serval-dna/nacl/nacl-20110221/crypto_scalarmult/curve25519/donna_c64/smult.c
Daniel O'Connor bf9710fd5a Unpacked nacl-20110221 after processing by nacl-prepare-sources.
This only affects build_android, if nacl-gcc-prep is run then build/`uname -s` will be created.
2012-02-27 12:40:14 +10:30

478 lines
14 KiB
C

/* Copyright 2008, Google Inc.
* All rights reserved.
*
* Code released into the public domain.
*
* curve25519-donna: Curve25519 elliptic curve, public key function
*
* http://code.google.com/p/curve25519-donna/
*
* Adam Langley <agl@imperialviolet.org>
*
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
*
* More information about curve25519 can be found here
* http://cr.yp.to/ecdh.html
*
* djb's sample implementation of curve25519 is written in a special assembly
* language called qhasm and uses the floating point registers.
*
* This is, almost, a clean room reimplementation from the curve25519 paper. It
* uses many of the tricks described therein. Only the crecip function is taken
* from the sample implementation.
*/
#include <string.h>
#include <stdint.h>
#include "crypto_scalarmult.h"
typedef uint8_t u8;
typedef uint64_t felem;
// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
// platforms only as far as I know.
typedef unsigned uint128_t __attribute__((mode(TI)));
/* Sum two numbers: output += in */
static void fsum(felem *output, const felem *in) {
unsigned i;
for (i = 0; i < 5; ++i) output[i] += in[i];
}
/* Find the difference of two numbers: output = in - output
* (note the order of the arguments!)
*/
static void fdifference_backwards(felem *ioutput, const felem *iin) {
static const int64_t twotothe51 = (1l << 51);
const int64_t *in = (const int64_t *) iin;
int64_t *out = (int64_t *) ioutput;
out[0] = in[0] - out[0];
out[1] = in[1] - out[1];
out[2] = in[2] - out[2];
out[3] = in[3] - out[3];
out[4] = in[4] - out[4];
// An arithmetic shift right of 63 places turns a positive number to 0 and a
// negative number to all 1's. This gives us a bitmask that lets us avoid
// side-channel prone branches.
int64_t t;
#define NEGCHAIN(a,b) \
t = out[a] >> 63; \
out[a] += twotothe51 & t; \
out[b] -= 1 & t;
#define NEGCHAIN19(a,b) \
t = out[a] >> 63; \
out[a] += twotothe51 & t; \
out[b] -= 19 & t;
NEGCHAIN(0, 1);
NEGCHAIN(1, 2);
NEGCHAIN(2, 3);
NEGCHAIN(3, 4);
NEGCHAIN19(4, 0);
NEGCHAIN(0, 1);
NEGCHAIN(1, 2);
NEGCHAIN(2, 3);
NEGCHAIN(3, 4);
}
/* Multiply a number by a scalar: output = in * scalar */
static void fscalar_product(felem *output, const felem *in, const felem scalar) {
uint128_t a;
a = ((uint128_t) in[0]) * scalar;
output[0] = a & 0x7ffffffffffff;
a = ((uint128_t) in[1]) * scalar + (a >> 51);
output[1] = a & 0x7ffffffffffff;
a = ((uint128_t) in[2]) * scalar + (a >> 51);
output[2] = a & 0x7ffffffffffff;
a = ((uint128_t) in[3]) * scalar + (a >> 51);
output[3] = a & 0x7ffffffffffff;
a = ((uint128_t) in[4]) * scalar + (a >> 51);
output[4] = a & 0x7ffffffffffff;
output[0] += (a >> 51) * 19;
}
/* Multiply two numbers: output = in2 * in
*
* output must be distinct to both inputs. The inputs are reduced coefficient
* form, the output is not.
