nastools_zerotierone/node/C25519.cpp
2016-11-01 16:45:16 -07:00

2399 lines
205 KiB
C++

// Code taken from NaCl by D. J. Bernstein and others
/*
Matthew Dempsky
Public domain.
Derived from public domain code by D. J. Bernstein.
*/
// Modified very slightly for ZeroTier One by Adam Ierymenko
// (no functional changes)
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include "Constants.hpp"
#include "C25519.hpp"
#include "SHA512.hpp"
#include "Buffer.hpp"
#ifdef __WINDOWS__
#pragma warning(disable: 4146)
#endif
namespace ZeroTier {
//////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////
#define crypto_int32 int32_t
#define crypto_uint32 uint32_t
#define crypto_int64 int64_t
#define crypto_uint64 uint64_t
#define crypto_hash_sha512_BYTES 64
static inline void add(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
{
unsigned int j;
unsigned int u;
u = 0;
for (j = 0;j < 31;++j) { u += a[j] + b[j]; out[j] = u & 255; u >>= 8; }
u += a[31] + b[31]; out[31] = u;
}
static inline void sub(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
{
unsigned int j;
unsigned int u;
u = 218;
for (j = 0;j < 31;++j) {
u += a[j] + 65280 - b[j];
out[j] = u & 255;
u >>= 8;
}
u += a[31] - b[31];
out[31] = u;
}
static inline void squeeze(unsigned int a[32])
{
unsigned int j;
unsigned int u;
u = 0;
for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
u += a[31]; a[31] = u & 127;
u = 19 * (u >> 7);
for (j = 0;j < 31;++j) { u += a[j]; a[j] = u & 255; u >>= 8; }
u += a[31]; a[31] = u;
}
static const unsigned int minusp[32] = {
19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128
} ;
static inline void freeze(unsigned int a[32])
{
unsigned int aorig[32];
unsigned int j;
unsigned int negative;
for (j = 0;j < 32;++j) aorig[j] = a[j];
add(a,a,minusp);
negative = -((a[31] >> 7) & 1);
for (j = 0;j < 32;++j) a[j] ^= negative & (aorig[j] ^ a[j]);
}
static inline void mult(unsigned int out[32],const unsigned int a[32],const unsigned int b[32])
{
unsigned int i;
unsigned int j;
unsigned int u;
for (i = 0;i < 32;++i) {
u = 0;
for (j = 0;j <= i;++j) u += a[j] * b[i - j];
for (j = i + 1;j < 32;++j) u += 38 * a[j] * b[i + 32 - j];
out[i] = u;
}
squeeze(out);
}
static inline void mult121665(unsigned int out[32],const unsigned int a[32])
{
unsigned int j;
unsigned int u;
u = 0;
for (j = 0;j < 31;++j) { u += 121665 * a[j]; out[j] = u & 255; u >>= 8; }
u += 121665 * a[31]; out[31] = u & 127;
u = 19 * (u >> 7);
for (j = 0;j < 31;++j) { u += out[j]; out[j] = u & 255; u >>= 8; }
u += out[j]; out[j] = u;
}
static inline void square(unsigned int out[32],const unsigned int a[32])
{
unsigned int i;
unsigned int j;
unsigned int u;
for (i = 0;i < 32;++i) {
u = 0;
for (j = 0;j < i - j;++j) u += a[j] * a[i - j];
for (j = i + 1;j < i + 32 - j;++j) u += 38 * a[j] * a[i + 32 - j];
u *= 2;
if ((i & 1) == 0) {
u += a[i / 2] * a[i / 2];
u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
}
out[i] = u;
}
squeeze(out);
}
static inline void select(unsigned int p[64],unsigned int q[64],const unsigned int r[64],const unsigned int s[64],unsigned int b)
{
unsigned int j;
unsigned int t;
unsigned int bminus1;
bminus1 = b - 1;
for (j = 0;j < 64;++j) {
t = bminus1 & (r[j] ^ s[j]);
p[j] = s[j] ^ t;
q[j] = r[j] ^ t;
}
}
static void mainloop(unsigned int work[64],const unsigned char e[32])
{
unsigned int xzm1[64];
unsigned int xzm[64];
unsigned int xzmb[64];
unsigned int xzm1b[64];
unsigned int xznb[64];
unsigned int xzn1b[64];
unsigned int a0[64];
unsigned int a1[64];
unsigned int b0[64];
unsigned int b1[64];
unsigned int c1[64];
unsigned int r[32];
unsigned int s[32];
unsigned int t[32];
unsigned int u[32];
//unsigned int i;
unsigned int j;
unsigned int b;
int pos;
for (j = 0;j < 32;++j) xzm1[j] = work[j];
xzm1[32] = 1;
for (j = 33;j < 64;++j) xzm1[j] = 0;
xzm[0] = 1;
for (j = 1;j < 64;++j) xzm[j] = 0;
for (pos = 254;pos >= 0;--pos) {
b = e[pos / 8] >> (pos & 7);
b &= 1;
select(xzmb,xzm1b,xzm,xzm1,b);
add(a0,xzmb,xzmb + 32);
sub(a0 + 32,xzmb,xzmb + 32);
add(a1,xzm1b,xzm1b + 32);
sub(a1 + 32,xzm1b,xzm1b + 32);
square(b0,a0);
square(b0 + 32,a0 + 32);
mult(b1,a1,a0 + 32);
mult(b1 + 32,a1 + 32,a0);
add(c1,b1,b1 + 32);
sub(c1 + 32,b1,b1 + 32);
square(r,c1 + 32);
