X-Git-Url: https://git.cryptolib.org/avr-crypto-lib.git?a=blobdiff_plain;f=bigint%2Fbigint.c;h=7ba80b3180eee62ac09300b989e8404f85212617;hb=872dff3138536a68b6dd96b182a386d242bee6cb;hp=3c0bb533c1bdb13bf23a81c9d92d892d80e54bfc;hpb=27f4804c185ae24b3b6367bb2fdb898d6692d0f6;p=avr-crypto-lib.git diff --git a/bigint/bigint.c b/bigint/bigint.c index 3c0bb53..7ba80b3 100644 --- a/bigint/bigint.c +++ b/bigint/bigint.c @@ -35,9 +35,10 @@ #define DEBUG 0 -#if DEBUG +#if DEBUG || 1 #include "cli.h" #include "bigint_io.h" +#include #endif #ifndef MAX @@ -61,16 +62,16 @@ /******************************************************************************/ void bigint_adjust(bigint_t* a){ - while(a->length_B!=0 && a->wordv[a->length_B-1]==0){ - a->length_B--; + 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; } bigint_word_t t; uint8_t i = BIGINT_WORD_SIZE-1; - t = a->wordv[a->length_B-1]; + t = a->wordv[a->length_W-1]; while((t&(1L<<(BIGINT_WORD_SIZE-1)))==0 && i){ t<<=1; i--; @@ -81,25 +82,25 @@ void bigint_adjust(bigint_t* a){ /******************************************************************************/ uint16_t bigint_length_b(const bigint_t* a){ - if(!a->length_B || a->length_B==0){ + if(!a->length_W || a->length_W==0){ return 0; } - return (a->length_B-1) * BIGINT_WORD_SIZE + GET_FBS(a); + return (a->length_W-1) * BIGINT_WORD_SIZE + GET_FBS(a); } /******************************************************************************/ uint16_t bigint_length_B(const bigint_t* a){ - return a->length_B * sizeof(bigint_word_t); + return a->length_W * sizeof(bigint_word_t); } /******************************************************************************/ uint32_t bigint_get_first_set_bit(const bigint_t* a){ - if(a->length_B==0){ + if(a->length_W==0){ return (uint32_t)(-1); } - return (a->length_B-1)*sizeof(bigint_word_t)*8+GET_FBS(a); + return (a->length_W-1)*sizeof(bigint_word_t)*8+GET_FBS(a); } @@ -109,10 +110,10 @@ uint32_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_B==0){ + if(a->length_W==0){ return (uint32_t)(-1); } - while(a->wordv[r]==0 && rlength_B){ + while(a->wordv[r]==0 && rlength_W){ ++r; } if(a->wordv[r] == 0){ @@ -128,8 +129,10 @@ uint32_t bigint_get_last_set_bit(const bigint_t* a){ /******************************************************************************/ void bigint_copy(bigint_t* dest, const bigint_t* src){ - memcpy(dest->wordv, src->wordv, src->length_B*sizeof(bigint_word_t)); - dest->length_B = src->length_B; + 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; } @@ -139,16 +142,17 @@ void bigint_copy(bigint_t* dest, const bigint_t* src){ void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ uint16_t i; bigint_wordplus_t t = 0LL; - if(a->length_B < b->length_B){ + if(a->length_W < b->length_W){ XCHG_PTR(a,b); } - for(i = 0; i < b->length_B; ++i){ + for(i = 0; i < b->length_W; ++i){ +// t = (bigint_wordplus_t)(a->wordv[i]) + (bigint_wordplus_t)(b->wordv[i]) + t; t += a->wordv[i]; t += b->wordv[i]; dest->wordv[i] = (bigint_word_t)t; t >>= BIGINT_WORD_SIZE; } - for(; i < a->length_B; ++i){ + for(; ilength_W; ++i){ t += a->wordv[i]; dest->wordv[i] = (bigint_word_t)t; t >>= BIGINT_WORD_SIZE; @@ -156,7 +160,7 @@ void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ if(t){ dest->wordv[i++] = (bigint_word_t)t; } - dest->length_B = i; + dest->length_W = i; bigint_adjust(dest); } @@ -164,100 +168,51 @@ void bigint_add_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ /* this