ZeroTierOne/core/C25519.cpp
2021-05-19 16:24:21 -04:00

3197 lines
227 KiB
C++

/*
(c) Matthew Dempsky
Public domain.
Derived from public domain code by D. J. Bernstein.
*/
// Modified slightly for ZeroTier but remains in the public domain as per
// its original license.
#include "C25519.hpp"
#include "SHA512.hpp"
#include "Utils.hpp"
#ifdef __WINDOWS__
#pragma warning(disable : 4146)
#endif
#ifdef __GNUC__
#pragma GCC diagnostic ignored "-Wunused-function"
#pragma GCC diagnostic ignored "-Wuninitialized"
#endif
using namespace ZeroTier;
namespace {
// --------------------------------------------------------------------------------------------------------------------
#define crypto_hash_sha512_BYTES 64
typedef uint8_t u8;
typedef int32_t s32;
typedef int64_t limb;
ZT_INLINE void fsum(limb *output, const limb *in)
{
for (int i = 0; i < 10; i += 2) {
output[0 + i] = output[0 + i] + in[0 + i];
output[1 + i] = output[1 + i] + in[1 + i];
}
}
ZT_INLINE void fdifference(limb *output, const limb *in)
{
for (int i = 0; i < 10; ++i)
output[i] = in[i] - output[i];
}
ZT_INLINE void fscalar_product(limb *output, const limb *in, const limb scalar)
{
for (int i = 0; i < 10; ++i)
output[i] = in[i] * scalar;
}
void fproduct(limb *output, const limb *in2, const limb *in)
{
output[0] = ((limb)((s32)in2[0])) * ((s32)in[0]);
output[1] = ((limb)((s32)in2[0])) * ((s32)in[1]) + ((limb)((s32)in2[1])) * ((s32)in[0]);
output[2] = 2 * ((limb)((s32)in2[1])) * ((s32)in[1]) + ((limb)((s32)in2[0])) * ((s32)in[2])
+ ((limb)((s32)in2[2])) * ((s32)in[0]);
output[3] = ((limb)((s32)in2[1])) * ((s32)in[2]) + ((limb)((s32)in2[2])) * ((s32)in[1])
+ ((limb)((s32)in2[0])) * ((s32)in[3]) + ((limb)((s32)in2[3])) * ((s32)in[0]);
output[4] = ((limb)((s32)in2[2])) * ((s32)in[2])
+ 2 * (((limb)((s32)in2[1])) * ((s32)in[3]) + ((limb)((s32)in2[3])) * ((s32)in[1]))
+ ((limb)((s32)in2[0])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[0]);
output[5] = ((limb)((s32)in2[2])) * ((s32)in[3]) + ((limb)((s32)in2[3])) * ((s32)in[2])
+ ((limb)((s32)in2[1])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[1])
+ ((limb)((s32)in2[0])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[0]);
output[6] = 2
* (((limb)((s32)in2[3])) * ((s32)in[3]) + ((limb)((s32)in2[1])) * ((s32)in[5])
+ ((limb)((s32)in2[5])) * ((s32)in[1]))
+ ((limb)((s32)in2[2])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[2])
+ ((limb)((s32)in2[0])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[0]);
output[7] = ((limb)((s32)in2[3])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[3])
+ ((limb)((s32)in2[2])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[2])
+ ((limb)((s32)in2[1])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[1])
+ ((limb)((s32)in2[0])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[0]);
output[8] = ((limb)((s32)in2[4])) * ((s32)in[4])
+ 2
* (((limb)((s32)in2[3])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[3])
+ ((limb)((s32)in2[1])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[1]))
+ ((limb)((s32)in2[2])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[2])
+ ((limb)((s32)in2[0])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[0]);
output[9] = ((limb)((s32)in2[4])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[4])
+ ((limb)((s32)in2[3])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[3])
+ ((limb)((s32)in2[2])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[2])
+ ((limb)((s32)in2[1])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[1])
+ ((limb)((s32)in2[0])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[0]);
output[10] = 2
* (((limb)((s32)in2[5])) * ((s32)in[5]) + ((limb)((s32)in2[3])) * ((s32)in[7])
+ ((limb)((s32)in2[7])) * ((s32)in[3]) + ((limb)((s32)in2[1])) * ((s32)in[9])
+ ((limb)((s32)in2[9])) * ((s32)in[1]))
+ ((limb)((s32)in2[4])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[4])
+ ((limb)((s32)in2[2])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[2]);
output[11] = ((limb)((s32)in2[5])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[5])
+ ((limb)((s32)in2[4])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[4])
+ ((limb)((s32)in2[3])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[3])
+ ((limb)((s32)in2[2])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[2]);
output[12] = ((limb)((s32)in2[6])) * ((s32)in[6])
+ 2
* (((limb)((s32)in2[5])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[5])
+ ((limb)((s32)in2[3])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[3]))
+ ((limb)((s32)in2[4])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[4]);
output[13] = ((limb)((s32)in2[6])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[6])
+ ((limb)((s32)in2[5])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[5])
+ ((limb)((s32)in2[4])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[4]);
output[14] = 2
* (((limb)((s32)in2[7])) * ((s32)in[7]) + ((limb)((s32)in2[5])) * ((s32)in[9])
+ ((limb)((s32)in2[9])) * ((s32)in[5]))
+ ((limb)((s32)in2[6])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[6]);
output[15] = ((limb)((s32)in2[7])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[7])
+ ((limb)((s32)in2[6])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[6]);
output[16] = ((limb)((s32)in2[8])) * ((s32)in[8])
+ 2 * (((limb)((s32)in2[7])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[7]));
output[17] = ((limb)((s32)in2[8])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[8]);
output[18] = 2 * ((limb)((s32)in2[9])) * ((s32)in[9]);
}
ZT_INLINE void freduce_degree(limb *output)
{
output[8] += output[18] << 4;
output[8] += output[18] << 1;
output[8] += output[18];
output[7] += output[17] << 4;
output[7] += output[17] << 1;
output[7] += output[17];
output[6] += output[16] << 4;
output[6] += output[16] << 1;
output[6] += output[16];
output[5] += output[15] << 4;
output[5] += output[15] << 1;
output[5] += output[15];
output[4] += output[14] << 4;
output[4] += output[14] << 1;
output[4] += output[14];
output[3] += output[13] << 4;
output[3] += output[13] << 1;
output[3] += output[13];
output[2] += output[12] << 4;
output[2] += output[12] << 1;