sub(s,b0,b0 + 32);
mult121665(t,s);
add(u,t,b0);
mult(xznb,b0,b0 + 32);
mult(xznb + 32,s,u);
square(xzn1b,c1);
mult(xzn1b + 32,r,work);
select(xzm,xzm1,xznb,xzn1b,b);
}
for (j = 0;j < 64;++j) work[j] = xzm[j];
}
static void recip(unsigned int out[32],const unsigned int z[32])
{
unsigned int z2[32];
unsigned int z9[32];
unsigned int z11[32];
unsigned int z2_5_0[32];
unsigned int z2_10_0[32];
unsigned int z2_20_0[32];
unsigned int z2_50_0[32];
unsigned int z2_100_0[32];
unsigned int t0[32];
unsigned int t1[32];
int i;
/* 2 */ square(z2,z);
/* 4 */ square(t1,z2);
/* 8 */ square(t0,t1);
/* 9 */ mult(z9,t0,z);
/* 11 */ mult(z11,z9,z2);
/* 22 */ square(t0,z11);
/* 2^5 - 2^0 = 31 */ mult(z2_5_0,t0,z9);
/* 2^6 - 2^1 */ square(t0,z2_5_0);
/* 2^7 - 2^2 */ square(t1,t0);
/* 2^8 - 2^3 */ square(t0,t1);
/* 2^9 - 2^4 */ square(t1,t0);
/* 2^10 - 2^5 */ square(t0,t1);
/* 2^10 - 2^0 */ mult(z2_10_0,t0,z2_5_0);
/* 2^11 - 2^1 */ square(t0,z2_10_0);
/* 2^12 - 2^2 */ square(t1,t0);
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t0,t1); square(t1,t0); }
/* 2^20 - 2^0 */ mult(z2_20_0,t1,z2_10_0);
/* 2^21 - 2^1 */ square(t0,z2_20_0);
/* 2^22 - 2^2 */ square(t1,t0);
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { square(t0,t1); square(t1,t0); }
/* 2^40 - 2^0 */ mult(t0,t1,z2_20_0);
/* 2^41 - 2^1 */ square(t1,t0);
/* 2^42 - 2^2 */ square(t0,t1);
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { square(t1,t0); square(t0,t1); }
/* 2^50 - 2^0 */ mult(z2_50_0,t0,z2_10_0);
/* 2^51 - 2^1 */ square(t0,z2_50_0);
/* 2^52 - 2^2 */ square(t1,t0);
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
/* 2^100 - 2^0 */ mult(z2_100_0,t1,z2_50_0);
/* 2^101 - 2^1 */ square(t1,z2_100_0);
/* 2^102 - 2^2 */ square(t0,t1);
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { square(t1,t0); square(t0,t1); }
/* 2^200 - 2^0 */ mult(t1,t0,z2_100_0);
/* 2^201 - 2^1 */ square(t0,t1);
/* 2^202 - 2^2 */ square(t1,t0);
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { square(t0,t1); square(t1,t0); }
/* 2^250 - 2^0 */ mult(t0,t1,z2_50_0);
/* 2^251 - 2^1 */ square(t1,t0);
/* 2^252 - 2^2 */ square(t0,t1);
/* 2^253 - 2^3 */ square(t1,t0);
/* 2^254 - 2^4 */ square(t0,t1);
/* 2^255 - 2^5 */ square(t1,t0);
/* 2^255 - 21 */ mult(out,t1,z11);
}
static inline int crypto_scalarmult(unsigned char *q,
const unsigned char *n,
const unsigned char *p)
{
unsigned int work[96];
unsigned char e[32];
unsigned int i;
for (i = 0;i < 32;++i) e[i] = n[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
for (i = 0;i < 32;++i) work[i] = p[i];
mainloop(work,e);
recip(work + 32,work + 32);
mult(work + 64,work,work + 32);
freeze(work + 64);
for (i = 0;i < 32;++i) q[i] = work[64 + i];
return 0;
}
static const unsigned char base[32] = {9};
static inline int crypto_scalarmult_base(unsigned char *q,
const unsigned char *n)
{
return crypto_scalarmult(q,n,base);
}
//////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////
// This is the Ed25519 stuff from SUPERCOP:
// http://bench.cr.yp.to/supercop.html
// Also public domain, newer version than the Ed25519 found in NaCl
typedef struct
{
crypto_uint32 v[32];
}
fe25519;
static void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y);
static inline crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
{
crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */
x -= 1; /* 4294967295: yes; 0..65534: no */
x >>= 31; /* 1: yes; 0: no */
return x;
}
static inline crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */
{
unsigned int x = a;
x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */
x >>= 31; /* 0: yes; 1: no */
x ^= 1; /* 1: yes; 0: no */
return x;
}
static inline crypto_uint32 times19(crypto_uint32 a)
{
return (a << 4) + (a << 1) + a;
}
static inline crypto_uint32 times38(crypto_uint32 a)
{
return (a << 5) + (a << 2) + (a << 1);
}
static inline void reduce_add_sub(fe25519 *r)
{
crypto_uint32 t;
int i,rep;
for(rep=0;rep<4;rep++)
{
t = r->v[31] >> 7;
r->v[31] &= 127;
t = times19(t);
r->v[0] += t;
for(i=0;i<31;i++)
{
t = r->v[i] >> 8;
r->v[i+1] += t;
r->v[i] &= 255;
}
}
}
static inline void reduce_mul(fe25519 *r)
{
crypto_uint32 t;
int i,rep;
for(rep=0;rep<2;rep++)
{
t = r->v[31] >> 7;
r->v[31] &= 127;