should be implemented in assembly */ void bigint_add_scale_u(bigint_t* dest, const bigint_t* a, uint16_t scale){ - if(a->length_B == 0){ + if(a->length_W == 0){ return; } if(scale == 0){ bigint_add_u(dest, dest, a); return; } -#if DEBUG_ADD_SCALE - cli_putstr_P(PSTR("\r\nDBG: bigint_add_scale(")); - bigint_print_hex(dest); - cli_putc(','); - bigint_print_hex(dest); - cli_putc(','); - cli_hexdump_rev(&scale, 2); - cli_putc(')'); -#endif -#if BIGINT_WORD_SIZE == 8 - if(scale >= dest->length_B){ -#if DEBUG_ADD_SCALE - cli_putstr_P(PSTR("\r\n\tpath one")); -#endif - memset(dest->wordv + dest->length_B, 0, scale - dest->length_B); - memcpy(dest->wordv + scale, a->wordv, a->length_B); - dest->info = a->info; - dest->length_B = a->length_B + scale; - return; - } bigint_t x; -#if DEBUG_ADD_SCALE - cli_putstr_P(PSTR("\r\n\tpath two")); -#endif - x.length_B = dest->length_B - scale; - x.info = dest->info; +#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_B = x.length_B + scale; + dest->length_W = x.length_W + scale; dest->info = 0; bigint_adjust(dest); #else bigint_t s; uint16_t word_shift = scale / sizeof(bigint_word_t), byte_shift = scale % sizeof(bigint_word_t); - bigint_word_t bv[a->length_B + 1]; + bigint_word_t bv[a->length_W + 1]; s.wordv = bv; - bv[0] = bv[a->length_B] = 0; - memcpy((uint8_t*)bv + byte_shift, a->wordv, a->length_B * sizeof(bigint_word_t)); - s.length_B = a->length_B + 1; + 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_B, 0, (MAX(dest->length_B, s.length_B + word_shift) - dest->length_B) * sizeof(bigint_word_t)); + 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_B = dest->length_B - word_shift; - if((int16_t)x.length_B < 0){ - x.length_B = 0; + 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_B = x.length_B + word_shift; + dest->length_W = x.length_W + word_shift; dest->info = 0; bigint_adjust(dest); #endif - - -/* uint16_t i,j=0; - uint16_t scale_w; - bigint_word_t *dst; - bigint_wordplus_t t=0; - scale_w = (scale+sizeof(bigint_word_t)-1)/sizeof(bigint_word_t); - if(scale>dest->length_B*sizeof(bigint_word_t)){ - memset(((uint8_t*)dest->wordv)+dest->length_B*sizeof(bigint_word_t), 0, scale-dest->length_B*sizeof(bigint_word_t)); - } - // a->wordv = (const uint32_t*)(((uint8_t*)a->wordv)+(scale&3)); - dst = dest->wordv + (scale&(sizeof(bigint_word_t)-1)); - for(i=scale/sizeof(bigint_word_t); ilength_B+scale_w; ++i,++j){ - t += a->wordv[j]; - if(dest->length_B>i){ - t += dst[i]; - } - dst[i] = (bigint_word_t)t; - t>>=BIGINT_WORD_SIZE; - } - while(t){ - if(dest->length_B>i){ - t += dst[i]; - } - dst[i] = (bigint_word_t)t; - t>>=BIGINT_WORD_SIZE; - ++i; - } - if(dest->length_B < i){ - dest->length_B = i; - } - bigint_adjust(dest); - */ } /******************************************************************************/ @@ -268,29 +223,29 @@ void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ int8_t r; bigint_wordplus_signed_t t=0LL; uint16_t i; - r = bigint_cmp_u(a,b); - if(r==0){ - bigint_set_zero(dest); - return; - } - if(b->length_B==0){ + if(b->length_W == 0){ bigint_copy(dest, a); SET_POS(dest); return; } - if(a->length_B==0){ + 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); return; } - for(i=0; i < a->length_B; ++i){ + for(i = 0; i < a->length_W; ++i){ t = a->wordv[i]; - if(i < b->length_B){ + if(i < b->length_W){ t -= b->wordv[i]; } t -= borrow; @@ -302,24 +257,24 @@ void bigint_sub_u(bigint_t* dest, const bigint_t* a, const bigint_t* b){ } } SET_POS(dest); - dest->length_B = i; + 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){ + 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; + i = a->length_W-1; do{ if(a->wordv[i] != b->wordv[i]){ if(a->wordv[i] > b->wordv[i]){ @@ -389,7 +344,7 @@ 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){ 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; @@ -420,29 +375,34 @@ void bigint_shiftleft(bigint_t* a, uint16_t shift){ int16_t i; uint8_t bitshift; bigint_word_t *p; - bigint_wordplus_t t=0; + bigint_wordplus_t t = 0; if(shift == 0){ return; } byteshift = shift / 8; bitshift = shift & 7; - memset(&a->wordv[a->length_B], 0x00, byteshift); + if(byteshift){ - memmove(((uint8_t*)a->wordv)+byteshift, a->wordv, a->length_B * sizeof(bigint_word_t)); + memmove(((uint8_t*)a->wordv) + byteshift, a->wordv, a->length_W * sizeof(bigint_word_t)); memset(a->wordv, 0, byteshift); } - if(bitshift != 0){ - p = (bigint_word_t*)((uint8_t*)a->wordv + byteshift / sizeof(bigint_word_t)); - words_to_shift = a->length_B + ((byteshift % sizeof(bigint_word_t))?1:0); - /* XXX */ - 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; - } - p[i] = (bigint_word_t)t; + if(bitshift == 0){ + a->length_W += (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t); + bigint_adjust(a); + return; } - a->length_B += (shift + BIGINT_WORD_SIZE - 1) / BIGINT_WORD_SIZE; + 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); } @@ -452,26 +412,28 @@ void bigint_shiftright(bigint_t* a, uint16_t shift){ uint16_t byteshift; uint16_t i; uint8_t bitshift; - bigint_wordplus_t t=0; - byteshift = shift/8; - bitshift = shift&7; - if(byteshift >= a->length_B * sizeof(bigint_word_t)){ /* we would shift out more than we have */ + 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_B * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){ + if(byteshift == a->length_W * sizeof(bigint_word_t) - 1 && bitshift > GET_FBS(a)){ bigint_set_zero(a); return; } + if(byteshift){ - memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_B * sizeof(bigint_word_t) - byteshift); - memset((uint8_t*)a->wordv + a->length_B * sizeof(bigint_word_t) - byteshift, 0, byteshift); + memmove(a->wordv, (uint8_t*)a->wordv + byteshift, a->length_W * sizeof(bigint_word_t) - byteshift); } - byteshift /= sizeof(bigint_word_t); - a->length_B -= (byteshift + sizeof(bigint_word_t) - 1) / sizeof(bigint_word_t); - if(bitshift != 0 && a->length_B){ + + byteshift /= sizeof(bigint_word_t); /* byteshift is now wordshift */ + a->length_W -= byteshift; + if(bitshift != 0 && a->length_W){ /* shift to the right */ - i = a->length_B - 1; + 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); @@ -485,7 +447,7 @@ void bigint_shiftright(bigint_t* a, uint16_t shift){ void bigint_xor(bigint_t* dest, const bigint_t* a){ uint16_t i; - for(i=0; ilength_B; ++i){ + for(i=0; ilength_W; ++i){ dest->wordv[i] ^= a->wordv[i]; } bigint_adjust(dest); @@ -494,7 +456,7 @@ void bigint_xor(bigint_t* dest, const bigint_t* a){ /******************************************************************************/ void bigint_set_zero(bigint_t* a){ - a->length_B=0; + a->length_W=0; } /******************************************************************************/ @@ -502,138 +464,102 @@ void bigint_set_zero(bigint_t* a){ /* 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){ + if(a->length_W == 0 || b->length_W == 0){ bigint_set_zero(dest); return; } - if(dest==a || dest==b){ + if(dest == a || dest == b){ bigint_t d; - bigint_word_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==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); } - bigint_wordplus_t t=0; + bigint_wordplus_t t = 0; uint16_t i; bigint_word_t x = a->wordv[0]; - for(i=0; i < b->length_B; ++i){ + 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; + t >>= BIGINT_WORD_SIZE; + } + dest->length_W = i; + if(t){ + dest->wordv[i] = (bigint_word_t)t; + dest->length_W += 1; } - dest->wordv[i] = (bigint_word_t)t; - dest->length_B = i+1; dest->info = 0; bigint_adjust(dest); return; } - if(a->length_B * sizeof(bigint_word_t) <= 4 && b->length_B * sizeof(bigint_word_t) <= 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*sizeof(bigint_word_t)); - memcpy(&q, b->wordv, b->length_B*sizeof(bigint_word_t)); + 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_B = a->length_B + b->length_B)*sizeof(bigint_word_t)); + memcpy(dest->wordv, &r, (dest->length_W = a->length_W + b->length_W)*sizeof(bigint_word_t)); bigint_adjust(dest); return; } -#if BIGINT_WORD_SIZE == 8 - if(a->length_B <= 4 || b->length_B <= 4){ - if(a->length_B > 4){ - XCHG_PTR(a,b); - } - uint32_t x = 0, y = 0; - uint16_t j = b->length_B / 4, idx = 0; - uint64_t r = 0; - memcpy(&x, a->wordv, a->length_B); - while(j){ - r += (uint64_t)((uint32_t*)b->wordv)[idx] * (uint64_t)x; - ((uint32_t*)dest->wordv)[idx] = (uint32_t)r; - r >>= 32; - ++idx; - --j; - } - idx *= 4; - memcpy(&y, b->wordv + idx, b->length_B - idx); - r += (uint64_t)y * (uint64_t)x; - while(r){ - dest->wordv[idx++] = (uint8_t)r; - r >>= 8; - } - dest->length_B = idx; - bigint_adjust(dest); - return; - } -#endif /* split a in xh & xl; split b in yh & yl */ - const uint16_t n = (MAX(a->length_B, b->length_B)+1)/2; + const uint16_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){ + if(a->length_W<=n){ bigint_set_zero(&xh); - xl.length_B = a->length_B; + 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.length_W = a->length_W-n; xh.info = a->info; } - if(b->length_B <= n){ + if(b->length_W<=n){ bigint_set_zero(&yh); - yl.length_B = b->length_B; + 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.length_W = b->length_W-n; yh.info = b->info; } /* now we have split up a and b */ /* remember we want to do: - * x*y = (xh * b ** n + xl) * (yh * b ** n + 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 + * 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 tmp1_b[n*2+2]; - bigint_t tmp1, tmp2; - tmp1.wordv = tmp1_b; - tmp2.wordv = &tmp1_b[n+1]; - - bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh + xl */ - bigint_add_u(&tmp1, &yh, &yl); /* 3: tmp1 <= yh + yl */ - bigint_mul_u(dest, &tmp2, &tmp1); /* 4: dest <= tmp2 * tmp1 */ - bigint_mul_u(&tmp1, &xh, &yh); /* 5: tmp1 <= xh * yh */ - bigint_sub_u(dest, dest, &tmp1); /* 7: dest <= dest - tmp1 */ - bigint_word_t tmp3_b[2*n]; - tmp2.wordv = tmp3_b; - bigint_mul_u(&tmp2, &xl, &yl); /* 1: tmp3 <= xl * yl */ - bigint_sub_u(dest, dest, &tmp2); /* 6: dest <= dest - tmp3 */ - bigint_shiftleft(dest, n * sizeof(bigint_word_t) * 8); - bigint_add_u(dest, dest, &tmp2); /* 8: dest <= tmp3 + dest ** n */ - bigint_add_scale_u(dest, &tmp1, 2*n*sizeof(bigint_word_t)); /* 9: dest <= dest + tmp1 ** (2 * n) */ - -#if 0 - bigint_mul_u(dest, &xl, &yl); /* 1: dest <= xl * yl */ - bigint_add_u(&tmp2, &xh, &xl); /* 2: tmp2 <= xh + xl */ - bigint_add_u(&tmp1, &yh, &yl); /* 3: tmp1 <= yh + yl */ - bigint_mul_u(&tmp3, &tmp2, &tmp1); /* 4: tmp3 <= tmp2 * tmp1 */ - bigint_mul_u(&tmp1, &xh, &yh); /* 5: h <= xh * yh */ - bigint_sub_u(&tmp3, &tmp3, dest); /* 6: tmp3 <= tmp3 - dest */ - bigint_sub_u(&tmp3, &tmp3, &tmp1); /* 7: tmp3 <= tmp3 - h */ - bigint_add_scale_u(dest, &tmp3, n*sizeof(bigint_word_t)); /* 8: dest <= dest + tmp3 ** n */ - bigint_add_scale_u(dest, &tmp1, 2*n*sizeof(bigint_word_t)); /* 9: dest <= dest + tmp1 ** (2 * n) */ -#endif + bigint_word_t tmp_b[2 * n + 2], m_b[2 * (n + 1)]; + 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); /* 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) */ } /******************************************************************************/ @@ -666,65 +592,104 @@ void bigint_mul_s(bigint_t* dest, const bigint_t* a, const bigint_t* b){ /******************************************************************************/ + +#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 * sizeof(bigint_word_t) <= 4){ + if(a->length_W * sizeof(bigint_word_t) <= 4){ uint64_t r = 0; - memcpy(&r, a->wordv, a->length_B * sizeof(bigint_word_t)); + memcpy(&r, a->wordv, a->length_W * sizeof(bigint_word_t)); r = r * r; - memcpy(dest->wordv, &r, 2 * a->length_B*sizeof(bigint_word_t)); + 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; } - if(dest==a){ + if(dest->wordv == a->wordv){ bigint_t d; - bigint_word_t d_b[a->length_B * 2]; + bigint_word_t d_b[a->length_W*2]; d.wordv = d_b; bigint_square(&d, a); bigint_copy(dest, &d); return; } + +#if DEBUG_SQUARE + square_depth += 1; +#endif + uint16_t n; - n = (a->length_B + 1) / 2; + n=(a->length_W+1)/2; bigint_t xh, xl, tmp; /* x-high, x-low, temp */ - bigint_word_t buffer[2 * n + 1]; + bigint_word_t buffer[2*n+1]; xl.wordv = a->wordv; - xl.length_B = n; + xl.length_W = n; xl.info = 0; xh.wordv = &(a->wordv[n]); - xh.length_B = a->length_B - 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 */ - -// cli_putstr("\r\nDBG (a): xl: "); bigint_print_hex(&xl); -// cli_putstr("\r\nDBG (b): xh: "); bigint_print_hex(&xh); +#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); -// cli_putstr("\r\nDBG (1): xl**2: "); bigint_print_hex(dest); - bigint_square(&tmp, &xh); -// cli_putstr("\r\nDBG (2): xh**2: "); bigint_print_hex(&tmp); +#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)); -// cli_putstr("\r\nDBG (3): xl**2 + xh**2*n**2: "); bigint_print_hex(dest); +#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); -// cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp); +#if DEBUG_SQUARE + if(square_depth == 1){ + cli_putstr("\r\nDBG (4): xl*xh: "); bigint_print_hex(&tmp); + } +#endif bigint_shiftleft(&tmp, 1); -// cli_putstr("\r\nDBG (5): xl*xh*2: "); bigint_print_hex(&tmp); - bigint_add_scale_u(dest, &tmp, n*sizeof(bigint_word_t)); -// cli_putstr("\r\nDBG (6): x**2: "); bigint_print_hex(dest); -// cli_putstr("\r\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 } /******************************************************************************/ + void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){ bigint_t tmp, x; - bigint_word_t tmp_b[b->length_B + 1]; + bigint_word_t tmp_b[b->length_W + 1]; const uint16_t word_shift = bitscale / BIGINT_WORD_SIZE; - if(a->length_B < b->length_B + word_shift){ + if(a->length_W < b->length_W + word_shift){ #if DEBUG cli_putstr("\r\nDBG: *bang*\r\n"); #endif @@ -735,14 +700,11 @@ void bigint_sub_u_bitscale(bigint_t* a, const bigint_t* b, uint16_t bitscale){ bigint_copy(&tmp, b); bigint_shiftleft(&tmp, bitscale % BIGINT_WORD_SIZE); -// cli_putstr_P(PSTR("\r\nDBG: shifted value: ")); bigint_print_hex(&tmp); - x.info = a->info; x.wordv = &(a->wordv[word_shift]); - x.length_B = a->length_B - word_shift; + x.length_W = a->length_W - word_shift; bigint_sub_u(&x, &x, &tmp); - a->length_B = x.length_B + word_shift; bigint_adjust(a); return; } @@ -755,51 +717,52 @@ void bigint_reduce(bigint_t* a, const bigint_t* r){ #if DEBUG cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a); #endif - if(r->length_B==0 || a->length_B==0){ - return; - } - if((r->length_B*sizeof(bigint_word_t)<=4) && (a->length_B*sizeof(bigint_word_t)<=4)){ - uint32_t p=0, q=0; - memcpy(&p, a->wordv, a->length_B*sizeof(bigint_word_t)); - memcpy(&q, r->wordv, r->length_B*sizeof(bigint_word_t)); - p %= q; - memcpy(a->wordv, &p, a->length_B*sizeof(bigint_word_t)); - bigint_adjust(a); -// cli_putstr("\r\nDBG: (0) = "); bigint_print_hex(a); + if(r->length_W==0 || a->length_W==0){ return; } - uint16_t shift; - while(a->length_B > r->length_B){ - shift = (a->length_B - r->length_B) * 8 * sizeof(bigint_word_t) + GET_FBS(a) - rfbs - 1; - /* - if((a->wordv[a->length_B-1] & ((1LL< r->wordv[r->length_B-1]){ - // cli_putc('~'); - cli_putstr("\r\n ~ [a] = "); - cli_hexdump_rev(&a->wordv[a->length_B-1], 4); - cli_putstr(" [r] = "); - cli_hexdump_rev(&r->wordv[r->length_B-1], 4); - shift += 1; - } - */ -// cli_putstr("\r\nDBG: (p) shift = "); cli_hexdump_rev(&shift, 2); -// cli_putstr(" a_len = "); cli_hexdump_rev(&a->length_B, 2); -// cli_putstr(" r_len = "); cli_hexdump_rev(&r->length_B, 2); -// uart_flush(0); - bigint_sub_u_bitscale(a, r, shift); -// cli_putstr("\r\nDBG: (1) = "); bigint_print_hex(a); - } - while((GET_FBS(a) > rfbs) && (a->length_B == r->length_B)){ - shift = GET_FBS(a)-rfbs-1; -// cli_putstr("\r\nDBG: (2a) = "); bigint_print_hex(a); -// cli_putstr("\r\nDBG: (q) shift = "); cli_hexdump_rev(&shift, 2); - bigint_sub_u_bitscale(a, r, shift); -// cli_putstr("\r\nDBG: (2b) = "); bigint_print_hex(a); + + 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)); + 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); + 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); + 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); } -// cli_putc(' '); bigint_adjust(a); // cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a); // cli_putstr("\r\n"); @@ -809,13 +772,13 @@ 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){ - if(a->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 || r->length_W==0){ return; } bigint_t res, base; - bigint_word_t t, base_b[MAX(a->length_B,r->length_B)], res_b[r->length_B*2]; + bigint_word_t t, base_b[MAX(a->length_W,r->length_W)], res_b[r->length_W*2]; uint16_t i; uint8_t j; // uint16_t *xaddr = &i; @@ -828,16 +791,16 @@ void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, con // cli_putstr("\r\npost-copy"); bigint_reduce(&base, r); res.wordv[0]=1; - res.length_B=1; + res.length_W=1; res.info = 0; bigint_adjust(&res); - if(exp->length_B == 0){ + if(exp->length_W == 0){ bigint_copy(dest, &res); return; } uint8_t flag = 0; - t=exp->wordv[exp->length_B - 1]; - for(i=exp->length_B; 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){ @@ -848,12 +811,12 @@ void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, con if(flag){ bigint_square(&res, &res); bigint_reduce(&res, r); - if(t & (1<<(BIGINT_WORD_SIZE-1))){ + if(t & (1 << (BIGINT_WORD_SIZE - 1))){ bigint_mul_u(&res, &res, &base); bigint_reduce(&res, r); } } - t<<=1; + t <<= 1; } } @@ -863,24 +826,43 @@ void bigint_expmod_u(bigint_t* dest, const bigint_t* a, const bigint_t* exp, con } /******************************************************************************/ - +#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){ - bigint_t g, x_, y_, u, v, a_, b_, c_, d_; - uint16_t i=0; - if(x->length_B==0 || y->length_B==0){ + uint16_t i = 0; + printf_P(PSTR("\nDBG: gcdext( ")); + bigint_print_hex(x); + printf_P(PSTR(", ")); + bigint_print_hex(y); + printf_P(PSTR(")\n")); + 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); + } + if(a){ + bigint_set_zero(a); + } + if(b){ + bigint_set_zero(b); + } return; } - if(x->length_B==1 && x->wordv[0]==1){ - gcd->length_B = 1; - gcd->wordv[0] = 1; + 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_B = 1; + a->length_W = 1; a->wordv[0] = 1; SET_POS(a); bigint_adjust(a); @@ -890,11 +872,14 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c } return; } - if(y->length_B==1 && y->wordv[0]==1){ - gcd->length_B = 1; - gcd->wordv[0] = 1; + 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_B = 1; + b->length_W = 1; b->wordv[0] = 1; SET_POS(b); bigint_adjust(b); @@ -905,27 +890,28 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c return; } - while(x->wordv[i]==0 && y->wordv[i]==0){ + while(x->wordv[i] == 0 && y->wordv[i] == 0){ ++i; } - bigint_word_t g_b[i+2], x_b[x->length_B-i], y_b[y->length_B-i]; - bigint_word_t u_b[x->length_B-i], v_b[y->length_B-i]; - bigint_word_t a_b[y->length_B+2], c_b[y->length_B+2]; - bigint_word_t b_b[x->length_B+2], d_b[x->length_B+2]; + 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_B = i+1; - g.info=0; + 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_B = x->length_B-i; - y_.length_B = y->length_B-i; - memcpy(x_.wordv, x->wordv+i, x_.length_B*sizeof(bigint_word_t)); - memcpy(y_.wordv, y->wordv+i, y_.length_B*sizeof(bigint_word_t)); - 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] & (1 << i)) == 0 && (y_.wordv[0] & (1 << i)) == 0; ++i){ } bigint_adjust(&x_); @@ -947,46 +933,69 @@ void bigint_gcdext(bigint_t* gcd, bigint_t* a, bigint_t* b, const bigint_t* x, c 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_); + printf_P(PSTR("\nloop: x_ = ")); + bigint_print_hex(&x_); + printf_P(PSTR("; y_ = ")); + bigint_print_hex(&y_); do{ - cli_putstr("\r\nDBG (gcdext) 0"); - while((u.wordv[0]&1)==0){ - cli_putstr("\r\nDBG (gcdext) 0.1"); + printf_P(PSTR("\nDBG (gcdext) 0")); + while((u.wordv[0] & 1) == 0){ + printf_P(PSTR("\nDBG (gcdext) 0.1")); bigint_shiftright(&u, 1); - if((a_.wordv[0]&1) || (b_.wordv[0]&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); + printf_P(PSTR(" a_ = ")); + bigint_print_hex(&a_); + printf_P(PSTR("; b_ = ")); + bigint_print_hex(&b_); } - while((v.wordv[0]&1)==0){ - cli_putstr("\r\nDBG (gcdext) 0.2"); + while((v.wordv[0] & 1) == 0){ + printf_P(PSTR("\nDBG (gcdext) 0.2")); bigint_shiftright(&v, 1); - if((c_.wordv[0]&1) || (d_.wordv[0]&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){ + 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_B); + }while(u.length_W); if(gcd){ bigint_mul_s(gcd, &v, &g); } @@ -1012,7 +1021,7 @@ void bigint_inverse(bigint_t* dest, const bigint_t* a, const bigint_t* m){ void bigint_changeendianess(bigint_t* a){ uint8_t t, *p, *q; p = (uint8_t*)(a->wordv); - q = p + a->length_B * sizeof(bigint_word_t) - 1; + q = p + a->length_W * sizeof(bigint_word_t) - 1; while(p