You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
682 lines
26 KiB
682 lines
26 KiB
/*
|
|
Public domain by Andrew M. <liquidsun@gmail.com>
|
|
See: https://github.com/floodyberry/curve25519-donna
|
|
|
|
32 bit integer curve25519 implementation
|
|
*/
|
|
|
|
#include "ed25519-donna.h"
|
|
|
|
static const uint32_t reduce_mask_25 = (1 << 25) - 1;
|
|
static const uint32_t reduce_mask_26 = (1 << 26) - 1;
|
|
|
|
/* out = in */
|
|
void curve25519_copy(bignum25519 out, const bignum25519 in) {
|
|
out[0] = in[0];
|
|
out[1] = in[1];
|
|
out[2] = in[2];
|
|
out[3] = in[3];
|
|
out[4] = in[4];
|
|
out[5] = in[5];
|
|
out[6] = in[6];
|
|
out[7] = in[7];
|
|
out[8] = in[8];
|
|
out[9] = in[9];
|
|
}
|
|
|
|
/* out = a + b */
|
|
void curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
out[0] = a[0] + b[0];
|
|
out[1] = a[1] + b[1];
|
|
out[2] = a[2] + b[2];
|
|
out[3] = a[3] + b[3];
|
|
out[4] = a[4] + b[4];
|
|
out[5] = a[5] + b[5];
|
|
out[6] = a[6] + b[6];
|
|
out[7] = a[7] + b[7];
|
|
out[8] = a[8] + b[8];
|
|
out[9] = a[9] + b[9];
|
|
}
|
|
|
|
void curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
uint32_t c = 0;
|
|
out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
|
|
out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
|
|
out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
|
|
out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
|
|
out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
|
|
out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
|
|
out[0] += 19 * c;
|
|
}
|
|
|
|
void curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
uint32_t c = 0;
|
|
out[0] = a[0] + b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
|
|
out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
|
|
out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
|
|
out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
|
|
out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
|
|
out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
|
|
out[0] += 19 * c;
|
|
}
|
|
|
|
/* multiples of p */
|
|
static const uint32_t twoP0 = 0x07ffffda;
|
|
static const uint32_t twoP13579 = 0x03fffffe;
|
|
static const uint32_t twoP2468 = 0x07fffffe;
|
|
static const uint32_t fourP0 = 0x0fffffb4;
|
|
static const uint32_t fourP13579 = 0x07fffffc;
|
|
static const uint32_t fourP2468 = 0x0ffffffc;
|
|
|
|
/* out = a - b */
|
|
void curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
uint32_t c = 0;
|
|
out[0] = twoP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = twoP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = twoP2468 + a[4] - b[4] + c;
|
|
out[5] = twoP13579 + a[5] - b[5] ;
|
|
out[6] = twoP2468 + a[6] - b[6] ;
|
|
out[7] = twoP13579 + a[7] - b[7] ;
|
|
out[8] = twoP2468 + a[8] - b[8] ;
|
|
out[9] = twoP13579 + a[9] - b[9] ;
|
|
}
|
|
|
|
/* out = in * scalar */
|
|
void curve25519_scalar_product(bignum25519 out, const bignum25519 in, const uint32_t scalar) {
|
|
uint64_t a = 0;
|
|
uint32_t c = 0;
|
|
a = mul32x32_64(in[0], scalar); out[0] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
|
|
a = mul32x32_64(in[1], scalar) + c; out[1] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
|
|
a = mul32x32_64(in[2], scalar) + c; out[2] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
|
|
a = mul32x32_64(in[3], scalar) + c; out[3] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
|
|
a = mul32x32_64(in[4], scalar) + c; out[4] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
|
|
a = mul32x32_64(in[5], scalar) + c; out[5] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
|
|
a = mul32x32_64(in[6], scalar) + c; out[6] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
|
|
a = mul32x32_64(in[7], scalar) + c; out[7] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
|
|
a = mul32x32_64(in[8], scalar) + c; out[8] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