*/
static void fmul(felem *output, const felem *in2, const felem *in) {
uint128_t t[9];
t[0] = ((uint128_t) in[0]) * in2[0];
t[1] = ((uint128_t) in[0]) * in2[1] +
((uint128_t) in[1]) * in2[0];
t[2] = ((uint128_t) in[0]) * in2[2] +
((uint128_t) in[2]) * in2[0] +
((uint128_t) in[1]) * in2[1];
t[3] = ((uint128_t) in[0]) * in2[3] +
((uint128_t) in[3]) * in2[0] +
((uint128_t) in[1]) * in2[2] +
((uint128_t) in[2]) * in2[1];
t[4] = ((uint128_t) in[0]) * in2[4] +
((uint128_t) in[4]) * in2[0] +
((uint128_t) in[3]) * in2[1] +
((uint128_t) in[1]) * in2[3] +
((uint128_t) in[2]) * in2[2];
t[5] = ((uint128_t) in[4]) * in2[1] +
((uint128_t) in[1]) * in2[4] +
((uint128_t) in[2]) * in2[3] +
((uint128_t) in[3]) * in2[2];
t[6] = ((uint128_t) in[4]) * in2[2] +
((uint128_t) in[2]) * in2[4] +
((uint128_t) in[3]) * in2[3];
t[7] = ((uint128_t) in[3]) * in2[4] +
((uint128_t) in[4]) * in2[3];
t[8] = ((uint128_t) in[4]) * in2[4];
t[0] += t[5] * 19;
t[1] += t[6] * 19;
t[2] += t[7] * 19;
t[3] += t[8] * 19;
t[1] += t[0] >> 51;
t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51;
t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51;
t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51;
t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51);
t[4] &= 0x7ffffffffffff;
t[1] += t[0] >> 51;
t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51;
t[1] &= 0x7ffffffffffff;
output[0] = t[0];
output[1] = t[1];
output[2] = t[2];
output[3] = t[3];
output[4] = t[4];
}
static void
fsquare(felem *output, const felem *in) {
uint128_t t[9];
t[0] = ((uint128_t) in[0]) * in[0];
t[1] = ((uint128_t) in[0]) * in[1] * 2;
t[2] = ((uint128_t) in[0]) * in[2] * 2 +
((uint128_t) in[1]) * in[1];
t[3] = ((uint128_t) in[0]) * in[3] * 2 +
((uint128_t) in[1]) * in[2] * 2;
t[4] = ((uint128_t) in[0]) * in[4] * 2 +
((uint128_t) in[3]) * in[1] * 2 +
((uint128_t) in[2]) * in[2];
t[5] = ((uint128_t) in[4]) * in[1] * 2 +
((uint128_t) in[2]) * in[3] * 2;
t[6] = ((uint128_t) in[4]) * in[2] * 2 +
((uint128_t) in[3]) * in[3];
t[7] = ((uint128_t) in[3]) * in[4] * 2;
t[8] = ((uint128_t) in[4]) * in[4];
t[0] += t[5] * 19;
t[1] += t[6] * 19;
t[2] += t[7] * 19;
t[3] += t[8] * 19;
t[1] += t[0] >> 51;
t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51;
t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51;
t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51;
t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51);
t[4] &= 0x7ffffffffffff;
t[1] += t[0] >> 51;
t[0] &= 0x7ffffffffffff;
output[0] = t[0];
output[1] = t[1];
output[2] = t[2];
output[3] = t[3];
output[4] = t[4];
}
/* Take a little-endian, 32-byte number and expand it into polynomial form */
static void
fexpand(felem *output, const u8 *in) {
output[0] = *((const uint64_t *)(in)) & 0x7ffffffffffff;
output[1] = (*((const uint64_t *)(in+6)) >> 3) & 0x7ffffffffffff;
output[2] = (*((const uint64_t *)(in+12)) >> 6) & 0x7ffffffffffff;
output[3] = (*((const uint64_t *)(in+19)) >> 1) & 0x7ffffffffffff;
output[4] = (*((const uint64_t *)(in+25)) >> 4) & 0x7ffffffffffff;
}
/* Take a fully reduced polynomial form number and contract it into a
* little-endian, 32-byte array
*/
static void
fcontract(u8 *output, const felem *input) {
uint128_t t[5];
t[0] = input[0];
t[1] = input[1];
t[2] = input[2];
t[3] = input[3];
t[4] = input[4];
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
/* now t is between 0 and 2^255-1, properly carried. */
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
t[0] += 19;
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
t[0] += 0x8000000000000 - 19;
t[1] += 0x8000000000000 - 1;
t[2] += 0x8000000000000 - 1;
t[3] += 0x8000000000000 - 1;
t[4] += 0x8000000000000 - 1;
/* now between 2^255 and 2^256-20, and offset by 2^255. */
t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
t[4] &= 0x7ffffffffffff;
*((uint64_t *)(output)) = t[0] | (t[1] << 51);
*((uint64_t *)(output+8)) = (t[1] >> 13) | (t[2] << 38);
*((uint64_t *)(output+16)) = (t[2] >> 26) | (t[3] << 25);
*((uint64_t *)(output+24)) = (t[3] >> 39) | (t[4] << 12);
}
/* Input: Q, Q', Q-Q'
* Output: 2Q, Q+Q'
*
* x2 z3: long form
* x3 z3: long form
* x z: short form, destroyed
* xprime zprime: short form, destroyed
* qmqp: short form, preserved
*/
static void
fmonty(felem *x2, felem *z2, /* output 2Q */
felem *x3, felem *z3, /* output Q + Q' */
felem *x, felem *z, /* input Q */
felem *xprime, felem *zprime, /* input Q' */
const felem *qmqp /* input Q - Q' */) {
felem origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5],
zzprime[5], zzzprime[5];
memcpy(origx, x, 5 * sizeof(felem));
fsum(x, z);
fdifference_backwards(z, origx); // does x - z
memcpy(origxprime, xprime, sizeof(felem) * 5);
fsum(xprime, zprime);
fdifference_backwards(zprime, origxprime);
fmul(xxprime, xprime, z);
fmul(zzprime, x, zprime);
memcpy(origxprime, xxprime, sizeof(felem) * 5);
fsum(xxprime, zzprime);
fdifference_backwards(zzprime, origxprime);
fsquare(x3, xxprime);
fsquare(zzzprime, zzprime);
fmul(z3, zzzprime, qmqp);
fsquare(xx, x);
fsquare(zz, z);
fmul(x2, xx, zz);
fdifference_backwards(zz, xx); // does zz = xx - zz
fscalar_product(zzz, zz, 121665);
fsum(zzz, xx);
fmul(z2, zz, zzz);
}
// -----------------------------------------------------------------------------
// Maybe swap the contents of two felem arrays (@a and @b), each @len elements
// long. Perform the swap iff @swap is non-zero.
