1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
|
/*
Public domain by Andrew M. <liquidsun@gmail.com>
See: https://github.com/floodyberry/curve25519-donna
Curve25519 implementation agnostic helpers
*/
/*
* In: b = 2^5 - 2^0
* Out: b = 2^250 - 2^0
*/
static void
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
bignum25519 ALIGN(16) t0,c;
/* 2^5 - 2^0 */ /* b */
/* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
/* 2^10 - 2^0 */ curve25519_mul_noinline(b, t0, b);
/* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
/* 2^20 - 2^0 */ curve25519_mul_noinline(c, t0, b);
/* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
/* 2^40 - 2^0 */ curve25519_mul_noinline(t0, t0, c);
/* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
/* 2^50 - 2^0 */ curve25519_mul_noinline(b, t0, b);
/* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
/* 2^100 - 2^0 */ curve25519_mul_noinline(c, t0, b);
/* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
/* 2^200 - 2^0 */ curve25519_mul_noinline(t0, t0, c);
/* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
/* 2^250 - 2^0 */ curve25519_mul_noinline(b, t0, b);
}
/*
* z^(p - 2) = z(2^255 - 21)
*/
static void
curve25519_recip(bignum25519 out, const bignum25519 z) {
bignum25519 ALIGN(16) a,t0,b;
/* 2 */ curve25519_square_times(a, z, 1); /* a = 2 */
/* 8 */ curve25519_square_times(t0, a, 2);
/* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */
/* 11 */ curve25519_mul_noinline(a, b, a); /* a = 11 */
/* 22 */ curve25519_square_times(t0, a, 1);
/* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b);
/* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
/* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
/* 2^255 - 21 */ curve25519_mul_noinline(out, b, a);
}
/*
* z^((p-5)/8) = z^(2^252 - 3)
*/
static void
curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
bignum25519 ALIGN(16) b,c,t0;
/* 2 */ curve25519_square_times(c, z, 1); /* c = 2 */
/* 8 */ curve25519_square_times(t0, c, 2); /* t0 = 8 */
/* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */
/* 11 */ curve25519_mul_noinline(c, b, c); /* c = 11 */
/* 22 */ curve25519_square_times(t0, c, 1);
/* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b);
/* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
/* 2^252 - 2^2 */ curve25519_square_times(b, b, 2);
/* 2^252 - 3 */ curve25519_mul_noinline(two252m3, b, z);
}
|