|
|
a = mul32x32_64(in[9], scalar) + c; out[9] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
|
|
out[0] += c * 19;
|
|
}
|
|
|
|
/* out = a - b, where a is the result of a basic op (add,sub) */
|
|
void curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
uint32_t c = 0;
|
|
out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
|
|
out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
|
|
out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
|
|
out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
|
|
out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
|
|
out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
|
|
out[0] += 19 * c;
|
|
}
|
|
|
|
void curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
uint32_t c = 0;
|
|
out[0] = fourP0 + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = fourP2468 + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = fourP2468 + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
|
|
out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
|
|
out[6] = fourP2468 + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
|
|
out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
|
|
out[8] = fourP2468 + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
|
|
out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
|
|
out[0] += 19 * c;
|
|
}
|
|
|
|
/* out = -a */
|
|
void curve25519_neg(bignum25519 out, const bignum25519 a) {
|
|
uint32_t c = 0;
|
|
out[0] = twoP0 - a[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = twoP2468 - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = twoP2468 - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
|
|
out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
|
|
out[6] = twoP2468 - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
|
|
out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
|
|
out[8] = twoP2468 - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
|
|
out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
|
|
out[0] += 19 * c;
|
|
}
|
|
|
|
/* out = a * b */
|
|
#define curve25519_mul_noinline curve25519_mul
|
|
void curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
|
uint32_t r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0, r6 = 0, r7 = 0, r8 = 0, r9 = 0;
|
|
uint32_t s0 = 0, s1 = 0, s2 = 0, s3 = 0, s4 = 0, s5 = 0, s6 = 0, s7 = 0, s8 = 0, s9 = 0;
|
|
uint64_t m0 = 0, m1 = 0, m2 = 0, m3 = 0, m4 = 0, m5 = 0, m6 = 0, m7 = 0, m8 = 0, m9 = 0, c = 0;
|
|
uint32_t p = 0;
|
|
|
|
r0 = b[0];
|
|
r1 = b[1];
|
|
r2 = b[2];
|
|
r3 = b[3];
|
|
r4 = b[4];
|
|
r5 = b[5];
|
|
r6 = b[6];
|
|
r7 = b[7];
|
|
r8 = b[8];
|
|
r9 = b[9];
|
|
|
|
s0 = a[0];
|
|
s1 = a[1];
|
|
s2 = a[2];
|
|
s3 = a[3];
|
|
s4 = a[4];
|
|
s5 = a[5];
|
|
s6 = a[6];
|
|
s7 = a[7];
|
|
s8 = a[8];
|
|
s9 = a[9];
|
|
|
|
m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
|
|
m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
|
|
m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
|
|
m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
|
|
m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
|
|
|
|
r1 *= 2;
|
|
r3 *= 2;
|
|
r5 *= 2;
|
|
r7 *= 2;
|
|
|
|
m0 = mul32x32_64(r0, s0);
|
|
m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
|
|
m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
|
|
m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
|
|
m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
|
|
|
|
r1 *= 19;
|
|
r2 *= 19;
|
|
r3 = (r3 / 2) * 19;
|
|
r4 *= 19;
|
|
r5 = (r5 / 2) * 19;
|
|
r6 *= 19;
|
|
r7 = (r7 / 2) * 19;
|
|
r8 *= 19;
|
|
r9 *= 19;
|
|
|
|
m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
|
|
m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
|
|
m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
|
|
m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
|
|
|
|
r3 *= 2;
|
|
r5 *= 2;
|
|
r7 *= 2;
|
|
r9 *= 2;