//
// This function performs the swap without leaking any side-channel
// information.
// -----------------------------------------------------------------------------
static void
swap_conditional(felem *a, felem *b, unsigned len, felem iswap) {
unsigned i;
const felem swap = -iswap;
for (i = 0; i < len; ++i) {
const felem x = swap & (a[i] ^ b[i]);
a[i] ^= x;
b[i] ^= x;
}
}
/* Calculates nQ where Q is the x-coordinate of a point on the curve
*
* resultx/resultz: the x coordinate of the resulting curve point (short form)
* n: a little endian, 32-byte number
* q: a point of the curve (short form)
*/
static void
cmult(felem *resultx, felem *resultz, const u8 *n, const felem *q) {
felem a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
felem *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
felem e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
felem *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
unsigned i, j;
memcpy(nqpqx, q, sizeof(felem) * 5);
for (i = 0; i < 32; ++i) {
u8 byte = n[31 - i];
for (j = 0; j < 8; ++j) {
const felem bit = byte >> 7;
swap_conditional(nqx, nqpqx, 5, bit);
swap_conditional(nqz, nqpqz, 5, bit);
fmonty(nqx2, nqz2,
nqpqx2, nqpqz2,
nqx, nqz,
nqpqx, nqpqz,
q);
swap_conditional(nqx2, nqpqx2, 5, bit);
swap_conditional(nqz2, nqpqz2, 5, 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;
}
}
memcpy(resultx, nqx, sizeof(felem) * 5);
memcpy(resultz, nqz, sizeof(felem) * 5);
}
// -----------------------------------------------------------------------------
// Shamelessly copied from djb's code
// -----------------------------------------------------------------------------
static void
crecip(felem *out, const felem *z) {
felem z2[5];
felem z9[5];
felem z11[5];
felem z2_5_0[5];
felem z2_10_0[5];
felem z2_20_0[5];
felem z2_50_0[5];
felem z2_100_0[5];
felem t0[5];
felem t1[5];
int i;
/* 2 */ fsquare(z2,z);
/* 4 */ fsquare(t1,z2);
/* 8 */ fsquare(t0,t1);
/* 9 */ fmul(z9,t0,z);
/* 11 */ fmul(z11,z9,z2);
/* 22 */ fsquare(t0,z11);
/* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
/* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
/* 2^7 - 2^2 */ fsquare(t1,t0);
/* 2^8 - 2^3 */ fsquare(t0,t1);
/* 2^9 - 2^4 */ fsquare(t1,t0);
/* 2^10 - 2^5 */ fsquare(t0,t1);
/* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
/* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
/* 2^12 - 2^2 */ fsquare(t1,t0);
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
/* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
/* 2^22 - 2^2 */ fsquare(t1,t0);
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
/* 2^41 - 2^1 */ fsquare(t1,t0);
/* 2^42 - 2^2 */ fsquare(t0,t1);
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
/* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
/* 2^52 - 2^2 */ fsquare(t1,t0);
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
/* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
/* 2^102 - 2^2 */ fsquare(t0,t1);
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
/* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
/* 2^201 - 2^1 */ fsquare(t0,t1);
/* 2^202 - 2^2 */ fsquare(t1,t0);
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
/* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
/* 2^251 - 2^1 */ fsquare(t1,t0);
/* 2^252 - 2^2 */ fsquare(t0,t1);
/* 2^253 - 2^3 */ fsquare(t1,t0);
/* 2^254 - 2^4 */ fsquare(t0,t1);
/* 2^255 - 2^5 */ fsquare(t1,t0);
/* 2^255 - 21 */ fmul(out,t1,z11);
}
int
crypto_scalarmult(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
felem bp[5], x[5], z[5], zmone[5];
unsigned char 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);
return 0;
}