output[2] += output[12];
output[1] += output[11] << 4;
output[1] += output[11] << 1;
output[1] += output[11];
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
}
#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif
ZT_INLINE limb div_by_2_26(const limb v)
{
const uint32_t highword = (uint32_t)(((uint64_t)v) >> 32);
const int32_t sign = ((int32_t)highword) >> 31;
const int32_t roundoff = ((uint32_t)sign) >> 6;
return (v + roundoff) >> 26;
}
ZT_INLINE limb div_by_2_25(const limb v)
{
const uint32_t highword = (uint32_t)(((uint64_t)v) >> 32);
const int32_t sign = ((int32_t)highword) >> 31;
const int32_t roundoff = ((uint32_t)sign) >> 7;
return (v + roundoff) >> 25;
}
ZT_INLINE void freduce_coefficients(limb *output)
{
output[10] = 0;
for (int i = 0; i < 10; i += 2) {
limb over = div_by_2_26(output[i]);
output[i] -= over << 26;
output[i + 1] += over;
over = div_by_2_25(output[i + 1]);
output[i + 1] -= over << 25;
output[i + 2] += over;
}
output[0] += output[10] << 4;
output[0] += output[10] << 1;
output[0] += output[10];
output[10] = 0;
limb over = div_by_2_26(output[0]);
output[0] -= over << 26;
output[1] += over;
}
ZT_INLINE void fmul(limb *output, const limb *in, const limb *in2)
{
limb t[19];
fproduct(t, in, in2);
freduce_degree(t);
freduce_coefficients(t);
Utils::copy<sizeof(limb) * 10>(output, t);
}
void fsquare_inner(limb *output, const limb *in)
{
output[0] = ((limb)((s32)in[0])) * ((s32)in[0]);
output[1] = 2 * ((limb)((s32)in[0])) * ((s32)in[1]);
output[2] = 2 * (((limb)((s32)in[1])) * ((s32)in[1]) + ((limb)((s32)in[0])) * ((s32)in[2]));
output[3] = 2 * (((limb)((s32)in[1])) * ((s32)in[2]) + ((limb)((s32)in[0])) * ((s32)in[3]));
output[4] = ((limb)((s32)in[2])) * ((s32)in[2]) + 4 * ((limb)((s32)in[1])) * ((s32)in[3])
+ 2 * ((limb)((s32)in[0])) * ((s32)in[4]);
output[5] = 2
* (((limb)((s32)in[2])) * ((s32)in[3]) + ((limb)((s32)in[1])) * ((s32)in[4])
+ ((limb)((s32)in[0])) * ((s32)in[5]));
output[6] = 2
* (((limb)((s32)in[3])) * ((s32)in[3]) + ((limb)((s32)in[2])) * ((s32)in[4])
+ ((limb)((s32)in[0])) * ((s32)in[6]) + 2 * ((limb)((s32)in[1])) * ((s32)in[5]));
output[7] = 2
* (((limb)((s32)in[3])) * ((s32)in[4]) + ((limb)((s32)in[2])) * ((s32)in[5])
+ ((limb)((s32)in[1])) * ((s32)in[6]) + ((limb)((s32)in[0])) * ((s32)in[7]));
output[8] = ((limb)((s32)in[4])) * ((s32)in[4])
+ 2
* (((limb)((s32)in[2])) * ((s32)in[6]) + ((limb)((s32)in[0])) * ((s32)in[8])
+ 2 * (((limb)((s32)in[1])) * ((s32)in[7]) + ((limb)((s32)in[3])) * ((s32)in[5])));
output[9] = 2
* (((limb)((s32)in[4])) * ((s32)in[5]) + ((limb)((s32)in[3])) * ((s32)in[6])
+ ((limb)((s32)in[2])) * ((s32)in[7]) + ((limb)((s32)in[1])) * ((s32)in[8])
+ ((limb)((s32)in[0])) * ((s32)in[9]));
output[10] = 2
* (((limb)((s32)in[5])) * ((s32)in[5]) + ((limb)((s32)in[4])) * ((s32)in[6])
+ ((limb)((s32)in[2])) * ((s32)in[8])
+ 2 * (((limb)((s32)in[3])) * ((s32)in[7]) + ((limb)((s32)in[1])) * ((s32)in[9])));
output[11] = 2
* (((limb)((s32)in[5])) * ((s32)in[6]) + ((limb)((s32)in[4])) * ((s32)in[7])
+ ((limb)((s32)in[3])) * ((s32)in[8]) + ((limb)((s32)in[2])) * ((s32)in[9]));
output[12] = ((limb)((s32)in[6])) * ((s32)in[6])
+ 2
* (((limb)((s32)in[4])) * ((s32)in[8])
+ 2 * (((limb)((s32)in[5])) * ((s32)in[7]) + ((limb)((s32)in[3])) * ((s32)in[9])));
output[13] = 2
* (((limb)((s32)in[6])) * ((s32)in[7]) + ((limb)((s32)in[5])) * ((s32)in[8])
+ ((limb)((s32)in[4])) * ((s32)in[9]));
output[14] = 2
* (((limb)((s32)in[7])) * ((s32)in[7]) + ((limb)((s32)in[6])) * ((s32)in[8])
+ 2 * ((limb)((s32)in[5])) * ((s32)in[9]));
output[15] = 2 * (((limb)((s32)in[7])) * ((s32)in[8]) + ((limb)((s32)in[6])) * ((s32)in[9]));
output[16] = ((limb)((s32)in[8])) * ((s32)in[8]) + 4 * ((limb)((s32)in[7])) * ((s32)in[9]);
output[17] = 2 * ((limb)((s32)in[8])) * ((s32)in[9]);
output[18] = 2 * ((limb)((s32)in[9])) * ((s32)in[9]);
}
ZT_INLINE void fsquare(limb *output, const limb *in)
{
limb t[19];
fsquare_inner(t, in);
freduce_degree(t);
freduce_coefficients(t);
Utils::copy<sizeof(limb) * 10>(output, t);
}
ZT_INLINE void fexpand(limb *output, const u8 *input)
{
#define F(n, start, shift, mask) \
output[n] = ((((limb)input[start + 0]) | ((limb)input[start + 1]) << 8 | ((limb)input[start + 2]) << 16 \
| ((limb)input[start + 3]) << 24) \
>> shift) \
& mask
F(0, 0, 0, 0x3ffffff);
F(1, 3, 2, 0x1ffffff);
F(2, 6, 3, 0x3ffffff);
F(3, 9, 5, 0x1ffffff);
F(4, 12, 6, 0x3ffffff);
F(5, 16, 0, 0x1ffffff);
F(6, 19, 1, 0x3ffffff);
F(7, 22, 3, 0x1ffffff);
F(8, 25, 4, 0x3ffffff);
F(9, 28, 6, 0x1ffffff);
#undef F
}
#if (-32 >> 1) != -16
#error "This code only works when >> does sign-extension on negative numbers"
#endif
ZT_INLINE s32 s32_eq(s32 a, s32 b)
{
a = ~(a ^ b);
a &= a << 16;
a &= a << 8;
a &= a << 4;
a &= a << 2;
a &= a << 1;
return a >> 31;
}
ZT_INLINE s32 s32_gte(s32 a, s32 b)
{
a -= b;
return ~(a >> 31);
}
void fcontract(u8 *output, limb *input_limbs)
{
int i, j;
s32 input[10], mask;
for (i = 0; i < 10; i++) {
input[i] = input_limbs[i];
}
for (j = 0; j < 2; ++j) {
for (i = 0; i < 9; ++i) {
if ((i & 1) == 1) {
const s32 mm = input[i] >> 31;
const s32 carry = -((input[i] & mm) >> 25);
input[i] = input[i] + (carry << 25);
input[i + 1] = input[i + 1] - carry;
}
else {
const s32 mm = input[i] >> 31;
const s32 carry = -((input[i] & mm) >> 26);
input[i] = input[i] + (carry << 26);
input[i + 1] = input[i + 1] - carry;
}
}
{
const s32 mm = input[9] >> 31;
const s32 carry = -((input[9] & mm) >> 25);
input[9] = input[9] + (carry << 25);
input[0] = input[0] - (carry * 19);
}
}
{
const s32 mm = input[0] >> 31;
const s32 carry = -((input[0] & mm) >> 26);
input[0] = input[0] + (carry << 26);
input[1] = input[1] - carry;
}
for (j = 0; j < 2; j++) {
for (i = 0; i < 9; i++) {
if ((i & 1) == 1) {
const s32 carry = input[i] >> 25;
input[i] &= 0x1ffffff;
input[i + 1] += carry;
}
else {
const s32 carry = input[i] >> 26;
input[i] &= 0x3ffffff;
input[i + 1] += carry;
}
}
{
const s32 carry = input[9] >> 25;
input[9] &= 0x1ffffff;
input[0] += 19 * carry;
}
}
mask = s32_gte(input[0], 0x3ffffed);
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
mask &= s32_eq(input[i], 0x1ffffff);
}
else {