|
|
|
|
m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
|
|
m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
|
|
m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
|
|
m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
|
|
m8 += (mul32x32_64(r9, s9));
|
|
|
|
r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
|
|
m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
|
|
m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
|
|
m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
|
|
m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
|
|
m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
|
|
m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
|
|
m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
|
|
m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
|
|
m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
|
|
m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
|
|
r1 += p;
|
|
|
|
out[0] = r0;
|
|
out[1] = r1;
|
|
out[2] = r2;
|
|
out[3] = r3;
|
|
out[4] = r4;
|
|
out[5] = r5;
|
|
out[6] = r6;
|
|
out[7] = r7;
|
|
out[8] = r8;
|
|
out[9] = r9;
|
|
}
|
|
|
|
/* out = in * in */
|
|
void curve25519_square(bignum25519 out, const bignum25519 in) {
|
|
uint32_t r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0, r6 = 0, r7 = 0, r8 = 0, r9 = 0;
|
|
uint32_t d6 = 0, d7 = 0, d8 = 0, d9 = 0;
|
|
uint64_t m0 = 0, m1 = 0, m2 = 0, m3 = 0, m4 = 0, m5 = 0, m6 = 0, m7 = 0, m8 = 0, m9 = 0, c = 0;
|
|
uint32_t p = 0;
|
|
|
|
r0 = in[0];
|
|
r1 = in[1];
|
|
r2 = in[2];
|
|
r3 = in[3];
|
|
r4 = in[4];
|
|
r5 = in[5];
|
|
r6 = in[6];
|
|
r7 = in[7];
|
|
r8 = in[8];
|
|
r9 = in[9];
|
|
|
|
m0 = mul32x32_64(r0, r0);
|
|
r0 *= 2;
|
|
m1 = mul32x32_64(r0, r1);
|
|
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
|
|
r1 *= 2;
|
|
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
|
|
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
|
|
r2 *= 2;
|
|
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
|
|
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
|
|
r3 *= 2;
|
|
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
|
|
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
|
|
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
|
|
|
|
d6 = r6 * 19;
|
|
d7 = r7 * 2 * 19;
|
|
d8 = r8 * 19;
|
|
d9 = r9 * 2 * 19;
|
|
|
|
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
|
|
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
|
|
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
|
|
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
|
|
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
|
|
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
|
|
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
|
|
m7 += (mul32x32_64(d9, r8 ));
|
|
m8 += (mul32x32_64(d9, r9 ));
|
|
|
|
r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
|
|
m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
|
|
m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
|
|
m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
|
|
m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
|
|
m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
|
|
m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
|
|
m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
|
|
m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
|
|
m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
|
|
m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
|
|
r1 += p;
|
|
|
|
out[0] = r0;
|
|
out[1] = r1;
|
|
out[2] = r2;
|
|
out[3] = r3;
|
|
out[4] = r4;
|
|
out[5] = r5;
|
|
out[6] = r6;
|
|
out[7] = r7;
|
|
out[8] = r8;
|
|
out[9] = r9;
|
|
}
|
|
|
|
/* out = in ^ (2 * count) */
|
|
void curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
|
|
uint32_t r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0, r6 = 0, r7 = 0, r8 = 0, r9 = 0;
|
|
uint32_t d6 = 0, d7 = 0, d8 = 0, d9 = 0;
