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/* $OpenBSD: fe25519.c,v 1.1 2014/07/22 00:41:19 deraadt Exp $ */ |
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/* |
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* Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange, |
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* Peter Schwabe, Bo-Yin Yang. |
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* Copied from supercop-20130419/crypto_sign/ed25519/ref/fe25519.c |
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*/ |
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#define WINDOWSIZE 1 /* Should be 1,2, or 4 */ |
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#define WINDOWMASK ((1<<WINDOWSIZE)-1) |
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#include "fe25519.h" |
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static crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ |
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{ |
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11098 |
crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */ |
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5549 |
x -= 1; /* 4294967295: yes; 0..65534: no */ |
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5549 |
x >>= 31; /* 1: yes; 0: no */ |
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return x; |
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} |
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static crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ |
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{ |
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unsigned int x = a; |
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x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */ |
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x >>= 31; /* 0: yes; 1: no */ |
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x ^= 1; /* 1: yes; 0: no */ |
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return x; |
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} |
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static crypto_uint32 times19(crypto_uint32 a) |
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{ |
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999276 |
return (a << 4) + (a << 1) + a; |
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} |
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static crypto_uint32 times38(crypto_uint32 a) |
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{ |
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5537406 |
return (a << 5) + (a << 2) + (a << 1); |
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} |
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static void reduce_add_sub(fe25519 *r) |
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{ |
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crypto_uint32 t; |
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int i,rep; |
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✓✓ |
882783 |
for(rep=0;rep<4;rep++) |
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{ |
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321012 |
t = r->v[31] >> 7; |
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321012 |
r->v[31] &= 127; |
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t = times19(t); |
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r->v[0] += t; |
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✓✓ |
20544768 |
for(i=0;i<31;i++) |
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{ |
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9951372 |
t = r->v[i] >> 8; |
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9951372 |
r->v[i+1] += t; |
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9951372 |
r->v[i] &= 255; |
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} |
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} |
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} |
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static void reduce_mul(fe25519 *r) |
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{ |
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crypto_uint32 t; |
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int i,rep; |
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✓✓ |
625191 |
for(rep=0;rep<2;rep++) |
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{ |
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t = r->v[31] >> 7; |
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r->v[31] &= 127; |
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t = times19(t); |
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r->v[0] += t; |
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✓✓ |
11432064 |
for(i=0;i<31;i++) |
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{ |
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5537406 |
t = r->v[i] >> 8; |
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5537406 |
r->v[i+1] += t; |
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5537406 |
r->v[i] &= 255; |
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} |
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} |
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} |
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/* reduction modulo 2^255-19 */ |
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void fe25519_freeze(fe25519 *r) |
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{ |
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int i; |
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crypto_uint32 m = equal(r->v[31],127); |
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✓✓ |
11098 |
for(i=30;i>0;i--) |
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m &= equal(r->v[i],255); |
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m &= ge(r->v[0],237); |
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m = -m; |
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r->v[31] -= m&127; |
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✓✓ |
11098 |
for(i=30;i>0;i--) |
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r->v[i] -= m&255; |
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r->v[0] -= m&237; |
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} |
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void fe25519_unpack(fe25519 *r, const unsigned char x[32]) |
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{ |
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int i; |
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✓✓ |
1407 |
for(i=0;i<32;i++) r->v[i] = x[i]; |
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r->v[31] &= 127; |
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} |
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/* Assumes input x being reduced below 2^255 */ |
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void fe25519_pack(unsigned char r[32], const fe25519 *x) |
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{ |
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int i; |
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fe25519 y = *x; |
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fe25519_freeze(&y); |
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✓✓ |
2442 |
for(i=0;i<32;i++) |
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r[i] = y.v[i]; |
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} |