mask &= s32_eq(input[i], 0x3ffffff);
}
}
input[0] -= mask & 0x3ffffed;
for (i = 1; i < 10; i++) {
if ((i & 1) == 1) {
input[i] -= mask & 0x1ffffff;
}
else {
input[i] -= mask & 0x3ffffff;
}
}
input[1] <<= 2;
input[2] <<= 3;
input[3] <<= 5;
input[4] <<= 6;
input[6] <<= 1;
input[7] <<= 3;
input[8] <<= 4;
input[9] <<= 6;
#define F(i, s) \
output[s + 0] |= input[i] & 0xff; \
output[s + 1] = (input[i] >> 8) & 0xff; \
output[s + 2] = (input[i] >> 16) & 0xff; \
output[s + 3] = (input[i] >> 24) & 0xff
output[0] = 0;
output[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
}
void fmonty(
limb *x2, limb *z2, /* output 2Q */
limb *x3, limb *z3, /* output Q + Q' */
limb *x, limb *z, /* input Q */
limb *xprime, limb *zprime, /* input Q' */
const limb *qmqp /* input Q - Q' */)
{
limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];
Utils::copy<10 * sizeof(limb)>(origx, x);
fsum(x, z);
fdifference(z, origx);
Utils::copy<sizeof(limb) * 10>(origxprime, xprime);
fsum(xprime, zprime);
fdifference(zprime, origxprime);
fproduct(xxprime, xprime, z);
fproduct(zzprime, x, zprime);
freduce_degree(xxprime);
freduce_coefficients(xxprime);
freduce_degree(zzprime);
freduce_coefficients(zzprime);
Utils::copy<sizeof(limb) * 10>(origxprime, xxprime);
fsum(xxprime, zzprime);
fdifference(zzprime, origxprime);
fsquare(xxxprime, xxprime);
fsquare(zzzprime, zzprime);
fproduct(zzprime, zzzprime, qmqp);
freduce_degree(zzprime);
freduce_coefficients(zzprime);
Utils::copy<sizeof(limb) * 10>(x3, xxxprime);
Utils::copy<sizeof(limb) * 10>(z3, zzprime);
fsquare(xx, x);
fsquare(zz, z);
fproduct(x2, xx, zz);
freduce_degree(x2);
freduce_coefficients(x2);
fdifference(zz, xx); // does zz = xx - zz
Utils::zero<sizeof(limb) * 9>(zzz + 10);
fscalar_product(zzz, zz, 121665);
freduce_coefficients(zzz);
fsum(zzz, xx);
fproduct(z2, zz, zzz);
freduce_degree(z2);
freduce_coefficients(z2);
}
ZT_INLINE void swap_conditional(limb a[19], limb b[19], limb iswap)
{
const s32 swap = (s32)-iswap;
for (int i = 0; i < 10; ++i) {
const s32 x = swap & (((s32)a[i]) ^ ((s32)b[i]));
a[i] = ((s32)a[i]) ^ x;
b[i] = ((s32)b[i]) ^ x;
}
}
void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
{
limb a[19] = { 0 }, b[19] = { 1 }, c[19] = { 1 }, d[19] = { 0 };
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
limb e[19] = { 0 }, f[19] = { 1 }, g[19] = { 0 }, h[19] = { 1 };
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
Utils::copy<sizeof(limb) * 10>(nqpqx, q);
for (int i = 0; i < 32; ++i) {
u8 byte = n[31 - i];
for (int j = 0; j < 8; ++j) {
const limb bit = byte >> 7;
swap_conditional(nqx, nqpqx, bit);
swap_conditional(nqz, nqpqz, bit);
fmonty(nqx2, nqz2, nqpqx2, nqpqz2, nqx, nqz, nqpqx, nqpqz, q);
swap_conditional(nqx2, nqpqx2, bit);
swap_conditional(nqz2, nqpqz2, bit);
t = nqx;
nqx = nqx2;
nqx2 = t;
t = nqz;
nqz = nqz2;
nqz2 = t;
t = nqpqx;
nqpqx = nqpqx2;
nqpqx2 = t;
t = nqpqz;
nqpqz = nqpqz2;
nqpqz2 = t;
byte <<= 1;
}
}
Utils::copy<sizeof(limb) * 10>(resultx, nqx);
Utils::copy<sizeof(limb) * 10>(resultz, nqz);
}
ZT_INLINE void crecip(limb *out, const limb *z)
{
limb z2[10], z9[10], z11[10], z2_5_0[10], z2_10_0[10], z2_20_0[10], z2_50_0[10], z2_100_0[10], t0[10], t1[10];
fsquare(z2, z);
fsquare(t1, z2);
fsquare(t0, t1);
fmul(z9, t0, z);
fmul(z11, z9, z2);
fsquare(t0, z11);
fmul(z2_5_0, t0, z9);
fsquare(t0, z2_5_0);
fsquare(t1, t0);
fsquare(t0, t1);
fsquare(t1, t0);
fsquare(t0, t1);
fmul(z2_10_0, t0, z2_5_0);
fsquare(t0, z2_10_0);
fsquare(t1, t0);
for (int i = 2; i < 10; i += 2) {
fsquare(t0, t1);
fsquare(t1, t0);
}
fmul(z2_20_0, t1, z2_10_0);
fsquare(t0, z2_20_0);
fsquare(t1, t0);
for (int i = 2; i < 20; i += 2) {
fsquare(t0, t1);
fsquare(t1, t0);
}
fmul(t0, t1, z2_20_0);
fsquare(t1, t0);
fsquare(t0, t1);
for (int i = 2; i < 10; i += 2) {
fsquare(t1, t0);
fsquare(t0, t1);
}
fmul(z2_50_0, t0, z2_10_0);
fsquare(t0, z2_50_0);
fsquare(t1, t0);
for (int i = 2; i < 50; i += 2) {
fsquare(t0, t1);
fsquare(t1, t0);
}
fmul(z2_100_0, t1, z2_50_0);
fsquare(t1, z2_100_0);
fsquare(t0, t1);
for (int i = 2; i < 100; i += 2) {
fsquare(t1, t0);
fsquare(t0, t1);
}
fmul(t1, t0, z2_100_0);
fsquare(t0, t1);
fsquare(t1, t0);
for (int i = 2; i < 50; i += 2) {
fsquare(t0, t1);
fsquare(t1, t0);
}
fmul(t0, t1, z2_50_0);
fsquare(t1, t0);
fsquare(t0, t1);
fsquare(t1, t0);
fsquare(t0, t1);
fsquare(t1, t0);
fmul(out, t1, z11);
}
void crypto_scalarmult(u8 *mypublic, const u8 *secret, const u8 *basepoint)
{
limb bp[10], x[10], z[11], zmone[10];
uint8_t e[32];
int i;
for (i = 0; i < 32; ++i)
e[i] = secret[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
fexpand(bp, basepoint);
cmult(x, z, e, bp);
crecip(zmone, z);
fmul(z, x, zmone);
fcontract(mypublic, z);
}
static const unsigned char s_base[32] = { 9 };
ZT_INLINE void crypto_scalarmult_base(unsigned char *q, const unsigned char *n) { crypto_scalarmult(q, n, s_base); }
// --------------------------------------------------------------------------------------------------------------------
// Ed25519 ref from: http://bench.cr.yp.to/supercop.html
typedef struct {
uint32_t v[32];
} fe25519;
typedef struct {
uint32_t v[32];
} sc25519;
typedef struct {
fe25519 x, y, z, t;
} ge25519;
#define ge25519_p3 ge25519
typedef struct {
fe25519 x, z, y, t;
} ge25519_p1p1;
typedef struct {
fe25519 x, y, z;
} ge25519_p2;
typedef struct {
fe25519 x, y;
} ge25519_aff;
void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y);
ZT_INLINE uint32_t equal(uint32_t a, uint32_t b)
{
uint32_t x = a ^ b;
x -= 1;
x >>= 31;
return x;
}
ZT_INLINE uint32_t ge(uint32_t a, uint32_t b)
{
unsigned int x = a;
x -= (unsigned int)b;
x >>= 31;
x ^= 1;
return x;
}
ZT_INLINE uint32_t times19(uint32_t a) { return (a << 4) + (a << 1) + a; }
ZT_INLINE uint32_t times38(uint32_t a) { return (a << 5) + (a << 2) + (a << 1); }
void reduce_add_sub(fe25519 *r)
{
for (int rep = 0; rep < 4; rep++) {
uint32_t t = r->v[31] >> 7;
r->v[31] &= 127;
t = times19(t);
r->v[0] += t;
for (int i = 0; i < 31; i++) {
t = r->v[i] >> 8;
r->v[i + 1] += t;
r->v[i] &= 255;
}
}
}
ZT_INLINE void reduce_mul(fe25519 *r)
{
for (int rep = 0; rep < 2; rep++) {
uint32_t t = r->v[31] >> 7;
r->v[31] &= 127;
t = times19(t);
r->v[0] += t;