t = times19(t);
r->v[0] += t;
for(i=0;i<31;i++)
{
t = r->v[i] >> 8;
r->v[i+1] += t;
r->v[i] &= 255;
}
}
}
/* reduction modulo 2^255-19 */
static inline void fe25519_freeze(fe25519 *r)
{
int i;
crypto_uint32 m = equal(r->v[31],127);
for(i=30;i>0;i--)
m &= equal(r->v[i],255);
m &= ge(r->v[0],237);
m = -m;
r->v[31] -= m&127;
for(i=30;i>0;i--)
r->v[i] -= m&255;
r->v[0] -= m&237;
}
static inline void fe25519_unpack(fe25519 *r, const unsigned char x[32])
{
int i;
for(i=0;i<32;i++) r->v[i] = x[i];
r->v[31] &= 127;
}
/* Assumes input x being reduced below 2^255 */
static inline void fe25519_pack(unsigned char r[32], const fe25519 *x)
{
int i;
fe25519 y = *x;
fe25519_freeze(&y);
for(i=0;i<32;i++)
r[i] = y.v[i];
}
#if 0
static int fe25519_iszero(const fe25519 *x)
{
int i;
int r;
fe25519 t = *x;
fe25519_freeze(&t);
r = equal(t.v[0],0);
for(i=1;i<32;i++)
r &= equal(t.v[i],0);
return r;
}
#endif
static inline int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y)
{
int i;
fe25519 t1 = *x;
fe25519 t2 = *y;
fe25519_freeze(&t1);
fe25519_freeze(&t2);
for(i=0;i<32;i++)
if(t1.v[i] != t2.v[i]) return 0;
return 1;
}
static inline void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
{
int i;
crypto_uint32 mask = b;
mask = -mask;
for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
}
static inline unsigned char fe25519_getparity(const fe25519 *x)
{
fe25519 t = *x;
fe25519_freeze(&t);
return t.v[0] & 1;
}
static inline void fe25519_setone(fe25519 *r)
{
int i;
r->v[0] = 1;
for(i=1;i<32;i++) r->v[i]=0;
}
static inline void fe25519_setzero(fe25519 *r)
{
int i;
for(i=0;i<32;i++) r->v[i]=0;
}
static inline void fe25519_neg(fe25519 *r, const fe25519 *x)
{
fe25519 t;
int i;
for(i=0;i<32;i++) t.v[i]=x->v[i];
fe25519_setzero(r);
fe25519_sub(r, r, &t);
}
static inline void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
int i;
for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
reduce_add_sub(r);
}
static inline void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
int i;
crypto_uint32 t[32];
t[0] = x->v[0] + 0x1da;
t[31] = x->v[31] + 0xfe;
for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe;
for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i];
reduce_add_sub(r);
}
static inline void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
int i,j;
crypto_uint32 t[63];
for(i=0;i<63;i++)t[i] = 0;
for(i=0;i<32;i++)
for(j=0;j<32;j++)
t[i+j] += x->v[i] * y->v[j];
for(i=32;i<63;i++)
r->v[i-32] = t[i-32] + times38(t[i]);
r->v[31] = t[31]; /* result now in r[0]...r[31] */
reduce_mul(r);
}
static inline void fe25519_square(fe25519 *r, const fe25519 *x)
{
fe25519_mul(r, x, x);
}
static void fe25519_invert(fe25519 *r, const fe25519 *x)
{
fe25519 z2;
fe25519 z9;
fe25519 z11;
fe25519 z2_5_0;
fe25519 z2_10_0;
fe25519 z2_20_0;
fe25519 z2_50_0;
fe25519 z2_100_0;
fe25519 t0;
fe25519 t1;
int i;
/* 2 */ fe25519_square(&z2,x);
/* 4 */ fe25519_square(&t1,&z2);
/* 8 */ fe25519_square(&t0,&t1);
/* 9 */ fe25519_mul(&z9,&t0,x);
/* 11 */ fe25519_mul(&z11,&z9,&z2);
/* 22 */ fe25519_square(&t0,&z11);
/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9);
/* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0);
/* 2^7 - 2^2 */ fe25519_square(&t1,&t0);
/* 2^8 - 2^3 */ fe25519_square(&t0,&t1);
/* 2^9 - 2^4 */ fe25519_square(&t1,&t0);
/* 2^10 - 2^5 */ fe25519_square(&t0,&t1);
/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0);
/* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0);
/* 2^12 - 2^2 */ fe25519_square(&t1,&t0);
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0);
/* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0);
/* 2^22 - 2^2 */ fe25519_square(&t1,&t0);
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
/* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0);
/* 2^41 - 2^1 */ fe25519_square(&t1,&t0);
/* 2^42 - 2^2 */ fe25519_square(&t0,&t1);
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0);
/* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0);
/* 2^52 - 2^2 */ fe25519_square(&t1,&t0);
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0);
/* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0);
/* 2^102 - 2^2 */ fe25519_square(&t0,&t1);
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); }
/* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0);
/* 2^201 - 2^1 */ fe25519_square(&t0,&t1);
/* 2^202 - 2^2 */ fe25519_square(&t1,&t0);
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); }
/* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0);
/* 2^251 - 2^1 */ fe25519_square(&t1,&t0);
/* 2^252 - 2^2 */ fe25519_square(&t0,&t1);
/* 2^253 - 2^3 */ fe25519_square(&t1,&t0);
/* 2^254 - 2^4 */ fe25519_square(&t0,&t1);
/* 2^255 - 2^5 */ fe25519_square(&t1,&t0);
/* 2^255 - 21 */ fe25519_mul(r,&t1,&z11);
}
static void fe25519_pow2523(fe25519 *r, const fe25519 *x)
{
fe25519 z2;
fe25519 z9;
fe25519 z11;
fe25519 z2_5_0;
fe25519 z2_10_0;
fe25519 z2_20_0;
fe25519 z2_50_0;
fe25519 z2_100_0;
fe25519 t;
int i;
/* 2 */ fe25519_square(&z2,x);
/* 4 */ fe25519_square(&t,&z2);
/* 8 */ fe25519_square(&t,&t);
/* 9 */ fe25519_mul(&z9,&t,x);
/* 11 */ fe25519_mul(&z11,&z9,&z2);
/* 22 */ fe25519_square(&t,&z11);
/* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9);
/* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0);
/* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); }
/* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0);
/* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0);
/* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
/* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0);
/* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0);
/* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); }
/* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0);
/* 2^41 - 2^1 */ fe25519_square(&t,&t);
/* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); }
/* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0);
/* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0);
/* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
/* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0);
/* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0);
/* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); }
/* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0);
/* 2^201 - 2^1 */ fe25519_square(&t,&t);
/* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); }
/* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0);
/* 2^251 - 2^1 */ fe25519_square(&t,&t);
/* 2^252 - 2^2 */ fe25519_square(&t,&t);
/* 2^252 - 3 */ fe25519_mul(r,&t,x);
}
typedef struct
{
crypto_uint32 v[32];
}
sc25519;
typedef struct
{
crypto_uint32 v[16];
}
shortsc25519;
static const crypto_uint32 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};
static const crypto_uint32 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};
static inline crypto_uint32 lt(crypto_uint32 a,crypto_uint32 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;
}
/* Reduce coefficients of r before calling reduce_add_sub */
static inline void reduce_add_sub(sc25519 *r)
{
crypto_uint32 pb = 0;
crypto_uint32 b;
crypto_uint32 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]);
}
/* Reduce coefficients of x before calling barrett_reduce */
static inline void barrett_reduce(sc25519 *r, const crypto_uint32 x[64])
{
/* See HAC, Alg. 14.42 */
int i,j;
crypto_uint32 q2[66];
crypto_uint32 *q3 = q2 + 33;
crypto_uint32 r1[33];
crypto_uint32 r2[33];
crypto_uint32 carry;
crypto_uint32 pb = 0;
crypto_uint32 b;
for (i = 0;i < 66;++i) q2[i] = 0;
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];
carry = q2[31] >> 8;
q2[32] += carry;
carry = q2[32] >> 8;
q2[33] += carry;
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++)
{
carry = r2[i] >> 8;
r2[i+1] += carry;
r2[i] &= 0xff;
}
for(i=0;i<32;i++)
{
pb += r2[i];
b = lt(r1[i],pb);
r->v[i] = r1[i]-pb+(b<<8);
pb = b;
}
/* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3
* If so: Handle it here!
*/
reduce_add_sub(r);
reduce_add_sub(r);
}
static inline void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
{
int i;
crypto_uint32 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);
}
#if 0
static void shortsc25519_from16bytes(shortsc25519 *r, const unsigned char x[16])
{
int i;
for(i=0;i<16;i++) r->v[i] = x[i];
}
#endif
static inline void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
{
int i;
crypto_uint32 t[64];
for(i=0;i<64;i++) t[i] = x[i];
barrett_reduce(r, t);
}
#if 0
