From b3cf9d2f35e428cae278fffb8a8f5820d40c833b Mon Sep 17 00:00:00 2001 From: bg Date: Fri, 20 Sep 2013 01:57:40 +0200 Subject: [PATCH] adding Montgomery-multiplication stuff and better squaring algo --- bigint/bigint.c | 447 ++++++++++++++++++++++++++---------- bigint/bigint.h | 38 ++- test_src/main-bigint-test.c | 154 ++++++++++++- 3 files changed, 508 insertions(+), 131 deletions(-) diff --git a/bigint/bigint.c b/bigint/bigint.c index bf854cc..af243cf 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 @@ -46,19 +47,19 @@ #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 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){ @@ -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; } @@ -90,7 +91,7 @@ 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); } @@ -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 = 0LL; + bigint_length_t i; if(b->length_W == 0){ bigint_copy(dest, a); SET_POS(dest); @@ -249,7 +250,7 @@ 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; + dest->wordv[i] = (bigint_word_t)t; if(t<0){ borrow = 1; }else{ @@ -270,11 +271,11 @@ 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]){ @@ -370,8 +371,8 @@ 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; @@ -408,9 +409,9 @@ void bigint_shiftleft(bigint_t *a, uint16_t shift){ /******************************************************************************/ -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; @@ -446,7 +447,7 @@ void bigint_shiftright(bigint_t *a, uint16_t shift){ /******************************************************************************/ void bigint_xor(bigint_t *dest, const bigint_t *a){ - uint16_t i; + bigint_length_t i; for(i=0; ilength_W; ++i){ dest->wordv[i] ^= a->wordv[i]; } @@ -481,7 +482,7 @@ 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 +509,7 @@ 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 +592,7 @@ 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 +601,7 @@ 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 +611,7 @@ 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 +620,13 @@ 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]; @@ -682,12 +685,71 @@ 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 { + 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 = a->wordv[i] * a->wordv[i] + 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 = a->wordv[i] * 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 = acc.u[1] + c2; + c2 = q + (c1 < c2); + } + dest->wordv[i + a->length_W] += c1; + dest->wordv[i + a->length_W + 1] = c2 + (dest->wordv[i + a->length_W] < c1); + } + SET_POS(dest); + 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 DEBUG @@ -712,11 +774,7 @@ 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){ return; } @@ -729,43 +787,22 @@ void bigint_reduce(bigint_t *a, const bigint_t *r){ 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; + bigint_length_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); } bigint_adjust(a); -// cli_putstr("\r\nDBG: (a) = "); bigint_print_hex(a); -// cli_putstr("\r\n"); } /******************************************************************************/ @@ -773,25 +810,26 @@ 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; +// bigint_length_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){ @@ -800,11 +838,11 @@ void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, } uint8_t flag = 0; t=exp->wordv[exp->length_W - 1]; - for(i=exp->length_W; i > 0; --i){ + for(i = exp->length_W; i > 0; --i){ t = exp->wordv[i - 1]; - for(j=BIGINT_WORD_SIZE; j > 0; --j){ + for(j = BIGINT_WORD_SIZE; j > 0; --j){ if(!flag){ - if(t & (1<<(BIGINT_WORD_SIZE-1))){ + if(t & (1 << (BIGINT_WORD_SIZE - 1))){ flag = 1; } } @@ -826,24 +864,10 @@ void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, } /******************************************************************************/ -#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 +964,8 @@ 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")); bigint_shiftright(&u, 1); if((a_.wordv[0] & 1) || (b_.wordv[0] & 1)){ bigint_add_s(&a_, &a_, &y_); @@ -955,45 +973,24 @@ 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); 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); if(gcd){ @@ -1032,13 +1029,229 @@ 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] + */ + +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 (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); + 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; + 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 * sizeof(bigint_word_t), 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_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_length_t s = r->length_W; + bigint_t res, m_, ax; + bigint_word_t t, res_w[r->length_W*2], ax_w[MAX(s, a->length_W)]; + bigint_word_t m_w_[s + 1]; + bigint_length_t i; + uint8_t j; + + res.wordv = res_w; + m_.wordv = m_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); + bigint_mont_gen_m_(&m_, 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 & (1 << (BIGINT_WORD_SIZE - 1))){ + flag = 1; + } + } + if (flag) { + bigint_square(&res, &res); + bigint_mont_red(&res, &res, r, &m_); + if (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_); +} + +/******************************************************************************/ + +#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); + } } diff --git a/bigint/bigint.h b/bigint/bigint.h index 59dcc35..f42ae18 100644 --- a/bigint/bigint.h +++ b/bigint/bigint.h @@ -28,19 +28,24 @@ #ifndef BIGINT_H_ #define BIGINT_H_ +#include #include -typedef uint8_t bigint_word_t; +typedef uint8_t bigint_word_t; typedef uint16_t bigint_wordplus_t; typedef int16_t bigint_wordplus_signed_t; #define BIGINT_WORD_SIZE 8 #define BIGINT_FBS_MASK (BIGINT_WORD_SIZE-1) /* the last five bits indicate which is the first bit set */ #define BIGINT_NEG_MASK 0x80 /* this bit indicates a negative value */ + +typedef size_t bigint_length_t; +typedef uint_fast8_t bigint_info_t; + typedef struct{ - uint16_t length_W; - uint8_t info; - bigint_word_t *wordv; /* word vector, pointing to the LSB */ + bigint_length_t length_W; + bigint_info_t info; + bigint_word_t *wordv; /* word vector, pointing to the LSB */ }bigint_t; @@ -50,29 +55,38 @@ typedef struct{ void bigint_adjust(bigint_t *a); uint32_t bigint_get_first_set_bit(const bigint_t *a); uint32_t bigint_get_last_set_bit(const bigint_t *a); -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); +bigint_length_t bigint_length_B(const bigint_t *a); 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); -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); void bigint_sub_u(bigint_t *dest, const bigint_t *a, const bigint_t *b); 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_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); -void bigint_shiftleft(bigint_t *a, uint16_t shift); -void bigint_shiftright(bigint_t *a, uint16_t shift); +void bigint_shiftleft(bigint_t *a, bigint_length_t shift); +void bigint_shiftright(bigint_t *a, bigint_length_t shift); void bigint_xor(bigint_t *dest, const bigint_t *a); void bigint_set_zero(bigint_t *a); void bigint_mul_u(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); void bigint_square(bigint_t *dest, const bigint_t *a); -void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, uint16_t bitscale); +void bigint_sub_u_bitscale(bigint_t *a, const bigint_t *b, bigint_length_t bitscale); void bigint_reduce(bigint_t *a, const bigint_t *r); -void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r); +void bigint_mul_word_u(bigint_t *a, bigint_word_t b); void bigint_gcdext(bigint_t *gcd, bigint_t *a, bigint_t *b, const bigint_t *x, const bigint_t *y); void bigint_inverse(bigint_t *dest, const bigint_t *a, const bigint_t *m); void bigint_changeendianess(bigint_t *a); -/******************************************************************************/ +void bigint_clip(bigint_t *dest, bigint_length_t s); +void bigint_mont_mul(bigint_t *dest, const bigint_t *a, const bigint_t *b, const bigint_t *m, const bigint_t *m_); +void bigint_mont_red(bigint_t *dest, const bigint_t *a, const bigint_t *m, const bigint_t *m_); +void bigint_mont_gen_m_(bigint_t* dest, const bigint_t* m); +void bigint_mont_trans(bigint_t *dest, const bigint_t *a, const bigint_t *m); + +void bigint_expmod_u(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r); +void bigint_expmod_u_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r); +void bigint_expmod_u_mont_sam(bigint_t *dest, const bigint_t *a, const bigint_t *exp, const bigint_t *r); + #endif /*BIGINT_H_*/ diff --git a/test_src/main-bigint-test.c b/test_src/main-bigint-test.c index 21ab09c..41dd45b 100644 --- a/test_src/main-bigint-test.c +++ b/test_src/main-bigint-test.c @@ -181,6 +181,99 @@ void test_mul_bigint(void){ } } +void test_mul_mont_bigint(void){ + bigint_t a, b, c, a_, b_, m_, res; + bigint_length_t s; + cli_putstr_P(PSTR("\r\nmul-mont test ( (a * b) % c )\r\n")); + for(;;){ + cli_putstr_P(PSTR("\r\nenter a:")); + if(bigint_read_hex_echo(&a)){ + cli_putstr_P(PSTR("\r\n end mul test")); + return; + } + cli_putstr_P(PSTR("\r\nenter b:")); + if(bigint_read_hex_echo(&b)){ + free(a.wordv); + cli_putstr_P(PSTR("\r\n end mul test")); + return; + } + cli_putstr_P(PSTR("\r\nenter c:")); + if(bigint_read_hex_echo(&c)){ + free(a.wordv); + free(b.wordv); + cli_putstr_P(PSTR("\r\n end mul test")); + return; + } + s = c.length_W; + cli_putstr_P(PSTR("\r\n (")); + bigint_print_hex(&a); + cli_putstr_P(PSTR(" * ")); + bigint_print_hex(&b); + cli_putstr_P(PSTR(") % ")); + bigint_print_hex(&c); + cli_putstr_P(PSTR(" = ")); + bigint_word_t res_w[s], a_w_[s], b_w_[s], m_w_[s + 1]; + res.wordv = res_w; + a_.wordv = a_w_; + b_.wordv = b_w_; + m_.wordv = m_w_; + bigint_mont_gen_m_(&m_, &c); + bigint_mont_trans(&a_, &a, &c); + bigint_mont_trans(&b_, &b, &c); + bigint_mont_mul(&res, &a_, &b_, &c, &m_); + bigint_mont_red(&res, &res, &c, &m_); + bigint_print_hex(&res); + putchar('\n'); + free(a.wordv); + free(b.wordv); + free(c.wordv); + } +} + +void test_mul_word_bigint(void){ + bigint_t a, b; + bigint_word_t *t; + cli_putstr_P(PSTR("\r\nmul test\r\n")); + for(;;){ + cli_putstr_P(PSTR("\r\nenter a:")); + if(bigint_read_hex_echo(&a)){ + cli_putstr_P(PSTR("\r\n end mul test")); + return; + } + cli_putstr_P(PSTR("\r\nenter b:")); + if(bigint_read_hex_echo(&b)){ + free(a.wordv); + cli_putstr_P(PSTR("\r\n end mul test")); + return; + } + cli_putstr_P(PSTR("\r\n ")); + bigint_print_hex(&a); + cli_putstr_P(PSTR(" * ")); + bigint_print_hex(&b); + cli_putstr_P(PSTR(" = ")); + + if(b.length_W > 1){ + free(a.wordv); + free(b.wordv); + cli_putstr_P(PSTR("\r\n end mul test")); + } + + t = realloc(a.wordv, a.length_W + 3); + if(t == NULL){ + cli_putstr_P(PSTR("\n\rERROR: Out of memory!")); + free(a.wordv); + free(b.wordv); + continue; + } + a.wordv = t; + bigint_mul_word_u(&a, b.wordv[0]); + bigint_print_hex(&a); + cli_putstr_P(PSTR("\r\n")); + free(a.wordv); + free(b.wordv); + } +} + void test_square_bigint(void){ bigint_t a, c; cli_putstr_P(PSTR("\r\nsquare test\r\n")); @@ -240,7 +333,7 @@ void test_reduce_bigint(void){ void test_expmod_bigint(void){ bigint_t a, b, c, d; uint8_t *d_b; - cli_putstr_P(PSTR("\r\nreduce test\r\n")); + cli_putstr_P(PSTR("\r\nexpnonentiation-modulo test\r\n")); for(;;){ cli_putstr_P(PSTR("\r\nenter a:")); if(bigint_read_hex_echo(&a)){ @@ -287,6 +380,57 @@ void test_expmod_bigint(void){ } } +/* d = a**b % c */ +void test_expmod_mont_bigint(void){ + bigint_t a, b, c, d; + uint8_t *d_b; + cli_putstr_P(PSTR("\r\nexpnonentiation-modulo-montgomory test\r\n")); + for(;;){ + cli_putstr_P(PSTR("\r\nenter a:")); + if(bigint_read_hex_echo(&a)){ + cli_putstr_P(PSTR("\r\n end expmod test")); + return; + } + cli_putstr_P(PSTR("\r\nenter b:")); + if(bigint_read_hex_echo(&b)){ + free(a.wordv); + cli_putstr_P(PSTR("\r\n end expmod test")); + return; + } + cli_putstr_P(PSTR("\r\nenter c:")); + if(bigint_read_hex_echo(&c)){ + free(a.wordv); + free(b.wordv); + cli_putstr_P(PSTR("\r\n end expmod test")); + return; + } + d_b = malloc(c.length_W); + if(d_b==NULL){ + cli_putstr_P(PSTR("\n\rERROR: Out of memory!")); + free(a.wordv); + free(b.wordv); + free(c.wordv); + continue; + } + d.wordv = d_b; + cli_putstr_P(PSTR("\r\n ")); + bigint_print_hex(&a); + cli_putstr_P(PSTR("**")); + bigint_print_hex(&b); + cli_putstr_P(PSTR(" % ")); + bigint_print_hex(&c); + cli_putstr_P(PSTR(" = ")); + bigint_expmod_u_mont_sam(&d, &a, &b, &c); + bigint_print_hex(&d); + cli_putstr_P(PSTR("\r\n")); + free(a.wordv); + free(b.wordv); + free(c.wordv); + free(d.wordv); + + } +} + void test_gcdext_bigint(void){ bigint_t a, b, c, d, e; cli_putstr_P(PSTR("\r\ngcdext test\r\n")); @@ -499,9 +643,12 @@ const char echo_test_str[] PROGMEM = "echo-test"; const char add_test_str[] PROGMEM = "add-test"; const char add_scale_test_str[] PROGMEM = "add-scale-test"; const char mul_test_str[] PROGMEM = "mul-test"; +const char mul_mont_test_str[] PROGMEM = "mul-mont-test"; +const char mul_word_test_str[] PROGMEM = "mul-word-test"; const char square_test_str[] PROGMEM = "square-test"; const char reduce_test_str[] PROGMEM = "reduce-test"; const char expmod_test_str[] PROGMEM = "expmod-test"; +const char expmod_mont_test_str[] PROGMEM = "expmod-mont-test"; const char gcdext_test_str[] PROGMEM = "gcdext-test"; const char quick_test_str[] PROGMEM = "quick-test"; const char performance_str[] PROGMEM = "performance"; @@ -511,9 +658,12 @@ const cmdlist_entry_t cmdlist[] PROGMEM = { { add_test_str, NULL, test_add_bigint }, { add_scale_test_str, NULL, test_add_scale_bigint }, { mul_test_str, NULL, test_mul_bigint }, + { mul_mont_test_str, NULL, test_mul_mont_bigint }, + { mul_word_test_str, NULL, test_mul_word_bigint }, { square_test_str, NULL, test_square_bigint }, { reduce_test_str, NULL, test_reduce_bigint }, - { expmod_test_str, NULL, test_expmod_bigint }, + { expmod_test_str, NULL, test_expmod_bigint }, + { expmod_mont_test_str, NULL, test_expmod_mont_bigint }, { gcdext_test_str, NULL, test_gcdext_bigint }, { quick_test_str, NULL, test_gcdext_simple }, { echo_test_str, NULL, test_echo_bigint },