|
|
uint64_t m0 = 0, m1 = 0, m2 = 0, m3 = 0, m4 = 0, m5 = 0, m6 = 0, m7 = 0, m8 = 0, m9 = 0, c = 0;
|
|
uint32_t p = 0;
|
|
|
|
r0 = in[0];
|
|
r1 = in[1];
|
|
r2 = in[2];
|
|
r3 = in[3];
|
|
r4 = in[4];
|
|
r5 = in[5];
|
|
r6 = in[6];
|
|
r7 = in[7];
|
|
r8 = in[8];
|
|
r9 = in[9];
|
|
|
|
do {
|
|
m0 = mul32x32_64(r0, r0);
|
|
r0 *= 2;
|
|
m1 = mul32x32_64(r0, r1);
|
|
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
|
|
r1 *= 2;
|
|
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
|
|
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
|
|
r2 *= 2;
|
|
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
|
|
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
|
|
r3 *= 2;
|
|
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
|
|
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
|
|
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
|
|
|
|
d6 = r6 * 19;
|
|
d7 = r7 * 2 * 19;
|
|
d8 = r8 * 19;
|
|
d9 = r9 * 2 * 19;
|
|
|
|
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
|
|
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
|
|
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
|
|
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
|
|
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
|
|
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
|
|
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
|
|
m7 += (mul32x32_64(d9, r8 ));
|
|
m8 += (mul32x32_64(d9, r9 ));
|
|
|
|
r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
|
|
m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
|
|
m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
|
|
m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
|
|
m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
|
|
m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
|
|
m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
|
|
m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
|
|
m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
|
|
m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
|
|
m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
|
|
r1 += p;
|
|
} while (--count);
|
|
|
|
out[0] = r0;
|
|
out[1] = r1;
|
|
out[2] = r2;
|
|
out[3] = r3;
|
|
out[4] = r4;
|
|
out[5] = r5;
|
|
out[6] = r6;
|
|
out[7] = r7;
|
|
out[8] = r8;
|
|
out[9] = r9;
|
|
}
|
|
|
|
/* Take a little-endian, 32-byte number and expand it into polynomial form */
|
|
void curve25519_expand(bignum25519 out, const unsigned char in[32]) {
|
|
uint32_t x0 = 0, x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, x7 = 0;
|
|
#define F(s) \
|
|
((((uint32_t)in[s + 0]) ) | \
|
|
(((uint32_t)in[s + 1]) << 8) | \
|
|
(((uint32_t)in[s + 2]) << 16) | \
|
|
(((uint32_t)in[s + 3]) << 24))
|
|
x0 = F(0);
|
|
x1 = F(4);
|
|
x2 = F(8);
|
|
x3 = F(12);
|
|
x4 = F(16);
|
|
x5 = F(20);
|
|
x6 = F(24);
|
|
x7 = F(28);
|
|
#undef F
|
|
|
|
out[0] = ( x0 ) & reduce_mask_26;
|
|
out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & reduce_mask_25;
|
|
out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & reduce_mask_26;
|
|
out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & reduce_mask_25;
|
|
out[4] = (( x3) >> 6) & reduce_mask_26;
|
|
out[5] = ( x4 ) & reduce_mask_25;
|
|
out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & reduce_mask_26;
|
|
out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & reduce_mask_25;
|
|
out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & reduce_mask_26;
|
|
out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
|
|
}
|
|
|
|
/* Take a fully reduced polynomial form number and contract it into a
|
|
* little-endian, 32-byte array
|
|
*/
|
|
void curve25519_contract(unsigned char out[32], const bignum25519 in) {
|
|
bignum25519 f = {0};
|
|
curve25519_copy(f, in);
|
|
|
|
#define carry_pass() \
|
|
f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
|
|