static void sc25519_from_shortsc(sc25519 *r, const shortsc25519 *x)
{
int i;
for(i=0;i<16;i++)
r->v[i] = x->v[i];
for(i=0;i<16;i++)
r->v[16+i] = 0;
}
#endif
static inline void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
{
int i;
for(i=0;i<32;i++) r[i] = x->v[i];
}
#if 0
static int sc25519_iszero_vartime(const sc25519 *x)
{
int i;
for(i=0;i<32;i++)
if(x->v[i] != 0) return 0;
return 1;
}
#endif
#if 0
static int sc25519_isshort_vartime(const sc25519 *x)
{
int i;
for(i=31;i>15;i--)
if(x->v[i] != 0) return 0;
return 1;
}
#endif
#if 0
static int sc25519_lt_vartime(const sc25519 *x, const sc25519 *y)
{
int i;
for(i=31;i>=0;i--)
{
if(x->v[i] < y->v[i]) return 1;
if(x->v[i] > y->v[i]) return 0;
}
return 0;
}
#endif
static inline void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
int i, carry;
for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i];
for(i=0;i<31;i++)
{
carry = r->v[i] >> 8;
r->v[i+1] += carry;
r->v[i] &= 0xff;
}
reduce_add_sub(r);
}
#if 0
static void sc25519_sub_nored(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
crypto_uint32 b = 0;
crypto_uint32 t;
int i;
for(i=0;i<32;i++)
{
t = x->v[i] - y->v[i] - b;
r->v[i] = t & 255;
b = (t >> 8) & 1;
}
}
#endif
static inline void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
int i,j,carry;
crypto_uint32 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];
/* Reduce coefficients */
for(i=0;i<63;i++)
{
carry = t[i] >> 8;
t[i+1] += carry;
t[i] &= 0xff;
}
barrett_reduce(r, t);
}
#if 0
static void sc25519_mul_shortsc(sc25519 *r, const sc25519 *x, const shortsc25519 *y)
{
sc25519 t;
sc25519_from_shortsc(&t, y);
sc25519_mul(r, x, &t);
}
#endif
static 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;
}
#if 0
static void sc25519_window5(signed char r[51], const sc25519 *s)
{
char carry;
int i;
for(i=0;i<6;i++)
{
r[8*i+0] = s->v[5*i+0] & 31;
r[8*i+1] = (s->v[5*i+0] >> 5) & 31;
r[8*i+1] ^= (s->v[5*i+1] << 3) & 31;
r[8*i+2] = (s->v[5*i+1] >> 2) & 31;
r[8*i+3] = (s->v[5*i+1] >> 7) & 31;
r[8*i+3] ^= (s->v[5*i+2] << 1) & 31;
r[8*i+4] = (s->v[5*i+2] >> 4) & 31;
r[8*i+4] ^= (s->v[5*i+3] << 4) & 31;
r[8*i+5] = (s->v[5*i+3] >> 1) & 31;
r[8*i+6] = (s->v[5*i+3] >> 6) & 31;
r[8*i+6] ^= (s->v[5*i+4] << 2) & 31;
r[8*i+7] = (s->v[5*i+4] >> 3) & 31;
}
r[8*i+0] = s->v[5*i+0] & 31;
r[8*i+1] = (s->v[5*i+0] >> 5) & 31;
r[8*i+1] ^= (s->v[5*i+1] << 3) & 31;
r[8*i+2] = (s->v[5*i+1] >> 2) & 31;
/* Making it signed */
carry = 0;
for(i=0;i<50;i++)
{
r[i] += carry;
r[i+1] += r[i] >> 5;
r[i] &= 31;
carry = r[i] >> 4;
r[i] -= carry<<5;
}
r[50] += carry;
}
#endif
static 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);
}
typedef struct
{
fe25519 x;
fe25519 y;
fe25519 z;
fe25519 t;
} ge25519;
/* d */
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}};
/* 2*d */
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}};
/* sqrt(-1) */
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}};
#define ge25519_p3 ge25519
typedef struct
{
fe25519 x;
fe25519 z;
fe25519 y;
fe25519 t;
} ge25519_p1p1;
typedef struct
{
fe25519 x;
fe25519 y;
fe25519 z;
} ge25519_p2;
typedef struct
{
fe25519 x;
fe25519 y;
} ge25519_aff;
/* Packed coordinates of the base point */
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}}};
/* Multiples of the base point in affine representation */
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}},
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{{0xa3, 0x64, 0x17, 0x9b, 0x8b, 0xc8, 0x3a, 0x61, 0xe6, 0x9d, 0xc6, 0xed, 0x7b, 0x03, 0x52, 0x26, 0x9d, 0x3a, 0xb3, 0x13, 0xcc, 0x8a, 0xfd, 0x2c, 0x1a, 0x1d, 0xed, 0x13, 0xd0, 0x55, 0x57, 0x0e}}},
{{{0x1a, 0xea, 0xbf, 0xfd, 0x4a, 0x3c, 0x8e, 0xec, 0x29, 0x7e, 0x77, 0x77, 0x12, 0x99, 0xd7, 0x84, 0xf9, 0x55, 0x7f, 0xf1, 0x8b, 0xb4, 0xd2, 0x95, 0xa3, 0x8d, 0xf0, 0x8a, 0xa7, 0xeb, 0x82, 0x4b}} ,
{{0x2c, 0x28, 0xf4, 0x3a, 0xf6, 0xde, 0x0a, 0xe0, 0x41, 0x44, 0x23, 0xf8, 0x3f, 0x03, 0x64, 0x9f, 0xc3, 0x55, 0x4c, 0xc6, 0xc1, 0x94, 0x1c, 0x24, 0x5d, 0x5f, 0x92, 0x45, 0x96, 0x57, 0x37, 0x14}}},
{{{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}}},
{{{0xc1, 0xcd, 0x90, 0x66, 0xb9, 0x76, 0xa0, 0x5b, 0xa5, 0x85, 0x75, 0x23, 0xf9, 0x89, 0xa5, 0x82, 0xb2, 0x6f, 0xb1, 0xeb, 0xc4, 0x69, 0x6f, 0x18, 0x5a, 0xed, 0x94, 0x3d, 0x9d, 0xd9, 0x2c, 0x1a}} ,