for (int i = 0; i < 31; i++) {
t = r->v[i] >> 8;
r->v[i + 1] += t;
r->v[i] &= 255;
}
}
}
void fe25519_freeze(fe25519 *r)
{
uint32_t mm = equal(r->v[31], 127);
for (int i = 30; i > 0; i--)
mm &= equal(r->v[i], 255);
mm &= ge(r->v[0], 237);
mm = -mm;
r->v[31] -= mm & 127;
for (int i = 30; i > 0; i--)
r->v[i] -= mm & 255;
r->v[0] -= mm & 237;
}
ZT_INLINE void fe25519_unpack(fe25519 *r, const unsigned char x[32])
{
for (int i = 0; i < 32; i++)
r->v[i] = x[i];
r->v[31] &= 127;
}
ZT_INLINE void fe25519_pack(unsigned char r[32], const fe25519 *x)
{
fe25519 y = *x;
fe25519_freeze(&y);
for (int i = 0; i < 32; i++)
r[i] = y.v[i];
}
ZT_INLINE int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y)
{
fe25519 t1 = *x;
fe25519 t2 = *y;
fe25519_freeze(&t1);
fe25519_freeze(&t2);
for (int i = 0; i < 32; i++) {
if (t1.v[i] != t2.v[i])
return 0;
}
return 1;
}
ZT_INLINE void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
{
uint32_t mask = b;
mask = -mask;
for (int i = 0; i < 32; i++)
r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
}
ZT_INLINE unsigned char fe25519_getparity(const fe25519 *x)
{
fe25519 t = *x;
fe25519_freeze(&t);
return t.v[0] & 1;
}
ZT_INLINE void fe25519_setone(fe25519 *r)
{
r->v[0] = 1;
for (int i = 1; i < 32; i++)
r->v[i] = 0;
}
ZT_INLINE void fe25519_setzero(fe25519 *r)
{
for (int i = 0; i < 32; i++)
r->v[i] = 0;
}
void fe25519_neg(fe25519 *r, const fe25519 *x)
{
fe25519 t;
for (int i = 0; i < 32; i++)
t.v[i] = x->v[i];
fe25519_setzero(r);
fe25519_sub(r, r, &t);
}
ZT_INLINE void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
for (int 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)
{
uint32_t t[32];
t[0] = x->v[0] + 0x1da;
t[31] = x->v[31] + 0xfe;
for (int i = 1; i < 31; i++)
t[i] = x->v[i] + 0x1fe;
for (int 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)
{
uint32_t t[63];
for (int i = 0; i < 63; i++)
t[i] = 0;
for (int i = 0; i < 32; i++) {
for (int j = 0; j < 32; j++)
t[i + j] += x->v[i] * y->v[j];
}
for (int i = 32; i < 63; i++)
r->v[i - 32] = t[i - 32] + times38(t[i]);
r->v[31] = t[31];
reduce_mul(r);
}
ZT_INLINE void fe25519_square(fe25519 *r, const fe25519 *x) { fe25519_mul(r, x, x); }
ZT_INLINE void fe25519_invert(fe25519 *r, const fe25519 *x)
{
fe25519 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t0, t1;
fe25519_square(&z2, x);
fe25519_square(&t1, &z2);
fe25519_square(&t0, &t1);
fe25519_mul(&z9, &t0, x);
fe25519_mul(&z11, &z9, &z2);
fe25519_square(&t0, &z11);
fe25519_mul(&z2_5_0, &t0, &z9);
fe25519_square(&t0, &z2_5_0);
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
fe25519_mul(&z2_10_0, &t0, &z2_5_0);
fe25519_square(&t0, &z2_10_0);
fe25519_square(&t1, &t0);
for (int i = 2; i < 10; i += 2) {
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
}
fe25519_mul(&z2_20_0, &t1, &z2_10_0);
fe25519_square(&t0, &z2_20_0);
fe25519_square(&t1, &t0);
for (int i = 2; i < 20; i += 2) {
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
}
fe25519_mul(&t0, &t1, &z2_20_0);
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
for (int i = 2; i < 10; i += 2) {
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
}
fe25519_mul(&z2_50_0, &t0, &z2_10_0);
fe25519_square(&t0, &z2_50_0);
fe25519_square(&t1, &t0);
for (int i = 2; i < 50; i += 2) {
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
}
fe25519_mul(&z2_100_0, &t1, &z2_50_0);
fe25519_square(&t1, &z2_100_0);
fe25519_square(&t0, &t1);
for (int i = 2; i < 100; i += 2) {
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
}
fe25519_mul(&t1, &t0, &z2_100_0);
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
for (int i = 2; i < 50; i += 2) {
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
}
fe25519_mul(&t0, &t1, &z2_50_0);
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
fe25519_square(&t0, &t1);
fe25519_square(&t1, &t0);
fe25519_mul(r, &t1, &z11);
}
ZT_INLINE void fe25519_pow2523(fe25519 *r, const fe25519 *x)
{
fe25519 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t;
fe25519_square(&z2, x);
fe25519_square(&t, &z2);
fe25519_square(&t, &t);
fe25519_mul(&z9, &t, x);
fe25519_mul(&z11, &z9, &z2);
fe25519_square(&t, &z11);
fe25519_mul(&z2_5_0, &t, &z9);
fe25519_square(&t, &z2_5_0);
for (int i = 1; i < 5; i++)
fe25519_square(&t, &t);
fe25519_mul(&z2_10_0, &t, &z2_5_0);
fe25519_square(&t, &z2_10_0);
for (int i = 1; i < 10; i++)
fe25519_square(&t, &t);
fe25519_mul(&z2_20_0, &t, &z2_10_0);
fe25519_square(&t, &z2_20_0);
for (int i = 1; i < 20; i++)
fe25519_square(&t, &t);
fe25519_mul(&t, &t, &z2_20_0);
fe25519_square(&t, &t);
for (int i = 1; i < 10; i++)
fe25519_square(&t, &t);
fe25519_mul(&z2_50_0, &t, &z2_10_0);
fe25519_square(&t, &z2_50_0);
for (int i = 1; i < 50; i++)
fe25519_square(&t, &t);
fe25519_mul(&z2_100_0, &t, &z2_50_0);
fe25519_square(&t, &z2_100_0);
for (int i = 1; i < 100; i++)
fe25519_square(&t, &t);
fe25519_mul(&t, &t, &z2_100_0);
fe25519_square(&t, &t);
for (int i = 1; i < 50; i++)
fe25519_square(&t, &t);
fe25519_mul(&t, &t, &z2_50_0);
fe25519_square(&t, &t);
fe25519_square(&t, &t);
fe25519_mul(r, &t, x);
}
const uint32_t m[32] = {
0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
};
const uint32_t mu[33] = { 0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63,
0x08, 0x5D, 0x21, 0x06, 0x21, 0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F };
ZT_INLINE uint32_t lt(uint32_t a, uint32_t b) /* 16-bit inputs */
{
unsigned int x = a;
x -= (unsigned int)b; /* 0..65535: no; 4294901761..4294967295: yes */
x >>= 31; /* 0: no; 1: yes */
return x;
}
void reduce_add_sub(sc25519 *r)
{
uint32_t pb = 0;
uint32_t b;
uint32_t mask;
int i;
unsigned char t[32];
for (i = 0; i < 32; i++) {
pb += m[i];
b = lt(r->v[i], pb);
t[i] = r->v[i] - pb + (b << 8);
pb = b;
}
mask = b - 1;
for (i = 0; i < 32; i++)
r->v[i] ^= mask & (r->v[i] ^ t[i]);
}
void barrett_reduce(sc25519 *r, const uint32_t x[64])
{
/* See HAC, Alg. 14.42 */
int i, j;
uint32_t q2[66];
uint32_t *q3 = q2 + 33;
uint32_t r1[33];
uint32_t r2[33];
uint32_t pb = 0;
Utils::zero<sizeof(q2)>(q2);
// for (i = 0;i < 66;++i) q2[i] = 0;
Utils::zero<sizeof(r2)>(r2);
// for (i = 0;i < 33;++i) r2[i] = 0;
for (i = 0; i < 33; i++)