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int fe25519_iszero(const fe25519 *x) |
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{ |
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int i; |
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int r; |
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fe25519 t = *x; |
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fe25519_freeze(&t); |
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r = equal(t.v[0],0); |
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for(i=1;i<32;i++) |
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r &= equal(t.v[i],0); |
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return r; |
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} |
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int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y) |
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{ |
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int i; |
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fe25519 t1 = *x; |
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fe25519 t2 = *y; |
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fe25519_freeze(&t1); |
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fe25519_freeze(&t2); |
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✓✓ |
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for(i=0;i<32;i++) |
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✓✓ |
744 |
if(t1.v[i] != t2.v[i]) return 0; |
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return 1; |
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} |
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void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b) |
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{ |
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int i; |
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crypto_uint32 mask = b; |
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mask = -mask; |
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✓✓ |
807840 |
for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]); |
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} |
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unsigned char fe25519_getparity(const fe25519 *x) |
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{ |
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fe25519 t = *x; |
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fe25519_freeze(&t); |
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return t.v[0] & 1; |
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} |
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void fe25519_setone(fe25519 *r) |
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{ |
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int i; |
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r->v[0] = 1; |
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✓✓ |
5056 |
for(i=1;i<32;i++) r->v[i]=0; |
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} |
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void fe25519_setzero(fe25519 *r) |
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{ |
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int i; |
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✓✓ |
454059 |
for(i=0;i<32;i++) r->v[i]=0; |
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} |
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void fe25519_neg(fe25519 *r, const fe25519 *x) |
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{ |
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13470 |
fe25519 t; |
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int i; |
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✓✓ |
444510 |
for(i=0;i<32;i++) t.v[i]=x->v[i]; |
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6735 |
fe25519_setzero(r); |
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fe25519_sub(r, r, &t); |
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} |
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void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y) |
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{ |
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int i; |
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✓✓ |
2417427 |
for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; |
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36081 |
reduce_add_sub(r); |
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36081 |
} |
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void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y) |
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{ |
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int i; |
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88344 |
crypto_uint32 t[32]; |
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44172 |
t[0] = x->v[0] + 0x1da; |
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t[31] = x->v[31] + 0xfe; |
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✓✓ |
2738664 |
for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe; |
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✓✓ |
2915352 |
for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i]; |
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44172 |
reduce_add_sub(r); |
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} |
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void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y) |
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{ |
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int i,j; |
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178626 |
crypto_uint32 t[63]; |
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✓✓ |
11432064 |
for(i=0;i<63;i++)t[i] = 0; |
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✓✓ |
5894658 |
for(i=0;i<32;i++) |
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✓✓ |
188629056 |
for(j=0;j<32;j++) |
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91456512 |
t[i+j] += x->v[i] * y->v[j]; |
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✓✓ |
5716032 |
for(i=32;i<63;i++) |
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2768703 |
r->v[i-32] = t[i-32] + times38(t[i]); |
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89313 |
r->v[31] = t[31]; /* result now in r[0]...r[31] */ |
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reduce_mul(r); |
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} |
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void fe25519_square(fe25519 *r, const fe25519 *x) |
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{ |
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72388 |
fe25519_mul(r, x, x); |
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36194 |
} |
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void fe25519_invert(fe25519 *r, const fe25519 *x) |
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{ |
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fe25519 z2; |
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fe25519 z9; |
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fe25519 z11; |
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fe25519 z2_5_0; |
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fe25519 z2_10_0; |
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fe25519 z2_20_0; |
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fe25519 z2_50_0; |
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fe25519 z2_100_0; |