{{0x35, 0xb0, 0xe6, 0x73, 0x06, 0xb7, 0x37, 0xe0, 0xf8, 0xb0, 0x22, 0xe8, 0xd2, 0xed, 0x0b, 0xef, 0xe6, 0xc6, 0x5a, 0x99, 0x9e, 0x1a, 0x9f, 0x04, 0x97, 0xe4, 0x4d, 0x0b, 0xbe, 0xba, 0x44, 0x40}}},
{{{0xc1, 0x56, 0x96, 0x91, 0x5f, 0x1f, 0xbb, 0x54, 0x6f, 0x88, 0x89, 0x0a, 0xb2, 0xd6, 0x41, 0x42, 0x6a, 0x82, 0xee, 0x14, 0xaa, 0x76, 0x30, 0x65, 0x0f, 0x67, 0x39, 0xa6, 0x51, 0x7c, 0x49, 0x24}} ,
{{0x35, 0xa3, 0x78, 0xd1, 0x11, 0x0f, 0x75, 0xd3, 0x70, 0x46, 0xdb, 0x20, 0x51, 0xcb, 0x92, 0x80, 0x54, 0x10, 0x74, 0x36, 0x86, 0xa9, 0xd7, 0xa3, 0x08, 0x78, 0xf1, 0x01, 0x29, 0xf8, 0x80, 0x3b}}},
{{{0xdb, 0xa7, 0x9d, 0x9d, 0xbf, 0xa0, 0xcc, 0xed, 0x53, 0xa2, 0xa2, 0x19, 0x39, 0x48, 0x83, 0x19, 0x37, 0x58, 0xd1, 0x04, 0x28, 0x40, 0xf7, 0x8a, 0xc2, 0x08, 0xb7, 0xa5, 0x42, 0xcf, 0x53, 0x4c}} ,
{{0xa7, 0xbb, 0xf6, 0x8e, 0xad, 0xdd, 0xf7, 0x90, 0xdd, 0x5f, 0x93, 0x89, 0xae, 0x04, 0x37, 0xe6, 0x9a, 0xb7, 0xe8, 0xc0, 0xdf, 0x16, 0x2a, 0xbf, 0xc4, 0x3a, 0x3c, 0x41, 0xd5, 0x89, 0x72, 0x5a}}},
{{{0x1f, 0x96, 0xff, 0x34, 0x2c, 0x13, 0x21, 0xcb, 0x0a, 0x89, 0x85, 0xbe, 0xb3, 0x70, 0x9e, 0x1e, 0xde, 0x97, 0xaf, 0x96, 0x30, 0xf7, 0x48, 0x89, 0x40, 0x8d, 0x07, 0xf1, 0x25, 0xf0, 0x30, 0x58}} ,
{{0x1e, 0xd4, 0x93, 0x57, 0xe2, 0x17, 0xe7, 0x9d, 0xab, 0x3c, 0x55, 0x03, 0x82, 0x2f, 0x2b, 0xdb, 0x56, 0x1e, 0x30, 0x2e, 0x24, 0x47, 0x6e, 0xe6, 0xff, 0x33, 0x24, 0x2c, 0x75, 0x51, 0xd4, 0x67}}},
{{{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}}},
{{{0x2b, 0x06, 0xd9, 0xa1, 0x5d, 0xe1, 0xf4, 0xd1, 0x1e, 0x3c, 0x9a, 0xc6, 0x29, 0x2b, 0x13, 0x13, 0x78, 0xc0, 0xd8, 0x16, 0x17, 0x2d, 0x9e, 0xa9, 0xc9, 0x79, 0x57, 0xab, 0x24, 0x91, 0x92, 0x19}} ,
{{0x69, 0xfb, 0xa1, 0x9c, 0xa6, 0x75, 0x49, 0x7d, 0x60, 0x73, 0x40, 0x42, 0xc4, 0x13, 0x0a, 0x95, 0x79, 0x1e, 0x04, 0x83, 0x94, 0x99, 0x9b, 0x1e, 0x0c, 0xe8, 0x1f, 0x54, 0xef, 0xcb, 0xc0, 0x52}}},
{{{0x14, 0x89, 0x73, 0xa1, 0x37, 0x87, 0x6a, 0x7a, 0xcf, 0x1d, 0xd9, 0x2e, 0x1a, 0x67, 0xed, 0x74, 0xc0, 0xf0, 0x9c, 0x33, 0xdd, 0xdf, 0x08, 0xbf, 0x7b, 0xd1, 0x66, 0xda, 0xe6, 0xc9, 0x49, 0x08}} ,
{{0xe9, 0xdd, 0x5e, 0x55, 0xb0, 0x0a, 0xde, 0x21, 0x4c, 0x5a, 0x2e, 0xd4, 0x80, 0x3a, 0x57, 0x92, 0x7a, 0xf1, 0xc4, 0x2c, 0x40, 0xaf, 0x2f, 0xc9, 0x92, 0x03, 0xe5, 0x5a, 0xbc, 0xdc, 0xf4, 0x09}}},
{{{0xf3, 0xe1, 0x2b, 0x7c, 0x05, 0x86, 0x80, 0x93, 0x4a, 0xad, 0xb4, 0x8f, 0x7e, 0x99, 0x0c, 0xfd, 0xcd, 0xef, 0xd1, 0xff, 0x2c, 0x69, 0x34, 0x13, 0x41, 0x64, 0xcf, 0x3b, 0xd0, 0x90, 0x09, 0x1e}} ,
{{0x9d, 0x45, 0xd6, 0x80, 0xe6, 0x45, 0xaa, 0xf4, 0x15, 0xaa, 0x5c, 0x34, 0x87, 0x99, 0xa2, 0x8c, 0x26, 0x84, 0x62, 0x7d, 0xb6, 0x29, 0xc0, 0x52, 0xea, 0xf5, 0x81, 0x18, 0x0f, 0x35, 0xa9, 0x0e}}},
{{{0xe7, 0x20, 0x72, 0x7c, 0x6d, 0x94, 0x5f, 0x52, 0x44, 0x54, 0xe3, 0xf1, 0xb2, 0xb0, 0x36, 0x46, 0x0f, 0xae, 0x92, 0xe8, 0x70, 0x9d, 0x6e, 0x79, 0xb1, 0xad, 0x37, 0xa9, 0x5f, 0xc0, 0xde, 0x03}} ,
{{0x15, 0x55, 0x37, 0xc6, 0x1c, 0x27, 0x1c, 0x6d, 0x14, 0x4f, 0xca, 0xa4, 0xc4, 0x88, 0x25, 0x46, 0x39, 0xfc, 0x5a, 0xe5, 0xfe, 0x29, 0x11, 0x69, 0xf5, 0x72, 0x84, 0x4d, 0x78, 0x9f, 0x94, 0x15}}},
{{{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}}},
{{{0xec, 0xd3, 0xff, 0x57, 0x0b, 0xb0, 0xb2, 0xdc, 0xf8, 0x4f, 0xe2, 0x12, 0xd5, 0x36, 0xbe, 0x6b, 0x09, 0x43, 0x6d, 0xa3, 0x4d, 0x90, 0x2d, 0xb8, 0x74, 0xe8, 0x71, 0x45, 0x19, 0x8b, 0x0c, 0x6a}} ,
{{0xb8, 0x42, 0x1c, 0x03, 0xad, 0x2c, 0x03, 0x8e, 0xac, 0xd7, 0x98, 0x29, 0x13, 0xc6, 0x02, 0x29, 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}}}
};
static 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);
}
static 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);
}
static 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);
}
static 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); /* A = (Y1-X1)*(Y2-X2) */
fe25519_add(&b, &r->y, &r->x); /* B = (Y1+X1)*(Y2+X2) */
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); /* E = B-A */
fe25519_add(&h, &b, &a); /* H = B+A */
fe25519_mul(&c, &r->t, &qt); /* C = T1*k*T2 */
fe25519_mul(&c, &c, &ge25519_ec2d);
fe25519_add(&d, &r->z, &r->z); /* D = Z1*2 */
fe25519_sub(&f, &d, &c); /* F = D-C */
fe25519_add(&g, &d, &c); /* 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);
}