for (j = 0; j < 33; j++)
if (i + j >= 31)
q2[i + j] += mu[i] * x[j + 31];
q2[32] += (q2[31] >> 8);
q2[33] += (q2[32] >> 8);
for (i = 0; i < 33; i++)
r1[i] = x[i];
for (i = 0; i < 32; i++)
for (j = 0; j < 33; j++)
if (i + j < 33)
r2[i + j] += m[i] * q3[j];
for (i = 0; i < 32; i++) {
r2[i + 1] += (r2[i] >> 8);
r2[i] &= 0xff;
}
for (i = 0; i < 32; i++) {
pb += r2[i];
uint32_t b = lt(r1[i], pb);
r->v[i] = r1[i] - pb + (b << 8);
pb = b;
}
reduce_add_sub(r);
reduce_add_sub(r);
}
ZT_INLINE void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
{
int i;
uint32_t t[64];
for (i = 0; i < 32; i++)
t[i] = x[i];
for (i = 32; i < 64; ++i)
t[i] = 0;
barrett_reduce(r, t);
}
ZT_INLINE void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
{
int i;
uint32_t t[64];
for (i = 0; i < 64; i++)
t[i] = x[i];
barrett_reduce(r, t);
}
ZT_INLINE void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
{
int i;
for (i = 0; i < 32; i++)
r[i] = x->v[i];
}
ZT_INLINE void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
int i;
for (i = 0; i < 32; i++)
r->v[i] = x->v[i] + y->v[i];
for (i = 0; i < 31; i++) {
r->v[i + 1] += (r->v[i] >> 8);
r->v[i] &= 0xff;
}
reduce_add_sub(r);
}
ZT_INLINE void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
int i, j;
uint32_t t[64];
for (i = 0; i < 64; 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 = 0; i < 63; i++) {
t[i + 1] += (t[i] >> 8);
t[i] &= 0xff;
}
barrett_reduce(r, t);
}
ZT_INLINE void sc25519_window3(signed char r[85], const sc25519 *s)
{
char carry;
int i;
for (i = 0; i < 10; i++) {
r[8 * i + 0] = s->v[3 * i + 0] & 7;
r[8 * i + 1] = (s->v[3 * i + 0] >> 3) & 7;
r[8 * i + 2] = (s->v[3 * i + 0] >> 6) & 7;
r[8 * i + 2] ^= (s->v[3 * i + 1] << 2) & 7;
r[8 * i + 3] = (s->v[3 * i + 1] >> 1) & 7;
r[8 * i + 4] = (s->v[3 * i + 1] >> 4) & 7;
r[8 * i + 5] = (s->v[3 * i + 1] >> 7) & 7;
r[8 * i + 5] ^= (s->v[3 * i + 2] << 1) & 7;
r[8 * i + 6] = (s->v[3 * i + 2] >> 2) & 7;
r[8 * i + 7] = (s->v[3 * i + 2] >> 5) & 7;
}
r[8 * i + 0] = s->v[3 * i + 0] & 7;
r[8 * i + 1] = (s->v[3 * i + 0] >> 3) & 7;
r[8 * i + 2] = (s->v[3 * i + 0] >> 6) & 7;
r[8 * i + 2] ^= (s->v[3 * i + 1] << 2) & 7;
r[8 * i + 3] = (s->v[3 * i + 1] >> 1) & 7;
r[8 * i + 4] = (s->v[3 * i + 1] >> 4) & 7;
/* Making it signed */
carry = 0;
for (i = 0; i < 84; i++) {
r[i] += carry;
r[i + 1] += r[i] >> 3;
r[i] &= 7;
carry = r[i] >> 2;
r[i] -= carry << 3;
}
r[84] += carry;
}
ZT_INLINE void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2)
{
int i;
for (i = 0; i < 31; i++) {
r[4 * i] = (s1->v[i] & 3) ^ ((s2->v[i] & 3) << 2);
r[4 * i + 1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2);
r[4 * i + 2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2);
r[4 * i + 3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2);
}
r[124] = (s1->v[31] & 3) ^ ((s2->v[31] & 3) << 2);
r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2);
r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2);
}
static const fe25519 ge25519_ecd = { { 0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41,
0x41, 0x4D, 0x0A, 0x70, 0x00, 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40,
0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52 } };
static const fe25519 ge25519_ec2d = { { 0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83,
0x82, 0x9A, 0x14, 0xE0, 0x00, 0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80,
0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24 } };
static const fe25519 ge25519_sqrtm1 = { { 0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F,
0xAD, 0x06, 0x18, 0x43, 0x2F, 0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00,
0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B } };
static const ge25519 ge25519_base = {
{ { 0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21 } },
{ { 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67 } }
};
static const ge25519_aff ge25519_base_multiples_affine[425] = {
{ { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
{ { { 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69,
0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21 } },
{ { 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66 } } },
{ { { 0x0e, 0xce, 0x43, 0x28, 0x4e, 0xa1, 0xc5, 0x83, 0x5f, 0xa4, 0xd7, 0x15, 0x45, 0x8e, 0x0d, 0x08,
0xac, 0xe7, 0x33, 0x18, 0x7d, 0x3b, 0x04, 0x3d, 0x6c, 0x04, 0x5a, 0x9f, 0x4c, 0x38, 0xab, 0x36 } },
{ { 0xc9, 0xa3, 0xf8, 0x6a, 0xae, 0x46, 0x5f, 0x0e, 0x56, 0x51, 0x38, 0x64, 0x51, 0x0f, 0x39, 0x97,
0x56, 0x1f, 0xa2, 0xc9, 0xe8, 0x5e, 0xa2, 0x1d, 0xc2, 0x29, 0x23, 0x09, 0xf3, 0xcd, 0x60, 0x22 } } },
{ { { 0x5c, 0xe2, 0xf8, 0xd3, 0x5f, 0x48, 0x62, 0xac, 0x86, 0x48, 0x62, 0x81, 0x19, 0x98, 0x43, 0x63,
0x3a, 0xc8, 0xda, 0x3e, 0x74, 0xae, 0xf4, 0x1f, 0x49, 0x8f, 0x92, 0x22, 0x4a, 0x9c, 0xae, 0x67 } },
{ { 0xd4, 0xb4, 0xf5, 0x78, 0x48, 0x68, 0xc3, 0x02, 0x04, 0x03, 0x24, 0x67, 0x17, 0xec, 0x16, 0x9f,
0xf7, 0x9e, 0x26, 0x60, 0x8e, 0xa1, 0x26, 0xa1, 0xab, 0x69, 0xee, 0x77, 0xd1, 0xb1, 0x67, 0x12 } } },
{ { { 0x70, 0xf8, 0xc9, 0xc4, 0x57, 0xa6, 0x3a, 0x49, 0x47, 0x15, 0xce, 0x93, 0xc1, 0x9e, 0x73, 0x1a,
0xf9, 0x20, 0x35, 0x7a, 0xb8, 0xd4, 0x25, 0x83, 0x46, 0xf1, 0xcf, 0x56, 0xdb, 0xa8, 0x3d, 0x20 } },
{ { 0x2f, 0x11, 0x32, 0xca, 0x61, 0xab, 0x38, 0xdf, 0xf0, 0x0f, 0x2f, 0xea, 0x32, 0x28, 0xf2, 0x4c,
0x6c, 0x71, 0xd5, 0x80, 0x85, 0xb8, 0x0e, 0x47, 0xe1, 0x95, 0x15, 0xcb, 0x27, 0xe8, 0xd0, 0x47 } } },
{ { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
{ { { 0xc8, 0x84, 0xa5, 0x08, 0xbc, 0xfd, 0x87, 0x3b, 0x99, 0x8b, 0x69, 0x80, 0x7b, 0xc6, 0x3a, 0xeb,
0x93, 0xcf, 0x4e, 0xf8, 0x5c, 0x2d, 0x86, 0x42, 0xb6, 0x71, 0xd7, 0x97, 0x5f, 0xe1, 0x42, 0x67 } },
{ { 0xb4, 0xb9, 0x37, 0xfc, 0xa9, 0x5b, 0x2f, 0x1e, 0x93, 0xe4, 0x1e, 0x62, 0xfc, 0x3c, 0x78, 0x81,
0x8f, 0xf3, 0x8a, 0x66, 0x09, 0x6f, 0xad, 0x6e, 0x79, 0x73, 0xe5, 0xc9, 0x00, 0x06, 0xd3, 0x21 } } },
{ { { 0xf8, 0xf9, 0x28, 0x6c, 0x6d, 0x59, 0xb2, 0x59, 0x74, 0x23, 0xbf, 0xe7, 0x33, 0x8d, 0x57, 0x09,
0x91, 0x9c, 0x24, 0x08, 0x15, 0x2b, 0xe2, 0xb8, 0xee, 0x3a, 0xe5, 0x27, 0x06, 0x86, 0xa4, 0x23 } },
{ { 0xeb, 0x27, 0x67, 0xc1, 0x37, 0xab, 0x7a, 0xd8, 0x27, 0x9c, 0x07, 0x8e, 0xff, 0x11, 0x6a, 0xb0,
