X-Git-Url: https://git.cryptolib.org/?a=blobdiff_plain;f=bigint%2Fbigint.c;h=c5f799e52936b46f6d2d87db52b48df4edbea2d7;hb=d796b12dbb838974705d995369161d3836f9dad2;hp=bf854cc841496a355295fbcafbcf8fd9d8c00075;hpb=3a9f9d918fb95474996af535c225a7e187d88372;p=avr-crypto-lib.git diff --git a/bigint/bigint.c b/bigint/bigint.c index bf854cc..c5f799e 100644 --- a/bigint/bigint.c +++ b/bigint/bigint.c @@ -33,10 +33,11 @@ #include "bigint.h" #include -#define DEBUG 0 +#define DEBUG 1 #if DEBUG || 1 #include "cli.h" +#include "uart_i.h" #include "bigint_io.h" #include #endif @@ -46,34 +47,34 @@ #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 &=~BIGINT_FBS_MASK; (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(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) + 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_W!=0 && a->wordv[a->length_W-1]==0){ + while (a->length_W != 0 && a->wordv[a->length_W - 1] == 0) { a->length_W--; } - if(a->length_W==0){ + if (a->length_W == 0) { a->info=0; return; } bigint_word_t t; - uint8_t i = BIGINT_WORD_SIZE-1; - t = a->wordv[a->length_W-1]; - while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){ - t<<=1; + 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); @@ -81,7 +82,7 @@ void bigint_adjust(bigint_t *a){ /******************************************************************************/ -uint16_t bigint_length_b(const bigint_t *a){ +bigint_length_t bigint_length_b(const bigint_t *a){ if(!a->length_W || a->length_W==0){ return 0; } @@ -90,17 +91,17 @@ uint16_t bigint_length_b(const bigint_t *a){ /******************************************************************************/ -uint16_t bigint_length_B(const bigint_t *a){ +bigint_length_t bigint_length_B(const bigint_t *a){ return a->length_W * sizeof(bigint_word_t); } /******************************************************************************/ uint32_t bigint_get_first_set_bit(const bigint_t *a){ - if(a->length_W==0){ + if(a->length_W == 0) { return (uint32_t)(-1); } - return (a->length_W-1)*sizeof(bigint_word_t)*8+GET_FBS(a); + return (a->length_W-1) * sizeof(bigint_word_t) * CHAR_BIT + GET_FBS(a); } @@ -140,19 +141,18 @@ void bigint_copy(bigint_t *dest, const bigint_t *src){ /* this should be implemented in assembly */ void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ - uint16_t i; + bigint_length_t i; bigint_wordplus_t t = 0LL; - if(a->length_W < b->length_W){ - XCHG_PTR(a,b); + if (a->length_W < b->length_W) { + XCHG_PTR(a, b); } - for(i = 0; i < b->length_W; ++i){ -// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t; + 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(; ilength_W; ++i){ + for(; i < a->length_W; ++i){ t += a->wordv[i]; dest->wordv[i] = (bigint_word_t)t; t >>= BIGINT_WORD_SIZE; @@ -161,13 +161,14 @@ void bigint_add_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ 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){ +void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, bigint_length_t scale){ if(a->length_W == 0){ return; } @@ -192,7 +193,7 @@ void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, uint16_t scale){ bigint_adjust(dest); #else bigint_t s; - uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t); + 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; @@ -219,10 +220,10 @@ void bigint_add_scale_u(bigint_t *dest, const bigint_t *a, uint16_t scale){ /* 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; + int8_t borrow = 0; int8_t r; - bigint_wordplus_signed_t t=0LL; - uint16_t i; + bigint_wordplus_signed_t t = 0; + bigint_length_t i; if(b->length_W == 0){ bigint_copy(dest, a); SET_POS(dest); @@ -249,12 +250,8 @@ void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ t -= b->wordv[i]; } t -= borrow; - dest->wordv[i]=(bigint_word_t)t; - if(t<0){ - borrow = 1; - }else{ - borrow = 0; - } + dest->wordv[i] = (bigint_word_t)t; + borrow = t < 0 ? 1 : 0; } SET_POS(dest); dest->length_W = i; @@ -270,11 +267,11 @@ 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_W==0){ + if(a->length_W == 0){ return 0; } - uint16_t i; - i = a->length_W-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]){ @@ -370,68 +367,68 @@ 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, words_to_shift; +void bigint_shiftleft(bigint_t *a, bigint_length_t shift){ + bigint_length_t byteshift, words_to_shift; int16_t i; uint8_t bitshift; bigint_word_t *p; bigint_wordplus_t t = 0; - if(shift == 0){ + + if (shift == 0) { return; } byteshift = shift / 8; bitshift = shift & 7; - - if(byteshift){ + 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){ + 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){ + 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){ + 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); + 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; bigint_wordplus_t t = 0; byteshift = shift / 8; bitshift = shift & 7; - if(byteshift >= a->length_W * sizeof(bigint_word_t)){ /* we would shift out more than we have */ - bigint_set_zero(a); - return; - } - if(byteshift == a->length_W * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){ + 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, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift); + memset((uint8_t*)&a->wordv[a->length_W] - byteshift, 0, byteshift); } - byteshift /= sizeof(bigint_word_t); /* byteshift is now wordshift */ - a->length_W -= byteshift; - if(bitshift != 0 && a->length_W){ + a->length_W -= byteshift / sizeof(bigint_word_t); + + if(bitshift != 0 && a->length_W){ /* shift to the right */ i = a->length_W - 1; do{ @@ -446,7 +443,7 @@ void bigint_shiftright(bigint_t *a, uint16_t shift){ /******************************************************************************/ void bigint_xor(bigint_t *dest, const bigint_t *a){ - uint16_t i; + bigint_length_t i; for(i=0; ilength_W; ++i){ dest->wordv[i] ^= a->wordv[i]; } @@ -481,7 +478,7 @@ void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ XCHG_PTR(a,b); } bigint_wordplus_t t = 0; - uint16_t i; + 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); @@ -508,7 +505,7 @@ void bigint_mul_u(bigint_t *dest, const bigint_t *a, const bigint_t *b){ return; } /* split a in xh & xl; split b in yh & yl */ - const uint16_t n = (MAX(a->length_W, b->length_W)+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; @@ -591,7 +588,7 @@ 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; @@ -600,7 +597,7 @@ unsigned square_depth = 0; /* 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_W * sizeof(bigint_word_t) <= 4){ + 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; @@ -610,6 +607,7 @@ void bigint_square(bigint_t *dest, const bigint_t *a){ bigint_adjust(dest); return; } + if(dest->wordv == a->wordv){ bigint_t d; bigint_word_t d_b[a->length_W*2]; @@ -618,12 +616,13 @@ void bigint_square(bigint_t *dest, const bigint_t *a){ bigint_copy(dest, &d); return; } - + bigint_fast_square(dest, a); + return; #if DEBUG_SQUARE square_depth += 1; #endif - uint16_t n; + bigint_length_t n; n=(a->length_W+1)/2; bigint_t xh, xl, tmp; /* x-high, x-low, temp */ bigint_word_t buffer[2*n+1]; @@ -682,14 +681,75 @@ void bigint_square(bigint_t *dest, const bigint_t *a){ #endif } +#endif + /******************************************************************************/ -void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale){ +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 uint16_t word_shift = bitscale / BIGINT_WORD_SIZE; + const bigint_length_t word_shift = bitscale / BIGINT_WORD_SIZE; - if(a->length_W < b->length_W + word_shift){ + if (a->length_W < b->length_W + word_shift) { #if DEBUG cli_putstr("\r\nDBG: *bang*\r\n"); #endif @@ -712,60 +772,36 @@ void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale){ /******************************************************************************/ void bigint_reduce(bigint_t *a, const bigint_t *r){ -// bigint_adjust((bigint_t*)r); uint8_t rfbs = GET_FBS(r); -#if DEBUG - cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a); -#endif - if(r->length_W==0 || a->length_W==0){ + 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)); + 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)); + memcpy(a->wordv, &p, a->length_W * sizeof(bigint_word_t)); + a->length_W = r->length_W; bigint_adjust(a); - // cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a); return; } - uint16_t shift; - while(a->length_W > r->length_W){ - shift = (a->length_W - r->length_W) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1; - /* - if((a->wordv[a->length_W-1] & ((1LL< r->wordv[r->length_W-1]){ - // cli_putc('~'); - cli_putstr("\r\n ~ [a] = "); - cli_hexdump_rev(&a->wordv[a->length_W-1], 4); - cli_putstr(" [r] = "); - cli_hexdump_rev(&r->wordv[r->length_W-1], 4); - shift += 1; - } - */ - // cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2); - // cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_W, 2); - // cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_W, 2); - // uart_flush(0); + 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); - // cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a); } - while((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)){ - shift = GET_FBS(a)-rfbs-1; - // cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2); + while ((GET_FBS(a) > rfbs) && (a->length_W == r->length_W)) { + shift = GET_FBS(a) - rfbs - 1; bigint_sub_u_bitscale(a, r, shift); - // cli_putstr("\r\nDBG: (2) = "); bigint_print_hex(a); } } - while(bigint_cmp_u(a,r)>=0){ - bigint_sub_u(a,a,r); -// cli_putstr("\r\nDBG: (3) = "); bigint_print_hex(a); + while (bigint_cmp_u(a, r) >= 0) { + bigint_sub_u(a, a, r); } bigint_adjust(a); -// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a); -// cli_putstr("\r\n"); } /******************************************************************************/ @@ -773,45 +809,41 @@ void bigint_reduce(bigint_t *a, const bigint_t *r){ /* 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 || r->length_W==0){ + if(a->length_W == 0){ + bigint_set_zero(dest); return; } bigint_t res, base; - bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2]; - uint16_t i; + 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; -// uint16_t *xaddr = &i; -// cli_putstr("\r\npre-alloc ("); -// cli_hexdump_rev(&xaddr, 4); -// cli_putstr(") ..."); - res.wordv = res_b; - base.wordv = base_b; + res.wordv = res_w; + base.wordv = base_w; bigint_copy(&base, a); -// cli_putstr("\r\npost-copy"); bigint_reduce(&base, r); - res.wordv[0]=1; - res.length_W=1; + 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[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 & (1<<(BIGINT_WORD_SIZE-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){ + } else { bigint_square(&res, &res); bigint_reduce(&res, r); - if(t & (1 << (BIGINT_WORD_SIZE - 1))){ + if(t & (((bigint_word_t)1) << (BIGINT_WORD_SIZE - 1))){ bigint_mul_u(&res, &res, &base); bigint_reduce(&res, r); } @@ -820,30 +852,15 @@ void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, } } -// cli_putc('+'); SET_POS(&res); bigint_copy(dest, &res); } /******************************************************************************/ -#if 1 -#define cli_putstr(a) -#define cli_putstr_P(a) -#define bigint_print_hex(a) -#define cli_hexdump_rev(a,b) -#define uart_flush(a) -#define printf_P(...) -#endif /* 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){ - uint16_t i = 0; - printf_P(PSTR("\nDBG: gcdext( ")); - bigint_print_hex(x); - printf_P(PSTR(", ")); - bigint_print_hex(y); - printf_P(PSTR(")\n")); + bigint_length_t i = 0; if(x->length_W == 0 || y->length_W == 0){ - printf_P(PSTR("\nDBG: got zero in gcd <%s %s %d>\n"), __FILE__, __func__, __LINE__); if(gcd){ bigint_set_zero(gcd); } @@ -940,14 +957,8 @@ void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, c d_.info = 0; bigint_set_zero(&b_); bigint_set_zero(&c_); - printf_P(PSTR("\nloop: x_ = ")); - bigint_print_hex(&x_); - printf_P(PSTR("; y_ = ")); - bigint_print_hex(&y_); - do{ - printf_P(PSTR("\nDBG (gcdext) 0")); - while((u.wordv[0] & 1) == 0){ - printf_P(PSTR("\nDBG (gcdext) 0.1")); + 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_); @@ -955,47 +966,26 @@ void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, c } bigint_shiftright(&a_, 1); bigint_shiftright(&b_, 1); - printf_P(PSTR(" a_ = ")); - bigint_print_hex(&a_); - printf_P(PSTR("; b_ = ")); - bigint_print_hex(&b_); } - while((v.wordv[0] & 1) == 0){ - printf_P(PSTR("\nDBG (gcdext) 0.2")); - bigint_shiftright(&v, 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_); } - printf_P(PSTR(" c* = ")); - bigint_print_hex(&c_); bigint_shiftright(&c_, 1); bigint_shiftright(&d_, 1); - printf_P(PSTR(" c_ = ")); - bigint_print_hex(&c_); - printf_P(PSTR("; d_ = ")); - bigint_print_hex(&d_); } if(bigint_cmp_u(&u, &v) >= 0){ - printf_P(PSTR("\nDBG (gcdext) 0.3")); bigint_sub_u(&u, &u, &v); bigint_sub_s(&a_, &a_, &c_); bigint_sub_s(&b_, &b_, &d_); - printf_P(PSTR(" a_ = ")); - bigint_print_hex(&a_); - printf_P(PSTR("; b_ = ")); - bigint_print_hex(&b_); }else{ - printf_P(PSTR("\nDBG (gcdext) 0.4")); bigint_sub_u(&v, &v, &u); bigint_sub_s(&c_, &c_, &a_); bigint_sub_s(&d_, &d_, &b_); - printf_P(PSTR(" c_ = ")); - bigint_print_hex(&c_); - printf_P(PSTR("; d_ = ")); - bigint_print_hex(&d_); } - }while(u.length_W); + } while(u.length_W); if(gcd){ bigint_mul_s(gcd, &v, &g); } @@ -1032,13 +1022,263 @@ void bigint_changeendianess(bigint_t *a){ /******************************************************************************/ +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); +} + +/******************************************************************************/ +#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){ - bigint_expmod_u_sam(dest, a, exp, r); + if (r->wordv[0] & 1) { + bigint_expmod_u_mont_sam(dest, a, exp, r); + } else { + bigint_expmod_u_sam(dest, a, exp, r); + } }