f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
|
|
f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
|
|
f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
|
|
f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
|
|
f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
|
|
f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
|
|
f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
|
|
f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
|
|
|
|
#define carry_pass_full() \
|
|
carry_pass() \
|
|
f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
|
|
|
|
#define carry_pass_final() \
|
|
carry_pass() \
|
|
f[9] &= reduce_mask_25;
|
|
|
|
carry_pass_full()
|
|
carry_pass_full()
|
|
|
|
/* now t is between 0 and 2^255-1, properly carried. */
|
|
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
|
|
f[0] += 19;
|
|
carry_pass_full()
|
|
|
|
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
|
|
f[0] += (reduce_mask_26 + 1) - 19;
|
|
f[1] += (reduce_mask_25 + 1) - 1;
|
|
f[2] += (reduce_mask_26 + 1) - 1;
|
|
f[3] += (reduce_mask_25 + 1) - 1;
|
|
f[4] += (reduce_mask_26 + 1) - 1;
|
|
f[5] += (reduce_mask_25 + 1) - 1;
|
|
f[6] += (reduce_mask_26 + 1) - 1;
|
|
f[7] += (reduce_mask_25 + 1) - 1;
|
|
f[8] += (reduce_mask_26 + 1) - 1;
|
|
f[9] += (reduce_mask_25 + 1) - 1;
|
|
|
|
/* now between 2^255 and 2^256-20, and offset by 2^255. */
|
|
carry_pass_final()
|
|
|
|
#undef carry_pass
|
|
#undef carry_full
|
|
#undef carry_final
|
|
|
|
f[1] <<= 2;
|
|
f[2] <<= 3;
|
|
f[3] <<= 5;
|
|
f[4] <<= 6;
|
|
f[6] <<= 1;
|
|
f[7] <<= 3;
|
|
f[8] <<= 4;
|
|
f[9] <<= 6;
|
|
|
|
#define F(i, s) \
|
|
out[s+0] |= (unsigned char )(f[i] & 0xff); \
|
|
out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \
|
|
out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \
|
|
out[s+3] = (unsigned char )((f[i] >> 24) & 0xff);
|
|
|
|
out[0] = 0;
|
|
out[16] = 0;
|
|
F(0,0);
|
|
F(1,3);
|
|
F(2,6);
|
|
F(3,9);
|
|
F(4,12);
|
|
F(5,16);
|
|
F(6,19);
|
|
F(7,22);
|
|
F(8,25);
|
|
F(9,28);
|
|
#undef F
|
|
}
|
|
|
|
/* if (iswap) swap(a, b) */
|
|
void curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) {
|
|
const uint32_t swap = (uint32_t)(-(int32_t)iswap);
|
|
uint32_t x0 = 0, x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, x7 = 0, x8 = 0, x9 = 0;
|
|
|
|
x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
|
|
x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
|
|
x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
|
|
x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
|
|
x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
|
|
x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;
|
|
x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6;
|
|
x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7;
|
|
x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8;
|
|
x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9;
|
|
}
|
|
|
|
void curve25519_set(bignum25519 r, uint32_t x){
|
|
r[0] = x & reduce_mask_26; x >>= 26;
|
|
r[1] = x & reduce_mask_25;
|
|
r[2] = 0;
|
|
r[3] = 0;
|
|
r[4] = 0;
|
|
r[5] = 0;
|
|
r[6] = 0;
|
|
r[7] = 0;
|
|
r[8] = 0;
|
|
r[9] = 0;
|
|
}
|
|
|
|
void curve25519_set_d(bignum25519 r){
|
|
curve25519_copy(r, ge25519_ecd);
|
|
}
|
|
|
|
void curve25519_set_2d(bignum25519 r){
|
|
curve25519_copy(r, ge25519_ec2d);
|
|
}
|
|
|
|
void curve25519_set_sqrtneg1(bignum25519 r){
|
|
curve25519_copy(r, ge25519_sqrtneg1);
|
|
}
|
|
|
|
int curve25519_isnegative(const bignum25519 f) {
|
|
unsigned char s[32] = {0};
|
|
curve25519_contract(s, f);
|
|
return s[0] & 1;
|
|
}
|
|
|
|
int curve25519_isnonzero(const bignum25519 f) {
|
|
unsigned char s[32] = {0};
|
|
curve25519_contract(s, f);
|
|
return ((((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] |
|
|
s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] |
|
|
s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] |