static 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); /* A = (Y1-X1)*(Y2-X2) */
fe25519_sub(&t, &q->y, &q->x);
fe25519_mul(&a, &a, &t);
fe25519_add(&b, &p->x, &p->y); /* B = (Y1+X1)*(Y2+X2) */
fe25519_add(&t, &q->x, &q->y);
fe25519_mul(&b, &b, &t);
fe25519_mul(&c, &p->t, &q->t); /* C = T1*k*T2 */
fe25519_mul(&c, &c, &ge25519_ec2d);
fe25519_mul(&d, &p->z, &q->z); /* D = Z1*2*Z2 */
fe25519_add(&d, &d, &d);
fe25519_sub(&r->x, &b, &a); /* E = B-A */
fe25519_sub(&r->t, &d, &c); /* F = D-C */
fe25519_add(&r->z, &d, &c); /* G = D+C */
fe25519_add(&r->y, &b, &a); /* H = B+A */
}
/* See http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#doubling-dbl-2008-hwcd */
static 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);
}
/* Constant-time version of: if(b) r = p */
static 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);
}
static inline unsigned char equal(signed char b,signed char c)
{
unsigned char ub = b;
unsigned char uc = c;
unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
crypto_uint32 y = x; /* 0: yes; 1..255: no */
y -= 1; /* 4294967295: yes; 0..254: no */
y >>= 31; /* 1: yes; 0: no */
return (unsigned char)y;
}
static inline unsigned char negative(signed char b)
{
unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
x >>= 63; /* 1: yes; 0: no */
return (unsigned char)x;
}
static inline void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
{
/* constant time */
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));
}
static inline void setneutral(ge25519 *r)
{
fe25519_setzero(&r->x);
fe25519_setone(&r->y);
fe25519_setone(&r->z);
fe25519_setzero(&r->t);
}
/* return 0 on success, -1 otherwise */
static 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); /* x = y^2 */
fe25519_mul(&den, &num, &ge25519_ecd); /* den = dy^2 */
fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */
/* Computation of sqrt(num/den) */
/* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
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);
/* 2. computation of r->x = t * num * den^3 */
fe25519_mul(&t, &t, &num);
fe25519_mul(&t, &t, &den);
fe25519_mul(&t, &t, &den);
fe25519_mul(&r->x, &t, &den);
/* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not: */
fe25519_square(&chk, &r->x);
fe25519_mul(&chk, &chk, &den);
if (!fe25519_iseq_vartime(&chk, &num))
fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
/* 4. Now we have one of the two square roots, except if input was not a square */
fe25519_square(&chk, &r->x);
fe25519_mul(&chk, &chk, &den);
if (!fe25519_iseq_vartime(&chk, &num))
return -1;
/* 5. Choose the desired square root according to parity: */
if(fe25519_getparity(&r->x) != (1-par))
fe25519_neg(&r->x, &r->x);
fe25519_mul(&r->t, &r->x, &r->y);
return 0;
}
static inline 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;
}
#if 0
static int ge25519_isneutral_vartime(const ge25519_p3 *p)
{
int ret = 1;
if(!fe25519_iszero(&p->x)) ret = 0;
if(!fe25519_iseq_vartime(&p->y, &p->z)) ret = 0;
return ret;
}
#endif
/* computes [s1]p1 + [s2]p2 */
static 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])); // eliminate type punning warning
unsigned char b[127];
int i;
/* precomputation s2 s1 */
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);
/* scalar multiplication */
*r = pre[b[126]];
for(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);
}
}
static inline void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
{
signed char b[85];
int i;
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(i=1;i<85;i++)
{
choose_t(&t, (unsigned long long) i, b[i]);
ge25519_mixadd2(r, &t);
}
}
static inline void get_hram(unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground, unsigned long long smlen)
{
unsigned long long i;
for (i = 0;i < 32;++i) playground[i] = sm[i];
for (i = 32;i < 64;++i) playground[i] = pk[i-32];
for (i = 64;i < smlen;++i) playground[i] = sm[i];
//crypto_hash_sha512(hram,playground,smlen);
SHA512::hash(hram,playground,(unsigned int)smlen);
}
// This is the original sign and verify code -- the versions in sign() and
// verify() below the fold are slightly modified in terms of how they behave
// in relation to the message, but the algorithms are the same.