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fe25519 t0; |
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fe25519 t1; |
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int i; |
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/* 2 */ fe25519_square(&z2,x); |
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/* 4 */ fe25519_square(&t1,&z2); |
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/* 8 */ fe25519_square(&t0,&t1); |
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/* 9 */ fe25519_mul(&z9,&t0,x); |
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/* 11 */ fe25519_mul(&z11,&z9,&z2); |
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/* 22 */ fe25519_square(&t0,&z11); |
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/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9); |
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/* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0); |
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/* 2^7 - 2^2 */ fe25519_square(&t1,&t0); |
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/* 2^8 - 2^3 */ fe25519_square(&t0,&t1); |
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/* 2^9 - 2^4 */ fe25519_square(&t1,&t0); |
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/* 2^10 - 2^5 */ fe25519_square(&t0,&t1); |
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/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0); |
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/* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0); |
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/* 2^12 - 2^2 */ fe25519_square(&t1,&t0); |
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✓✓ |
370 |
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
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/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0); |
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/* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0); |
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/* 2^22 - 2^2 */ fe25519_square(&t1,&t0); |
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✓✓ |
740 |
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
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/* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0); |
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/* 2^41 - 2^1 */ fe25519_square(&t1,&t0); |
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/* 2^42 - 2^2 */ fe25519_square(&t0,&t1); |
257 |
✓✓ |
370 |
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } |
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/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0); |
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/* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0); |
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/* 2^52 - 2^2 */ fe25519_square(&t1,&t0); |
262 |
✓✓ |
1850 |
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
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/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0); |
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|
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/* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0); |
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37 |
/* 2^102 - 2^2 */ fe25519_square(&t0,&t1); |
267 |
✓✓ |
3700 |
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } |
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|
37 |
/* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0); |
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|
37 |
/* 2^201 - 2^1 */ fe25519_square(&t0,&t1); |
271 |
|
37 |
/* 2^202 - 2^2 */ fe25519_square(&t1,&t0); |
272 |
✓✓ |
1850 |
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
273 |
|
37 |
/* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0); |
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|
37 |
/* 2^251 - 2^1 */ fe25519_square(&t1,&t0); |
276 |
|
37 |
/* 2^252 - 2^2 */ fe25519_square(&t0,&t1); |
277 |
|
37 |
/* 2^253 - 2^3 */ fe25519_square(&t1,&t0); |
278 |
|
37 |
/* 2^254 - 2^4 */ fe25519_square(&t0,&t1); |
279 |
|
37 |
/* 2^255 - 2^5 */ fe25519_square(&t1,&t0); |
280 |
|
37 |
/* 2^255 - 21 */ fe25519_mul(r,&t1,&z11); |
281 |
|
37 |
} |
282 |
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283 |
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void fe25519_pow2523(fe25519 *r, const fe25519 *x) |
284 |
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{ |
285 |
|
42 |
fe25519 z2; |
286 |
|
21 |
fe25519 z9; |
287 |
|
21 |
fe25519 z11; |
288 |
|
21 |
fe25519 z2_5_0; |
289 |
|
21 |
fe25519 z2_10_0; |
290 |
|
21 |
fe25519 z2_20_0; |
291 |
|
21 |
fe25519 z2_50_0; |
292 |
|
21 |
fe25519 z2_100_0; |
293 |
|
21 |
fe25519 t; |
294 |
|
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int i; |
295 |
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296 |
|
21 |
/* 2 */ fe25519_square(&z2,x); |
297 |
|
21 |
/* 4 */ fe25519_square(&t,&z2); |
298 |
|
21 |
/* 8 */ fe25519_square(&t,&t); |
299 |
|
21 |
/* 9 */ fe25519_mul(&z9,&t,x); |
300 |
|
21 |
/* 11 */ fe25519_mul(&z11,&z9,&z2); |
301 |
|
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/* 22 */ fe25519_square(&t,&z11); |
302 |
|
21 |
/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9); |
303 |
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304 |
|
21 |
/* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0); |
305 |
✓✓ |
210 |
/* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); } |
306 |
|
21 |
/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0); |
307 |
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308 |
|
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/* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0); |
309 |
✓✓ |
420 |
/* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } |
310 |
|
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/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0); |
311 |
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312 |
|
21 |
/* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0); |
313 |
✓✓ |
840 |
/* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); } |
314 |
|
21 |
/* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0); |
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316 |
|
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/* 2^41 - 2^1 */ fe25519_square(&t,&t); |
317 |
✓✓ |
420 |
/* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } |
318 |
|
21 |
/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0); |
319 |
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320 |
|
21 |
/* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0); |
321 |
✓✓ |
2100 |
/* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } |
322 |
|
21 |
/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0); |
323 |
|
|
|
324 |
|
21 |
/* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0); |
325 |
✓✓ |
4200 |
/* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); } |
326 |
|
21 |
/* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0); |
327 |
|
|
|
328 |
|
21 |
/* 2^201 - 2^1 */ fe25519_square(&t,&t); |
329 |
✓✓ |
2100 |
/* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } |
330 |
|
21 |
/* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0); |
331 |
|
|
|
332 |
|
21 |
/* 2^251 - 2^1 */ fe25519_square(&t,&t); |
333 |
|
21 |
/* 2^252 - 2^2 */ fe25519_square(&t,&t); |
334 |
|
21 |
/* 2^252 - 3 */ fe25519_mul(r,&t,x); |
335 |
|
21 |
} |