0x78, 0x6e, 0xad, 0x3a, 0x2e, 0x0f, 0x98, 0x9f, 0x72, 0xc3, 0x7f, 0x82, 0xf2, 0x96, 0x96, 0x70 } } },
{ { { 0x81, 0x6b, 0x88, 0xe8, 0x1e, 0xc7, 0x77, 0x96, 0x0e, 0xa1, 0xa9, 0x52, 0xe0, 0xd8, 0x0e, 0x61,
0x9e, 0x79, 0x2d, 0x95, 0x9c, 0x8d, 0x96, 0xe0, 0x06, 0x40, 0x5d, 0x87, 0x28, 0x5f, 0x98, 0x70 } },
{ { 0xf1, 0x79, 0x7b, 0xed, 0x4f, 0x44, 0xb2, 0xe7, 0x08, 0x0d, 0xc2, 0x08, 0x12, 0xd2, 0x9f, 0xdf,
0xcd, 0x93, 0x20, 0x8a, 0xcf, 0x33, 0xca, 0x6d, 0x89, 0xb9, 0x77, 0xc8, 0x93, 0x1b, 0x4e, 0x60 } } },
{ { { 0x26, 0x4f, 0x7e, 0x97, 0xf6, 0x40, 0xdd, 0x4f, 0xfc, 0x52, 0x78, 0xf9, 0x90, 0x31, 0x03, 0xe6,
0x7d, 0x56, 0x39, 0x0b, 0x1d, 0x56, 0x82, 0x85, 0xf9, 0x1a, 0x42, 0x17, 0x69, 0x6c, 0xcf, 0x39 } },
{ { 0x69, 0xd2, 0x06, 0x3a, 0x4f, 0x39, 0x2d, 0xf9, 0x38, 0x40, 0x8c, 0x4c, 0xe7, 0x05, 0x12, 0xb4,
0x78, 0x8b, 0xf8, 0xc0, 0xec, 0x93, 0xde, 0x7a, 0x6b, 0xce, 0x2c, 0xe1, 0x0e, 0xa9, 0x34, 0x44 } } },
{ { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
{ { { 0x0b, 0xa4, 0x3c, 0xb0, 0x0f, 0x7a, 0x51, 0xf1, 0x78, 0xd6, 0xd9, 0x6a, 0xfd, 0x46, 0xe8, 0xb8,
0xa8, 0x79, 0x1d, 0x87, 0xf9, 0x90, 0xf2, 0x9c, 0x13, 0x29, 0xf8, 0x0b, 0x20, 0x64, 0xfa, 0x05 } },
{ { 0x26, 0x09, 0xda, 0x17, 0xaf, 0x95, 0xd6, 0xfb, 0x6a, 0x19, 0x0d, 0x6e, 0x5e, 0x12, 0xf1, 0x99,
0x4c, 0xaa, 0xa8, 0x6f, 0x79, 0x86, 0xf4, 0x72, 0x28, 0x00, 0x26, 0xf9, 0xea, 0x9e, 0x19, 0x3d } } },
{ { { 0x87, 0xdd, 0xcf, 0xf0, 0x5b, 0x49, 0xa2, 0x5d, 0x40, 0x7a, 0x23, 0x26, 0xa4, 0x7a, 0x83, 0x8a,
0xb7, 0x8b, 0xd2, 0x1a, 0xbf, 0xea, 0x02, 0x24, 0x08, 0x5f, 0x7b, 0xa9, 0xb1, 0xbe, 0x9d, 0x37 } },
{ { 0xfc, 0x86, 0x4b, 0x08, 0xee, 0xe7, 0xa0, 0xfd, 0x21, 0x45, 0x09, 0x34, 0xc1, 0x61, 0x32, 0x23,
0xfc, 0x9b, 0x55, 0x48, 0x53, 0x99, 0xf7, 0x63, 0xd0, 0x99, 0xce, 0x01, 0xe0, 0x9f, 0xeb, 0x28 } } },
{ { { 0x47, 0xfc, 0xab, 0x5a, 0x17, 0xf0, 0x85, 0x56, 0x3a, 0x30, 0x86, 0x20, 0x28, 0x4b, 0x8e, 0x44,
0x74, 0x3a, 0x6e, 0x02, 0xf1, 0x32, 0x8f, 0x9f, 0x3f, 0x08, 0x35, 0xe9, 0xca, 0x16, 0x5f, 0x6e } },
{ { 0x1c, 0x59, 0x1c, 0x65, 0x5d, 0x34, 0xa4, 0x09, 0xcd, 0x13, 0x9c, 0x70, 0x7d, 0xb1, 0x2a, 0xc5,
0x88, 0xaf, 0x0b, 0x60, 0xc7, 0x9f, 0x34, 0x8d, 0xd6, 0xb7, 0x7f, 0xea, 0x78, 0x65, 0x8d, 0x77 } } },
{ { { 0x56, 0xa5, 0xc2, 0x0c, 0xdd, 0xbc, 0xb8, 0x20, 0x6d, 0x57, 0x61, 0xb5, 0xfb, 0x78, 0xb5, 0xd4,
0x49, 0x54, 0x90, 0x26, 0xc1, 0xcb, 0xe9, 0xe6, 0xbf, 0xec, 0x1d, 0x4e, 0xed, 0x07, 0x7e, 0x5e } },
{ { 0xc7, 0xf6, 0x6c, 0x56, 0x31, 0x20, 0x14, 0x0e, 0xa8, 0xd9, 0x27, 0xc1, 0x9a, 0x3d, 0x1b, 0x7d,
0x0e, 0x26, 0xd3, 0x81, 0xaa, 0xeb, 0xf5, 0x6b, 0x79, 0x02, 0xf1, 0x51, 0x5c, 0x75, 0x55, 0x0f } } },
{ { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
{ { { 0x0a, 0x34, 0xcd, 0x82, 0x3c, 0x33, 0x09, 0x54, 0xd2, 0x61, 0x39, 0x30, 0x9b, 0xfd, 0xef, 0x21,
0x26, 0xd4, 0x70, 0xfa, 0xee, 0xf9, 0x31, 0x33, 0x73, 0x84, 0xd0, 0xb3, 0x81, 0xbf, 0xec, 0x2e } },
{ { 0xe8, 0x93, 0x8b, 0x00, 0x64, 0xf7, 0x9c, 0xb8, 0x74, 0xe0, 0xe6, 0x49, 0x48, 0x4d, 0x4d, 0x48,
0xb6, 0x19, 0xa1, 0x40, 0xb7, 0xd9, 0x32, 0x41, 0x7c, 0x82, 0x37, 0xa1, 0x2d, 0xdc, 0xd2, 0x54 } } },
{ { { 0x68, 0x2b, 0x4a, 0x5b, 0xd5, 0xc7, 0x51, 0x91, 0x1d, 0xe1, 0x2a, 0x4b, 0xc4, 0x47, 0xf1, 0xbc,
0x7a, 0xb3, 0xcb, 0xc8, 0xb6, 0x7c, 0xac, 0x90, 0x05, 0xfd, 0xf3, 0xf9, 0x52, 0x3a, 0x11, 0x6b } },
{ { 0x3d, 0xc1, 0x27, 0xf3, 0x59, 0x43, 0x95, 0x90, 0xc5, 0x96, 0x79, 0xf5, 0xf4, 0x95, 0x65, 0x29,
0x06, 0x9c, 0x51, 0x05, 0x18, 0xda, 0xb8, 0x2e, 0x79, 0x7e, 0x69, 0x59, 0x71, 0x01, 0xeb, 0x1a } } },
{ { { 0x15, 0x06, 0x49, 0xb6, 0x8a, 0x3c, 0xea, 0x2f, 0x34, 0x20, 0x14, 0xc3, 0xaa, 0xd6, 0xaf, 0x2c,
0x3e, 0xbd, 0x65, 0x20, 0xe2, 0x4d, 0x4b, 0x3b, 0xeb, 0x9f, 0x4a, 0xc3, 0xad, 0xa4, 0x3b, 0x60 } },
{ { 0xbc, 0x58, 0xe6, 0xc0, 0x95, 0x2a, 0x2a, 0x81, 0x9a, 0x7a, 0xf3, 0xd2, 0x06, 0xbe, 0x48, 0xbc,
0x0c, 0xc5, 0x46, 0xe0, 0x6a, 0xd4, 0xac, 0x0f, 0xd9, 0xcc, 0x82, 0x34, 0x2c, 0xaf, 0xdb, 0x1f } } },
{ { { 0xf7, 0x17, 0x13, 0xbd, 0xfb, 0xbc, 0xd2, 0xec, 0x45, 0xb3, 0x15, 0x31, 0xe9, 0xaf, 0x82, 0x84,
0x3d, 0x28, 0xc6, 0xfc, 0x11, 0xf5, 0x41, 0xb5, 0x8b, 0xd3, 0x12, 0x76, 0x52, 0xe7, 0x1a, 0x3c } },
{ { 0x4e, 0x36, 0x11, 0x07, 0xa2, 0x15, 0x20, 0x51, 0xc4, 0x2a, 0xc3, 0x62, 0x8b, 0x5e, 0x7f, 0xa6,
0x0f, 0xf9, 0x45, 0x85, 0x6c, 0x11, 0x86, 0xb7, 0x7e, 0xe5, 0xd7, 0xf9, 0xc3, 0x91, 0x1c, 0x05 } } },
{ { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
{ { { 0xea, 0xd6, 0xde, 0x29, 0x3a, 0x00, 0xb9, 0x02, 0x59, 0xcb, 0x26, 0xc4, 0xba, 0x99, 0xb1, 0x97,
0x2f, 0x8e, 0x00, 0x92, 0x26, 0x4f, 0x52, 0xeb, 0x47, 0x1b, 0x89, 0x8b, 0x24, 0xc0, 0x13, 0x7d } },
{ { 0xd5, 0x20, 0x5b, 0x80, 0xa6, 0x80, 0x20, 0x95, 0xc3, 0xe9, 0x9f, 0x8e, 0x87, 0x9e, 0x1e, 0x9e,
0x7a, 0xc7, 0xcc, 0x75, 0x6c, 0xa5, 0xf1, 0x91, 0x1a, 0xa8, 0x01, 0x2c, 0xab, 0x76, 0xa9, 0x59 } } },
{ { { 0xde, 0xc9, 0xb1, 0x31, 0x10, 0x16, 0xaa, 0x35, 0x14, 0x6a, 0xd4, 0xb5, 0x34, 0x82, 0x71, 0xd2,
0x4a, 0x5d, 0x9a, 0x1f, 0x53, 0x26, 0x3c, 0xe5, 0x8e, 0x8d, 0x33, 0x7f, 0xff, 0xa9, 0xd5, 0x17 } },
{ { 0x89, 0xaf, 0xf6, 0xa4, 0x64, 0xd5, 0x10, 0xe0, 0x1d, 0xad, 0xef, 0x44, 0xbd, 0xda, 0x83, 0xac,
0x7a, 0xa8, 0xf0, 0x1c, 0x07, 0xf9, 0xc3, 0x43, 0x6c, 0x3f, 0xb7, 0xd3, 0x87, 0x22, 0x02, 0x73 } } },
{ { { 0x64, 0x1d, 0x49, 0x13, 0x2f, 0x71, 0xec, 0x69, 0x87, 0xd0, 0x42, 0xee, 0x13, 0xec, 0xe3, 0xed,
0x56, 0x7b, 0xbf, 0xbd, 0x8c, 0x2f, 0x7d, 0x7b, 0x9d, 0x28, 0xec, 0x8e, 0x76, 0x2f, 0x6f, 0x08 } },
{ { 0x22, 0xf5, 0x5f, 0x4d, 0x15, 0xef, 0xfc, 0x4e, 0x57, 0x03, 0x36, 0x89, 0xf0, 0xeb, 0x5b, 0x91,
0xd6, 0xe2, 0xca, 0x01, 0xa5, 0xee, 0x52, 0xec, 0xa0, 0x3c, 0x8f, 0x33, 0x90, 0x5a, 0x94, 0x72 } } },
{ { { 0x8a, 0x4b, 0xe7, 0x38, 0xbc, 0xda, 0xc2, 0xb0, 0x85, 0xe1, 0x4a, 0xfe, 0x2d, 0x44, 0x84, 0xcb,
0x20, 0x6b, 0x2d, 0xbf, 0x11, 0x9c, 0xd7, 0xbe, 0xd3, 0x3e, 0x5f, 0xbf, 0x68, 0xbc, 0xa8, 0x07 } },
{ { 0x01, 0x89, 0x28, 0x22, 0x6a, 0x78, 0xaa, 0x29, 0x03, 0xc8, 0x74, 0x95, 0x03, 0x3e, 0xdc, 0xbd,
0x07, 0x13, 0xa8, 0xa2, 0x20, 0x2d, 0xb3, 0x18, 0x70, 0x42, 0xfd, 0x7a, 0xc4, 0xd7, 0x49, 0x72 } } },
{ { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
{ { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
{ { { 0x02, 0xff, 0x32, 0x2b, 0x5c, 0x93, 0x54, 0x32, 0xe8, 0x57, 0x54, 0x1a, 0x8b, 0x33, 0x60, 0x65,