#if 0
int crypto_sign_keypair(
unsigned char *pk,
unsigned char *sk
)
{
sc25519 scsk;
ge25519 gepk;
unsigned char extsk[64];
int i;
randombytes(sk, 32);
crypto_hash_sha512(extsk, sk, 32);
extsk[0] &= 248;
extsk[31] &= 127;
extsk[31] |= 64;
sc25519_from32bytes(&scsk,extsk);
ge25519_scalarmult_base(&gepk, &scsk);
ge25519_pack(pk, &gepk);
for(i=0;i<32;i++)
sk[32 + i] = pk[i];
return 0;
}
static int crypto_sign(
unsigned char *sm,unsigned long long *smlen,
const unsigned char *m,unsigned long long mlen,
const unsigned char *sk
)
{
sc25519 sck, scs, scsk;
ge25519 ger;
unsigned char r[32];
unsigned char s[32];
unsigned char extsk[64];
unsigned long long i;
unsigned char hmg[crypto_hash_sha512_BYTES];
unsigned char hram[crypto_hash_sha512_BYTES];
crypto_hash_sha512(extsk, sk, 32);
extsk[0] &= 248;
extsk[31] &= 127;
extsk[31] |= 64;
*smlen = mlen+64;
for(i=0;i<mlen;i++)
sm[64 + i] = m[i];
for(i=0;i<32;i++)
sm[32 + i] = extsk[32+i];
crypto_hash_sha512(hmg, sm+32, mlen+32); /* Generate k as h(extsk[32],...,extsk[63],m) */
/* Computation of R */
sc25519_from64bytes(&sck, hmg);
ge25519_scalarmult_base(&ger, &sck);
ge25519_pack(r, &ger);
/* Computation of s */
for(i=0;i<32;i++)
sm[i] = r[i];
get_hram(hram, sm, sk+32, sm, mlen+64);
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(i=0;i<32;i++)
sm[32 + i] = s[i];
return 0;
}
static int crypto_sign_open(
unsigned char *m,unsigned long long *mlen,
const unsigned char *sm,unsigned long long smlen,
const unsigned char *pk
)
{
int i, ret;
unsigned char t2[32];
ge25519 get1, get2;
sc25519 schram, scs;
unsigned char hram[crypto_hash_sha512_BYTES];
*mlen = (unsigned long long) -1;
if (smlen < 64) return -1;
if (ge25519_unpackneg_vartime(&get1, pk)) return -1;
get_hram(hram,sm,pk,m,smlen);
sc25519_from64bytes(&schram, hram);
sc25519_from32bytes(&scs, sm+32);
ge25519_double_scalarmult_vartime(&get2, &get1, &schram, &ge25519_base, &scs);
ge25519_pack(t2, &get2);
ret = crypto_verify_32(sm, t2);
if (!ret)
{
for(i=0;i<smlen-64;i++)
m[i] = sm[i + 64];
*mlen = smlen-64;
}
else
{
for(i=0;i<smlen-64;i++)
m[i] = 0;
}
return ret;
}
#endif // 0
//////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////
void C25519::agree(const C25519::Private &mine,const C25519::Public &their,void *keybuf,unsigned int keylen)
throw()
{
unsigned char rawkey[32];
unsigned char digest[64];
crypto_scalarmult(rawkey,mine.data,their.data);
SHA512::hash(digest,rawkey,32);
for(unsigned int i=0,k=0;i<keylen;) {
if (k == 64) {
k = 0;
SHA512::hash(digest,digest,64);
}
((unsigned char *)keybuf)[i++] = digest[k++];
}
}
void C25519::sign(const C25519::Private &myPrivate,const C25519::Public &myPublic,const void *msg,unsigned int len,void *signature)
throw()
{
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;
unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg)
SHA512::hash(digest,msg,len);
SHA512::hash(extsk,myPrivate.data + 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::hash(hmg,sig + 32,64);
//crypto_hash_sha512(hmg, sm+32, mlen+32); /* Generate k as h(extsk[32],...,extsk[63],m) */
/* 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.data + 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 C25519::Public &their,const void *msg,unsigned int len,const void *signature)
throw()
{
unsigned char t2[32];
ge25519 get1, get2;
sc25519 schram, scs;
unsigned char hram[crypto_hash_sha512_BYTES];
unsigned char m[96];
unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg)
const unsigned char *sig = (const unsigned char *)signature;
// First check the message's integrity
SHA512::hash(digest,msg,len);
if (!Utils::secureEq(sig + 64,digest,32))
return false;
if (ge25519_unpackneg_vartime(&get1,their.data + 32))
return false;
get_hram(hram,sig,their.data + 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::_calcPubDH(C25519::Pair &kp)
throw()
{
// 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(kp.pub.data,kp.priv.data);
}
void C25519::_calcPubED(C25519::Pair &kp)
throw()
{
unsigned char extsk[64];
sc25519 scsk;
ge25519 gepk;
// Second 32 bytes of pub and priv are the keys for ed25519
// signing and verification.
SHA512::hash(extsk,kp.priv.data + 32,32);
extsk[0] &= 248;
extsk[31] &= 127;
extsk[31] |= 64;
sc25519_from32bytes(&scsk,extsk);
ge25519_scalarmult_base(&gepk,&scsk);
ge25519_pack(kp.pub.data + 32,&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.
}
} // namespace ZeroTier