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 /* \$OpenBSD: fe25519.c,v 1.3 2013/12/09 11:03:45 markus Exp \$ */ /* * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange, * Peter Schwabe, Bo-Yin Yang. * Copied from supercop-20130419/crypto_sign/ed25519/ref/fe25519.c */ #include "includes.h" #define WINDOWSIZE 1 /* Should be 1,2, or 4 */ #define WINDOWMASK ((1<>= 31; /* 1: yes; 0: no */ return x; } static crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ { unsigned int x = a; x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */ x >>= 31; /* 0: yes; 1: no */ x ^= 1; /* 1: yes; 0: no */ return x; } static crypto_uint32 times19(crypto_uint32 a) { return (a << 4) + (a << 1) + a; } static crypto_uint32 times38(crypto_uint32 a) { return (a << 5) + (a << 2) + (a << 1); } static void reduce_add_sub(fe25519 *r) { crypto_uint32 t; int i,rep; for(rep=0;rep<4;rep++) { t = r->v[31] >> 7; r->v[31] &= 127; t = times19(t); r->v[0] += t; for(i=0;i<31;i++) { t = r->v[i] >> 8; r->v[i+1] += t; r->v[i] &= 255; } } } static void reduce_mul(fe25519 *r) { crypto_uint32 t; int i,rep; for(rep=0;rep<2;rep++) { t = r->v[31] >> 7; r->v[31] &= 127; t = times19(t); r->v[0] += t; for(i=0;i<31;i++) { t = r->v[i] >> 8; r->v[i+1] += t; r->v[i] &= 255; } } } /* reduction modulo 2^255-19 */ void fe25519_freeze(fe25519 *r) { int i; crypto_uint32 m = equal(r->v[31],127); for(i=30;i>0;i--) m &= equal(r->v[i],255); m &= ge(r->v[0],237); m = -m; r->v[31] -= m&127; for(i=30;i>0;i--) r->v[i] -= m&255; r->v[0] -= m&237; } void fe25519_unpack(fe25519 *r, const unsigned char x[32]) { int i; for(i=0;i<32;i++) r->v[i] = x[i]; r->v[31] &= 127; } /* Assumes input x being reduced below 2^255 */ void fe25519_pack(unsigned char r[32], const fe25519 *x) { int i; fe25519 y = *x; fe25519_freeze(&y); for(i=0;i<32;i++) r[i] = y.v[i]; } int fe25519_iszero(const fe25519 *x) { int i; int r; fe25519 t = *x; fe25519_freeze(&t); r = equal(t.v[0],0); for(i=1;i<32;i++) r &= equal(t.v[i],0); return r; } int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y) { int i; fe25519 t1 = *x; fe25519 t2 = *y; fe25519_freeze(&t1); fe25519_freeze(&t2); for(i=0;i<32;i++) if(t1.v[i] != t2.v[i]) return 0; return 1; } void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b) { int i; crypto_uint32 mask = b; mask = -mask; for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]); } unsigned char fe25519_getparity(const fe25519 *x) { fe25519 t = *x; fe25519_freeze(&t); return t.v[0] & 1; } void fe25519_setone(fe25519 *r) { int i; r->v[0] = 1; for(i=1;i<32;i++) r->v[i]=0; } void fe25519_setzero(fe25519 *r) { int i; for(i=0;i<32;i++) r->v[i]=0; } void fe25519_neg(fe25519 *r, const fe25519 *x) { fe25519 t; int i; for(i=0;i<32;i++) t.v[i]=x->v[i]; fe25519_setzero(r); fe25519_sub(r, r, &t); } void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y) { int i; for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; reduce_add_sub(r); } void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y) { int i; crypto_uint32 t[32]; t[0] = x->v[0] + 0x1da; t[31] = x->v[31] + 0xfe; for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe; for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i]; reduce_add_sub(r); } void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y) { int i,j; crypto_uint32 t[63]; for(i=0;i<63;i++)t[i] = 0; for(i=0;i<32;i++) for(j=0;j<32;j++) t[i+j] += x->v[i] * y->v[j]; for(i=32;i<63;i++) r->v[i-32] = t[i-32] + times38(t[i]); r->v[31] = t[31]; /* result now in r[0]...r[31] */ reduce_mul(r); } void fe25519_square(fe25519 *r, const fe25519 *x) { fe25519_mul(r, x, x); } void fe25519_invert(fe25519 *r, const fe25519 *x) { fe25519 z2; fe25519 z9; fe25519 z11; fe25519 z2_5_0; fe25519 z2_10_0; fe25519 z2_20_0; fe25519 z2_50_0; fe25519 z2_100_0; fe25519 t0; fe25519 t1; int i; /* 2 */ fe25519_square(&z2,x); /* 4 */ fe25519_square(&t1,&z2); /* 8 */ fe25519_square(&t0,&t1); /* 9 */ fe25519_mul(&z9,&t0,x); /* 11 */ fe25519_mul(&z11,&z9,&z2); /* 22 */ fe25519_square(&t0,&z11); /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9); /* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0); /* 2^7 - 2^2 */ fe25519_square(&t1,&t0); /* 2^8 - 2^3 */ fe25519_square(&t0,&t1); /* 2^9 - 2^4 */ fe25519_square(&t1,&t0); /* 2^10 - 2^5 */ fe25519_square(&t0,&t1); /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0); /* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0); /* 2^12 - 2^2 */ fe25519_square(&t1,&t0); /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0); /* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0); /* 2^22 - 2^2 */ fe25519_square(&t1,&t0); /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0); /* 2^41 - 2^1 */ fe25519_square(&t1,&t0); /* 2^42 - 2^2 */ fe25519_square(&t0,&t1); /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0); /* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0); /* 2^52 - 2^2 */ fe25519_square(&t1,&t0); /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0); /* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0); /* 2^102 - 2^2 */ fe25519_square(&t0,&t1); /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } /* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0); /* 2^201 - 2^1 */ fe25519_square(&t0,&t1); /* 2^202 - 2^2 */ fe25519_square(&t1,&t0); /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } /* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0); /* 2^251 - 2^1 */ fe25519_square(&t1,&t0); /* 2^252 - 2^2 */ fe25519_square(&t0,&t1); /* 2^253 - 2^3 */ fe25519_square(&t1,&t0); /* 2^254 - 2^4 */ fe25519_square(&t0,&t1); /* 2^255 - 2^5 */ fe25519_square(&t1,&t0); /* 2^255 - 21 */ fe25519_mul(r,&t1,&z11); } void fe25519_pow2523(fe25519 *r, const fe25519 *x) { fe25519 z2; fe25519 z9; fe25519 z11; fe25519 z2_5_0; fe25519 z2_10_0; fe25519 z2_20_0; fe25519 z2_50_0; fe25519 z2_100_0; fe25519 t; int i; /* 2 */ fe25519_square(&z2,x); /* 4 */ fe25519_square(&t,&z2); /* 8 */ fe25519_square(&t,&t); /* 9 */ fe25519_mul(&z9,&t,x); /* 11 */ fe25519_mul(&z11,&z9,&z2); /* 22 */ fe25519_square(&t,&z11); /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9); /* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0); /* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); } /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0); /* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0); /* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0); /* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0); /* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); } /* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0); /* 2^41 - 2^1 */ fe25519_square(&t,&t); /* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0); /* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0); /* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0); /* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0); /* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); } /* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0); /* 2^201 - 2^1 */ fe25519_square(&t,&t); /* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } /* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0); /* 2^251 - 2^1 */ fe25519_square(&t,&t); /* 2^252 - 2^2 */ fe25519_square(&t,&t); /* 2^252 - 3 */ fe25519_mul(r,&t,x); }