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// crypto_scalarmult/curve25519/ref/smult.c
/*
2010/04 (seb@dbzteam.org):
- Implements secret scalar randomization (using a 4 bytes random factor -
in the literature it is often referred to a 20 bits random value).
Obviously the cost of this paranoid mode is its noticeable although
relatively small computational overhead adding one Montgomery addition
as well as one Montgomery doubling for each additional private exponent
bit to process (for a total of 30 additional bits). Modifications
released to public domain.
Original public domain implementation by Matthew Dempsky (20081011).
Derived from public domain code by D. J. Bernstein.
*/
#include <string.h>
#include "randombytes.h"
// FIXME: uncomment the following include when compiled with NaCL -lnacl
//#include "crypto_scalarmult.h"
static 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 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 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 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 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 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 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 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 int 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 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 = 284; 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);
}
// out = a + b
static void add_i(unsigned int out[36],
const unsigned int a[32],
const unsigned int b[36]) {
unsigned int j;
unsigned int u;
u = 0;
for (j = 0; j < 32; ++j) {
u += a[j] + b[j];
out[j] = u & 255;
u >>= 8;
}
for (j = 32; j < 35; ++j) {
u += b[j];
out[j] = u & 255;
u >>= 8;
}
out[35] = u + b[35];
}
// out = a * b
static void mult_i(unsigned int out[36],
const unsigned int a[4],
const unsigned int b[32]) {
unsigned int i;
unsigned int j;
unsigned int c;
unsigned int t;
for (i = 0; i < 36; ++i)
out[i] = 0;
for (i = 0; i < 4; ++i) {
c = 0;
for (j = 0; j < 32; ++j) {
t = c + out[i + j] + a[i] * b[j];
out[i + j] = t & 255;
c = t >> 8;
}
out[i + 32] = c;
}
}
static const unsigned int orderp[32] = {
237, 211, 245 , 92, 26, 99, 18, 88,
214, 156, 247, 162, 222, 249, 222, 20,
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 16
};
int crypto_scalarmult(unsigned char *q,
const unsigned char *n,
const unsigned char *p) {
unsigned int work[96];
unsigned int e[36];
unsigned int t[32];
unsigned char r1[4];
unsigned int r2[4];
unsigned int i;
for (i = 0; i < 32; ++i)
t[i] = n[i];
t[0] &= 248;
t[31] &= 127;
t[31] |= 64;
randombytes(r1, 4);
for (i = 0; i < 4; ++i)
r2[i] = r1[i];
// e = clamp(n) + rand(r) * order(p)
mult_i(e, r2, orderp);
add_i(e, t, e);
memset(t, 0, sizeof(t));
for (i = 0; i < 32; ++i)
work[i] = p[i];
mainloop(work, e);
memset(e, 0, sizeof(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;
}