wordv[i]!=0xff){ - borrow=0; - } - ++i; - } + bigint_shiftleft_bits(&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); + FREE(tmp_w); bigint_adjust(a); + return; } /******************************************************************************/ -void bigint_reduce(bigint_t* a, const bigint_t* r){ +void bigint_reduce(bigint_t *a, const bigint_t *r){ uint8_t rfbs = GET_FBS(r); -/* - cli_putstr_P(PSTR("\r\nreduce ")); - bigint_print_hex(a); - cli_putstr_P(PSTR(" % ")); - bigint_print_hex(r); - cli_putstr_P(PSTR("\r\n")); -*/ - - if(r->length_B==0){ + if (r->length_W == 0 || a->length_W == 0) { return; } - while(a->length_B > r->length_B){ - bigint_sub_u_bitscale(a, r, (a->length_B-r->length_B)*8+GET_FBS(a)-rfbs-1); - } - while((GET_FBS(a) > rfbs+1) && (a->length_B == r->length_B)){ - bigint_sub_u_bitscale(a, r, GET_FBS(a)-rfbs-1); + 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); + while (bigint_cmp_u(a, r) >= 0) { + bigint_sub_u(a, a, r); } bigint_adjust(a); } @@ -626,183 +778,192 @@ void bigint_reduce(bigint_t* a, const bigint_t* r){ /* calculate dest = a**exp % r */ /* using square&multiply */ -void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, const bigint_t* r){ - bigint_t tmp, tmp2, x; - uint8_t x_b[MAX(r->length_B, a->length_B)], tmp_b[r->length_B*2], tmp2_b[r->length_B*2]; - int16_t i; - uint8_t j; - x.wordv = x_b; - tmp.wordv = tmp_b; - tmp2.wordv = tmp2_b; - bigint_copy(&x, a); - bigint_reduce(&x, r); - bigint_copy(&tmp, &x); - if(a->length_B==0 || exp->length_B==0 || r->length_B==0){ +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; } - i=exp->length_B-1; - if(exp->wordv[i]!=1){ - for(j=1<<(GET_FBS(exp)-1); j>0; j>>=1){ - // cli_putc('Q'); - bigint_square(&tmp2, &tmp); - bigint_reduce(&tmp2, r); - if(exp->wordv[i]&j){ - // cli_putc('M'); - bigint_mul_u(&tmp, &tmp2, &x); - bigint_reduce(&tmp, r); - }else{ - bigint_copy(&tmp, &tmp2); - } - } - } - for(--i; i>=0; --i){ - for(j=0x80; j>0; j>>=1){ -// cli_putc('q'); - bigint_square(&tmp2, &tmp); - bigint_reduce(&tmp2, r); - if(exp->wordv[i]&j){ -// cli_putc('m'); - bigint_mul_u(&tmp, &tmp2, &x); - bigint_reduce(&tmp, r); - }else{ - bigint_copy(&tmp, &tmp2); + + if(exp->length_W == 0){ + dest->info = 0; + dest->length_W = 1; + dest->wordv[0] = 1; + return; + } + + bigint_t res, base; + bigint_word_t t; + bigint_length_t i; + uint8_t j; + + ALLOC_BIGINT_WORDS(base_w, MAX(a->length_W, r->length_W)); + ALLOC_BIGINT_WORDS(res_w, r->length_W * 2); + + 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); + 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; } } -// cli_putstr_P(PSTR("\r\n")); - bigint_copy(dest, &tmp); + + SET_POS(&res); + bigint_copy(dest, &res); + FREE(res_w); + FREE(base_w); } -#define DEBUG 0 + /******************************************************************************/ /* 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_t g, x_, y_, u, v, a_, b_, c_, d_; - volatile uint16_t i=0; - if(x->length_B==0 || y->length_B==0){ +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){ + + while(x->wordv[i] == 0 && y->wordv[i] == 0){ ++i; } - uint8_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i]; - uint8_t u_b[x->length_B-i], v_b[y->length_B-i]; - uint8_t a_b[y->length_B+2], c_b[y->length_B+2]; - uint8_t b_b[x->length_B+2], d_b[x->length_B+2]; - - g.wordv = g_b; - x_.wordv = x_b; - y_.wordv = y_b; - memset(g_b, 0, i); - g_b[i]=1; - g.length_B = i+1; - g.info=0; + + ALLOC_BIGINT_WORDS(g_w, i + 2); + ALLOC_BIGINT_WORDS(x_w, x->length_W - i); + ALLOC_BIGINT_WORDS(y_w, y->length_W - i); + ALLOC_BIGINT_WORDS(u_w, x->length_W - i); + ALLOC_BIGINT_WORDS(v_w, y->length_W - i); + ALLOC_BIGINT_WORDS(a_w, y->length_W + 2); + ALLOC_BIGINT_WORDS(c_w, y->length_W + 2); + ALLOC_BIGINT_WORDS(b_w, x->length_W + 2); + ALLOC_BIGINT_WORDS(d_w, x->length_W + 2); + + bigint_t g, x_, y_, u, v, a_, b_, c_, d_; + + g.wordv = g_w; + x_.wordv = x_w; + y_.wordv = y_w; + memset(g_w, 0, i * sizeof(bigint_word_t)); + g_w[i] = 1; + g.length_W = i + 1; + g.info = 0; x_.info = y_.info = 0; - x_.length_B = x->length_B-i; - y_.length_B = y->length_B-i; - memcpy(x_.wordv, x->wordv+i, x_.length_B); - memcpy(y_.wordv, y->wordv+i, y_.length_B); - for(i=0; (x_.wordv[0]&(1<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] & ((bigint_word_t)1 << i)) == 0 && (y_.wordv[0] & ((bigint_word_t)1 << i)) == 0; ++i) + ; -#if DEBUG - cli_putstr_P(PSTR("\r\nDBG: initshift = ")); - cli_hexdump_rev(&i, 2); -#endif bigint_adjust(&x_); bigint_adjust(&y_); if(i){ - bigint_shiftleft(&g, i); -#if DEBUG - cli_putstr_P(PSTR("\r\nDBG: initshift (2) = ")); - cli_hexdump_rev(&i, 2); - cli_putstr_P(PSTR("\r\n x' = ")); - bigint_print_hex(&x_); - cli_putstr_P(PSTR("\r\n y' = ")); - bigint_print_hex(&y_); -#endif - bigint_shiftright(&x_, i); - bigint_shiftright(&y_, i); -#if DEBUG - cli_putstr_P(PSTR("\r\n x' = ")); - bigint_print_hex(&x_); - cli_putstr_P(PSTR("\r\n y' = ")); - bigint_print_hex(&y_); -#endif + bigint_shiftleft_bits(&g, i); + bigint_shiftright_bits(&x_, i); + bigint_shiftright_bits(&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; + + u.wordv = u_w; + v.wordv = v_w; + a_.wordv = a_w; + b_.wordv = b_w; + c_.wordv = c_w; + d_.wordv = d_w; bigint_copy(&u, &x_); bigint_copy(&v, &y_); a_.wordv[0] = 1; - a_.length_B = 1; + a_.length_W = 1; a_.info = 0; d_.wordv[0] = 1; - d_.length_B = 1; + d_.length_W = 1; d_.info = 0; bigint_set_zero(&b_); bigint_set_zero(&c_); - do{ -#if DEBUG - cli_putstr_P(PSTR("\r\n while u%2==0; u = ")); - bigint_print_hex(&u); - cli_putstr_P(PSTR("\r\nDBG: (10) a = ")); - bigint_print_hex(&a_); - cli_putstr_P(PSTR("\r\nDBG: (10) b = ")); - bigint_print_hex(&b_); - cli_putstr_P(PSTR("\r\nDBG: (10) c = ")); - bigint_print_hex(&c_); - cli_putstr_P(PSTR("\r\nDBG: (10) d = ")); - bigint_print_hex(&d_); -#endif - while((u.wordv[0]&1)==0){ - bigint_shiftright(&u, 1); - if((a_.wordv[0]&1) || (b_.wordv[0]&1)){ + do { + while ((u.wordv[0] & 1) == 0) { + bigint_shiftright_1bit(&u); + 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); + bigint_shiftright_1bit(&a_); + bigint_shiftright_1bit(&b_); } -#if DEBUG - cli_putstr_P(PSTR("\r\n while v%2==0; v = ")); - bigint_print_hex(&v); - cli_putstr_P(PSTR("\r\nDBG: (20) a = ")); - bigint_print_hex(&a_); - cli_putstr_P(PSTR("\r\nDBG: (20) b = ")); - bigint_print_hex(&b_); - cli_putstr_P(PSTR("\r\nDBG: (20) c = ")); - bigint_print_hex(&c_); - cli_putstr_P(PSTR("\r\nDBG: (20) d = ")); - bigint_print_hex(&d_); -#endif - while((v.wordv[0]&1)==0){ - bigint_shiftright(&v, 1); - if((c_.wordv[0]&1) || (d_.wordv[0]&1)){ + while ((v.wordv[0] & 1) == 0) { + bigint_shiftright_1bit(&v); + 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); - + bigint_shiftright_1bit(&c_); + bigint_shiftright_1bit(&d_); } -#if DEBUG - cli_putstr_P(PSTR("\r\n if u>=v ...")); - cli_putstr_P(PSTR("\r\nDBG: (30) a = ")); - bigint_print_hex(&a_); - cli_putstr_P(PSTR("\r\nDBG: (30) b = ")); - bigint_print_hex(&b_); - cli_putstr_P(PSTR("\r\nDBG: (30) c = ")); - bigint_print_hex(&c_); - cli_putstr_P(PSTR("\r\nDBG: (30) d = ")); - bigint_print_hex(&d_); -#endif - if(bigint_cmp_u(&u, &v)>=0){ + 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_); @@ -811,27 +972,7 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c bigint_sub_s(&c_, &c_, &a_); bigint_sub_s(&d_, &d_, &b_); } -#if DEBUG - if(GET_SIGN(&u)){ - cli_putstr_P(PSTR("\r\nDBG: u negative! u = ")); - bigint_print_hex(&u); - } - if(GET_SIGN(&v)){ - cli_putstr_P(PSTR("\r\nDBG: v negative! v = ")); - bigint_print_hex(&v); - } -#endif -/* - cli_putstr_P(PSTR("\r\nDBG: (2) a = ")); - bigint_print_hex(&a_); - cli_putstr_P(PSTR("\r\nDBG: (2) b = ")); - bigint_print_hex(&b_); - cli_putstr_P(PSTR("\r\nDBG: (2) c = ")); - bigint_print_hex(&c_); - cli_putstr_P(PSTR("\r\nDBG: (2) d = ")); - bigint_print_hex(&d_); -*/ - }while(u.length_B); + } while(u.length_W); if(gcd){ bigint_mul_s(gcd, &v, &g); } @@ -841,25 +982,305 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c if(b){ bigint_copy(b, &d_); } + + FREE(d_w); + FREE(b_w); + FREE(c_w); + FREE(a_w); + FREE(v_w); + FREE(u_w); + FREE(y_w); + FREE(x_w); + FREE(g_w); } /******************************************************************************/ -void bigint_inverse(bigint_t* dest, bigint_t* a, bigint_t* m){ +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(p < q){ + t = *p; + *p = *q; + *q = t; + ++p; --q; + } +} + +/******************************************************************************/ + +void bigint_mul_word_u(bigint_t *a, bigint_word_t b){ + bigint_wordplus_t c0 = 0, c1 = 0; + bigint_length_t i; + + if(b == 0){ + bigint_set_zero(a); + return; + } + + for(i = 0; i < a->length_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); +} + +/******************************************************************************/ + +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_length_t i; + + if (a->length_W == 0 || b->length_W == 0) { + bigint_set_zero(dest); + return; + } + ALLOC_BIGINT_WORDS(u_w, s + 2); + ALLOC_BIGINT_WORDS(t_w, s + 2); + 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_1word(&u); + } + 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_1word(&u); + } + bigint_reduce(&u, m); + bigint_copy(dest, &u); + FREE(t_w); + FREE(u_w); +} + +/******************************************************************************/ + +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, MAX(m->length_W, m_->length_W)); + + if (a->length_W == 0) { + bigint_set_zero(dest); + return; + } + + ALLOC_BIGINT_WORDS(u_w, s + 2); + ALLOC_BIGINT_WORDS(t_w, s + 2); + t.wordv = t_w; + u.wordv = u_w; + 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_1word(&u); + } + bigint_reduce(&u, m); + bigint_copy(dest, &u); + FREE(t_w); + FREE(u_w); +} + +/******************************************************************************/ +/* + * 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 (m->length_W == 0) { + bigint_set_zero(dest); + return; + } + if ((m->wordv[0] & 1) == 0) { +#if DEBUG + printf_P(PSTR("ERROR: m must not be even, m = ")); + bigint_print_hex(m); + putchar('\n'); + uart0_flush(); +#endif + 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); + bigint_inverse(dest, &m_0, &x); + bigint_sub_s(&x, &x, dest); + 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; + + ALLOC_BIGINT_WORDS(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); + FREE(t_w); +} +/******************************************************************************/ +/* 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_t res, ax; + bigint_word_t t; + bigint_length_t i; + uint8_t j; + + if (exp->length_W == 0) { + dest->length_W = 1; + dest->info = 0; + dest->wordv[0] = 1; + return; + } + + ALLOC_BIGINT_WORDS(res_w, r->length_W * 2); + ALLOC_BIGINT_WORDS(ax_w, MAX(r->length_W, a->length_W)); + + res.wordv = res_w; + ax.wordv = ax_w; + + res.wordv[0] = 1; + res.length_W = 1; + res.info = 0; + + 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_word_t)1) << (BIGINT_WORD_SIZE - 1))){ + flag = 1; + } + } + if (flag) { + bigint_square(&res, &res); + bigint_mont_red(&res, &res, r, m_); + if (t & (((bigint_word_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_); + FREE(ax_w); + FREE(res_w); +} +/******************************************************************************/ +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_); +} +/******************************************************************************/ + +void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r){ +#if 0 + printf("\nDBG: expmod_u (a ** e %% m) <%s %s %d>\n\ta: ", __FILE__, __func__, __LINE__); + bigint_print_hex(a); + printf("\n\te: "); + bigint_print_hex(exp); + printf("\n\tm: "); + bigint_print_hex(r); +#endif + if (r->wordv[0] & 1) { + bigint_expmod_u_mont_sam(dest, a, exp, r); + } else { + bigint_expmod_u_sam(dest, a, exp, r); + } +}