0xd3, 0x67, 0xa4, 0xc1, 0x26, 0xc4, 0xa4, 0x34, 0x1f, 0x9b, 0xa7, 0xa9, 0xf4, 0xd9, 0x4f, 0x5b } },
{ { 0x46, 0x8d, 0xb0, 0x33, 0x54, 0x26, 0x5b, 0x68, 0xdf, 0xbb, 0xc5, 0xec, 0xc2, 0xf9, 0x3c, 0x5a,
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0xb5, 0xd4, 0xe7, 0xcf, 0xcc, 0x8b, 0x83, 0xec, 0x35, 0xc7, 0x9c, 0x74, 0xb7, 0xad, 0x85, 0x5f } } },
{ { { 0x78, 0x84, 0xe1, 0x56, 0x45, 0x69, 0x68, 0x5a, 0x4f, 0xb8, 0xb1, 0x29, 0xff, 0x33, 0x03, 0x31,
0xb7, 0xcb, 0x96, 0x25, 0xe6, 0xe6, 0x41, 0x98, 0x1a, 0xbb, 0x03, 0x56, 0xf2, 0xb2, 0x91, 0x34 } },
{ { 0x2c, 0x6c, 0xf7, 0x66, 0xa4, 0x62, 0x6b, 0x39, 0xb3, 0xba, 0x65, 0xd3, 0x1c, 0xf8, 0x11, 0xaa,
0xbe, 0xdc, 0x80, 0x59, 0x87, 0xf5, 0x7b, 0xe5, 0xe3, 0xb3, 0x3e, 0x39, 0xda, 0xbe, 0x88, 0x09 } } },
{ { { 0x8b, 0xf1, 0xa0, 0xf5, 0xdc, 0x29, 0xb4, 0xe2, 0x07, 0xc6, 0x7a, 0x00, 0xd0, 0x89, 0x17, 0x51,
0xd4, 0xbb, 0xd4, 0x22, 0xea, 0x7e, 0x7d, 0x7c, 0x24, 0xea, 0xf2, 0xe8, 0x22, 0x12, 0x95, 0x06 } },
{ { 0xda, 0x7c, 0xa4, 0x0c, 0xf4, 0xba, 0x6e, 0xe1, 0x89, 0xb5, 0x59, 0xca, 0xf1, 0xc0, 0x29, 0x36,
0x09, 0x44, 0xe2, 0x7f, 0xd1, 0x63, 0x15, 0x99, 0xea, 0x25, 0xcf, 0x0c, 0x9d, 0xc0, 0x44, 0x6f } } },
{ { { 0x1d, 0x86, 0x4e, 0xcf, 0xf7, 0x37, 0x10, 0x25, 0x8f, 0x12, 0xfb, 0x19, 0xfb, 0xe0, 0xed, 0x10,
0xc8, 0xe2, 0xf5, 0x75, 0xb1, 0x33, 0xc0, 0x96, 0x0d, 0xfb, 0x15, 0x6c, 0x0d, 0x07, 0x5f, 0x05 } },
{ { 0x69, 0x3e, 0x47, 0x97, 0x2c, 0xaf, 0x52, 0x7c, 0x78, 0x83, 0xad, 0x1b, 0x39, 0x82, 0x2f, 0x02,
0x6f, 0x47, 0xdb, 0x2a, 0xb0, 0xe1, 0x91, 0x99, 0x55, 0xb8, 0x99, 0x3a, 0xa0, 0x44, 0x11, 0x51 } } }
};
ZT_INLINE void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
{
fe25519_mul(&r->x, &p->x, &p->t);
fe25519_mul(&r->y, &p->y, &p->z);
fe25519_mul(&r->z, &p->z, &p->t);
}
ZT_INLINE void p1p1_to_p2_2(ge25519_p3 *r, const ge25519_p1p1 *p)
{
fe25519_mul(&r->x, &p->x, &p->t);
fe25519_mul(&r->y, &p->y, &p->z);
fe25519_mul(&r->z, &p->z, &p->t);
}
ZT_INLINE void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
{
p1p1_to_p2_2(r, p);
fe25519_mul(&r->t, &p->x, &p->y);
}
ZT_INLINE void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)
{
fe25519 a, b, t1, t2, c, d, e, f, g, h, qt;
fe25519_mul(&qt, &q->x, &q->y);
fe25519_sub(&a, &r->y, &r->x);
fe25519_add(&b, &r->y, &r->x);
fe25519_sub(&t1, &q->y, &q->x);
fe25519_add(&t2, &q->y, &q->x);
fe25519_mul(&a, &a, &t1);
fe25519_mul(&b, &b, &t2);
fe25519_sub(&e, &b, &a);
fe25519_add(&h, &b, &a);
fe25519_mul(&c, &r->t, &qt);
fe25519_mul(&c, &c, &ge25519_ec2d);
fe25519_add(&d, &r->z, &r->z);
fe25519_sub(&f, &d, &c);
fe25519_add(&g, &d, &c);
fe25519_mul(&r->x, &e, &f);
fe25519_mul(&r->y, &h, &g);
fe25519_mul(&r->z, &g, &f);
fe25519_mul(&r->t, &e, &h);
}
ZT_INLINE void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
{
fe25519 a, b, c, d, t;
fe25519_sub(&a, &p->y, &p->x);
fe25519_sub(&t, &q->y, &q->x);
fe25519_mul(&a, &a, &t);
fe25519_add(&b, &p->x, &p->y);
fe25519_add(&t, &q->x, &q->y);
fe25519_mul(&b, &b, &t);
fe25519_mul(&c, &p->t, &q->t);
fe25519_mul(&c, &c, &ge25519_ec2d);
fe25519_mul(&d, &p->z, &q->z);
fe25519_add(&d, &d, &d);
fe25519_sub(&r->x, &b, &a);
fe25519_sub(&r->t, &d, &c);
fe25519_add(&r->z, &d, &c);
fe25519_add(&r->y, &b, &a);
}
ZT_INLINE void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
{
fe25519 a, b, c, d;
fe25519_square(&a, &p->x);
fe25519_square(&b, &p->y);
fe25519_square(&c, &p->z);
fe25519_add(&c, &c, &c);
fe25519_neg(&d, &a);
fe25519_add(&r->x, &p->x, &p->y);
fe25519_square(&r->x, &r->x);
fe25519_sub(&r->x, &r->x, &a);
fe25519_sub(&r->x, &r->x, &b);
fe25519_add(&r->z, &d, &b);
fe25519_sub(&r->t, &r->z, &c);
fe25519_sub(&r->y, &d, &b);
}
ZT_INLINE void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)
{
fe25519_cmov(&r->x, &p->x, b);
fe25519_cmov(&r->y, &p->y, b);
}
ZT_INLINE unsigned char equal(signed char b, signed char c)
{
unsigned char ub = b, uc = c, x = ub ^ uc;
uint32_t y = x;
y -= 1;
y >>= 31;
return (unsigned char)y;
}
ZT_INLINE unsigned char negative(signed char b)
{
unsigned long long x = b;
x >>= 63;
return (unsigned char)x;
}
ZT_INLINE void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
{
fe25519 v;
*t = ge25519_base_multiples_affine[5 * pos + 0];
cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 1], equal(b, 1) | equal(b, -1));
cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 2], equal(b, 2) | equal(b, -2));
cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 3], equal(b, 3) | equal(b, -3));
cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 4], equal(b, -4));
fe25519_neg(&v, &t->x);
fe25519_cmov(&t->x, &v, negative(b));
}
ZT_INLINE void setneutral(ge25519 *r)
{
fe25519_setzero(&r->x);
fe25519_setone(&r->y);
fe25519_setone(&r->z);
fe25519_setzero(&r->t);
}
ZT_INLINE int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
{
unsigned char par;
fe25519 t, chk, num, den, den2, den4, den6;
fe25519_setone(&r->z);
par = p[31] >> 7;
fe25519_unpack(&r->y, p);
fe25519_square(&num, &r->y);
fe25519_mul(&den, &num, &ge25519_ecd);
fe25519_sub(&num, &num, &r->z);
fe25519_add(&den, &r->z, &den);
fe25519_square(&den2, &den);
fe25519_square(&den4, &den2);
fe25519_mul(&den6, &den4, &den2);
fe25519_mul(&t, &den6, &num);
fe25519_mul(&t, &t, &den);
fe25519_pow2523(&t, &t);
fe25519_mul(&t, &t, &num);
fe25519_mul(&t, &t, &den);
fe25519_mul(&t, &t, &den);
fe25519_mul(&r->x, &t, &den);
fe25519_square(&chk, &r->x);
fe25519_mul(&chk, &chk, &den);
if (!fe25519_iseq_vartime(&chk, &num))
fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
fe25519_square(&chk, &r->x);
fe25519_mul(&chk, &chk, &den);
if (!fe25519_iseq_vartime(&chk, &num))
return -1;
if (fe25519_getparity(&r->x) != (1 - par))
fe25519_neg(&r->x, &r->x);
fe25519_mul(&r->t, &r->x, &r->y);
return 0;
}
void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
{
fe25519 tx, ty, zi;
fe25519_invert(&zi, &p->z);
fe25519_mul(&tx, &p->x, &zi);
fe25519_mul(&ty, &p->y, &zi);
fe25519_pack(r, &ty);
r[31] ^= fe25519_getparity(&tx) << 7;
}
ZT_INLINE void ge25519_double_scalarmult_vartime(
ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)
{
ge25519_p1p1 tp1p1;
ge25519_p3 pre[16];
char *pre5 = (char *)(&(pre[5]));