|
|
s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1) & 0x1;
|
|
}
|
|
|
|
void curve25519_reduce(bignum25519 out, const bignum25519 in) {
|
|
uint32_t c = 0;
|
|
out[0] = in[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
|
|
out[1] = in[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
|
|
out[2] = in[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
|
|
out[3] = in[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
|
|
out[4] = in[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
|
|
out[5] = in[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
|
|
out[6] = in[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
|
|
out[7] = in[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
|
|
out[8] = in[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
|
|
out[9] = in[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
|
|
out[0] += 19 * c;
|
|
}
|
|
|
|
void curve25519_divpowm1(bignum25519 r, const bignum25519 u, const bignum25519 v) {
|
|
bignum25519 v3={0}, uv7={0}, t0={0}, t1={0}, t2={0};
|
|
int i = 0;
|
|
|
|
curve25519_square(v3, v);
|
|
curve25519_mul(v3, v3, v); /* v3 = v^3 */
|
|
curve25519_square(uv7, v3);
|
|
curve25519_mul(uv7, uv7, v);
|
|
curve25519_mul(uv7, uv7, u); /* uv7 = uv^7 */
|
|
|
|
/*fe_pow22523(uv7, uv7);*/
|
|
/* From fe_pow22523.c */
|
|
|
|
curve25519_square(t0, uv7);
|
|
curve25519_square(t1, t0);
|
|
curve25519_square(t1, t1);
|
|
curve25519_mul(t1, uv7, t1);
|
|
curve25519_mul(t0, t0, t1);
|
|
curve25519_square(t0, t0);
|
|
curve25519_mul(t0, t1, t0);
|
|
curve25519_square(t1, t0);
|
|
for (i = 0; i < 4; ++i) {
|
|
curve25519_square(t1, t1);
|
|
}
|
|
curve25519_mul(t0, t1, t0);
|
|
curve25519_square(t1, t0);
|
|
for (i = 0; i < 9; ++i) {
|
|
curve25519_square(t1, t1);
|
|
}
|
|
curve25519_mul(t1, t1, t0);
|
|
curve25519_square(t2, t1);
|
|
for (i = 0; i < 19; ++i) {
|
|
curve25519_square(t2, t2);
|
|
}
|
|
curve25519_mul(t1, t2, t1);
|
|
for (i = 0; i < 10; ++i) {
|
|
curve25519_square(t1, t1);
|
|
}
|
|
curve25519_mul(t0, t1, t0);
|
|
curve25519_square(t1, t0);
|
|
for (i = 0; i < 49; ++i) {
|
|
curve25519_square(t1, t1);
|
|
}
|
|
curve25519_mul(t1, t1, t0);
|
|
curve25519_square(t2, t1);
|
|
for (i = 0; i < 99; ++i) {
|
|
curve25519_square(t2, t2);
|
|
}
|
|
curve25519_mul(t1, t2, t1);
|
|
for (i = 0; i < 50; ++i) {
|
|
curve25519_square(t1, t1);
|
|
}
|
|
curve25519_mul(t0, t1, t0);
|
|
curve25519_square(t0, t0);
|
|
curve25519_square(t0, t0);
|
|
curve25519_mul(t0, t0, uv7);
|
|
|
|
/* End fe_pow22523.c */
|
|
/* t0 = (uv^7)^((q-5)/8) */
|
|
curve25519_mul(t0, t0, v3);
|
|
curve25519_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */
|
|
}
|
|
|
|
void curve25519_expand_reduce(bignum25519 out, const unsigned char in[32]) {
|
|
uint32_t x0 = 0, x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0, x7 = 0;
|
|
#define F(s) \
|
|
((((uint32_t)in[s + 0]) ) | \
|
|
(((uint32_t)in[s + 1]) << 8) | \
|
|
(((uint32_t)in[s + 2]) << 16) | \
|
|
(((uint32_t)in[s + 3]) << 24))
|
|
x0 = F(0);
|
|
x1 = F(4);
|
|
x2 = F(8);
|
|
x3 = F(12);
|
|
x4 = F(16);
|
|
x5 = F(20);
|
|
x6 = F(24);
|
|
x7 = F(28);
|
|
#undef F
|
|
|
|
out[0] = ( x0 ) & reduce_mask_26;
|
|
out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & reduce_mask_25;
|
|
out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & reduce_mask_26;
|
|
out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & reduce_mask_25;
|
|
out[4] = (( x3) >> 6) & reduce_mask_26;
|
|
out[5] = ( x4 ) & reduce_mask_25;
|
|
out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & reduce_mask_26;
|
|
out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & reduce_mask_25;
|
|
out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & reduce_mask_26;
|
|
out[9] = (( x7) >> 6); // & reduce_mask_25; /* ignore the top bit */
|
|
out[0] += 19 * (out[9] >> 25);
|
|
out[9] &= reduce_mask_25;
|
|
}
|