unsigned char b[127];
setneutral(pre); /* 00 00 */
pre[1] = *p1; /* 00 01 */
dbl_p1p1(&tp1p1, (ge25519_p2 *)p1);
p1p1_to_p3(&pre[2], &tp1p1); /* 00 10 */
add_p1p1(&tp1p1, &pre[1], &pre[2]);
p1p1_to_p3(&pre[3], &tp1p1); /* 00 11 */
pre[4] = *p2; /* 01 00 */
add_p1p1(&tp1p1, &pre[1], &pre[4]);
p1p1_to_p3(&pre[5], &tp1p1); /* 01 01 */
add_p1p1(&tp1p1, &pre[2], &pre[4]);
p1p1_to_p3(&pre[6], &tp1p1); /* 01 10 */
add_p1p1(&tp1p1, &pre[3], &pre[4]);
p1p1_to_p3(&pre[7], &tp1p1); /* 01 11 */
dbl_p1p1(&tp1p1, (ge25519_p2 *)p2);
p1p1_to_p3(&pre[8], &tp1p1); /* 10 00 */
add_p1p1(&tp1p1, &pre[1], &pre[8]);
p1p1_to_p3(&pre[9], &tp1p1); /* 10 01 */
dbl_p1p1(&tp1p1, (ge25519_p2 *)pre5);
p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */
add_p1p1(&tp1p1, &pre[3], &pre[8]);
p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
add_p1p1(&tp1p1, &pre[4], &pre[8]);
p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
add_p1p1(&tp1p1, &pre[1], &pre[12]);
p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
add_p1p1(&tp1p1, &pre[2], &pre[12]);
p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
add_p1p1(&tp1p1, &pre[3], &pre[12]);
p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */
sc25519_2interleave2(b, s1, s2);
*r = pre[b[126]];
for (int i = 125; i >= 0; i--) {
dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
if (b[i] != 0) {
p1p1_to_p3(r, &tp1p1);
add_p1p1(&tp1p1, r, &pre[b[i]]);
}
if (i != 0)
p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
else
p1p1_to_p3(r, &tp1p1);
}
}
void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
{
signed char b[85];
ge25519_aff t;
sc25519_window3(b, s);
choose_t((ge25519_aff *)r, 0, b[0]);
fe25519_setone(&r->z);
fe25519_mul(&r->t, &r->x, &r->y);
for (int i = 1; i < 85; i++) {
choose_t(&t, (unsigned long long)i, b[i]);
ge25519_mixadd2(r, &t);
}
}
ZT_INLINE void get_hram(
unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground,
unsigned long long smlen)
{
for (int i = 0; i < 32; ++i)
playground[i] = sm[i];
for (int i = 32; i < 64; ++i)
playground[i] = pk[i - 32];
for (unsigned long long i = 64; i < smlen; ++i)
playground[i] = sm[i];
ZeroTier::SHA512(hram, playground, (unsigned int)smlen);
}
// --------------------------------------------------------------------------------------------------------------------
} // anonymous namespace
namespace ZeroTier {
void C25519::generateCombined(uint8_t *pub, uint8_t *priv)
{
Utils::getSecureRandom(priv, ZT_C25519_COMBINED_PRIVATE_KEY_SIZE);
s_calcPubDH(pub, priv);
s_calcPubED(pub, priv);
}
void C25519::generateC25519(uint8_t pub[ZT_C25519_ECDH_PUBLIC_KEY_SIZE], uint8_t priv[ZT_C25519_ECDH_PRIVATE_KEY_SIZE])
{
Utils::getSecureRandom(priv, ZT_C25519_ECDH_PRIVATE_KEY_SIZE);
s_calcPubDH(pub, priv);
}
void C25519::agree(
const uint8_t mine[ZT_C25519_ECDH_PRIVATE_KEY_SIZE], const uint8_t their[ZT_C25519_ECDH_PUBLIC_KEY_SIZE],
uint8_t rawkey[ZT_C25519_ECDH_SHARED_SECRET_SIZE])
{
crypto_scalarmult(rawkey, mine, their);
}
void C25519::sign(
const uint8_t myPrivate[ZT_C25519_COMBINED_PRIVATE_KEY_SIZE],
const uint8_t myPublic[ZT_C25519_COMBINED_PUBLIC_KEY_SIZE], const void *msg, unsigned int len, void *signature)
{
unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg)
SHA512(digest, msg, len);
sc25519 sck, scs, scsk;
ge25519 ger;
unsigned char r[32];
unsigned char s[32];
unsigned char extsk[64];
unsigned char hmg[crypto_hash_sha512_BYTES];
unsigned char hram[crypto_hash_sha512_BYTES];
unsigned char *sig = (unsigned char *)signature;
SHA512(extsk, myPrivate + 32, 32);
extsk[0] &= 248;
extsk[31] &= 127;
extsk[31] |= 64;
for (unsigned int i = 0; i < 32; i++)
sig[32 + i] = extsk[32 + i];
for (unsigned int i = 0; i < 32; i++)
sig[64 + i] = digest[i];
SHA512(hmg, sig + 32, 64);
/* Computation of R */
sc25519_from64bytes(&sck, hmg);
ge25519_scalarmult_base(&ger, &sck);
ge25519_pack(r, &ger);
/* Computation of s */
for (unsigned int i = 0; i < 32; i++)
sig[i] = r[i];
get_hram(hram, sig, myPublic + 32, sig, 96);
sc25519_from64bytes(&scs, hram);
sc25519_from32bytes(&scsk, extsk);
sc25519_mul(&scs, &scs, &scsk);
sc25519_add(&scs, &scs, &sck);
sc25519_to32bytes(s, &scs); /* cat s */
for (unsigned int i = 0; i < 32; i++)
sig[32 + i] = s[i];
}
bool C25519::verify(
const uint8_t their[ZT_C25519_COMBINED_PUBLIC_KEY_SIZE], const void *msg, unsigned int len, const void *signature,
const unsigned int siglen)
{
if (siglen < 64)
return false;
const unsigned char *sig = (const unsigned char *)signature;
unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg)
unsigned char sigtmp[96];
SHA512(digest, msg, len);
if ((siglen == 96) && (!Utils::secureEq(sig + 64, digest, 32))) {
return false;
}
else if (siglen == 64) {
Utils::copy<64>(sigtmp, sig);
Utils::copy<32>(sigtmp + 64, digest);
sig = sigtmp;
}
unsigned char t2[32];
ge25519 get1, get2;
sc25519 schram, scs;
unsigned char hram[crypto_hash_sha512_BYTES];
unsigned char m[96];
if (ge25519_unpackneg_vartime(&get1, their + 32))
return false;
get_hram(hram, sig, their + 32, m, 96);
sc25519_from64bytes(&schram, hram);
sc25519_from32bytes(&scs, sig + 32);
ge25519_double_scalarmult_vartime(&get2, &get1, &schram, &ge25519_base, &scs);
ge25519_pack(t2, &get2);
return Utils::secureEq(sig, t2, 32);
}
void C25519::s_calcPubDH(uint8_t *pub, const uint8_t *priv)
{
// First 32 bytes of pub and priv are the keys for ECDH key
// agreement. This generates the public portion from the private.
crypto_scalarmult_base(pub, priv);
}
void C25519::s_calcPubED(uint8_t *pub, const uint8_t *priv)
{
struct {
uint8_t extsk[64];
sc25519 scsk;
ge25519 gepk;
} s;
// Second 32 bytes of pub and priv are the keys for ed25519
// signing and verification.
SHA512(s.extsk, priv + 32, 32);
s.extsk[0] &= 248U;
s.extsk[31] &= 127U;
s.extsk[31] |= 64U;
sc25519_from32bytes(&s.scsk, s.extsk);
ge25519_scalarmult_base(&s.gepk, &s.scsk);
ge25519_pack(pub + 32, &s.gepk);
// In NaCl, the public key is crammed into the next 32 bytes
// of the private key for signing since both keys are required
// to sign. In this version we just get it from kp.pub, so we
// leave that out of private.
Utils::burn(&s, sizeof(s));
}
} // namespace ZeroTier