7fb0844174
The declaration is useless and triggers a warning with clang 3.5 (in code that's built with -Werror) Change-Id: I8fc42178df264509dcce6e1f1ba318bf849307e3 Signed-off-by: Bernhard Rosenkraenzer <Bernhard.Rosenkranzer@linaro.org>
373 lines
11 KiB
C
373 lines
11 KiB
C
/*
|
|
* Copyright 2013 The Android Open Source Project
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions are met:
|
|
* * Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* * Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* * Neither the name of Google Inc. nor the names of its contributors may
|
|
* be used to endorse or promote products derived from this software
|
|
* without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY Google Inc. ``AS IS'' AND ANY EXPRESS OR
|
|
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
|
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
|
|
* EVENT SHALL Google Inc. BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
|
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
|
|
* OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
|
|
* WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
|
|
* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
|
|
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*/
|
|
|
|
// This is an implementation of the P256 elliptic curve group. It's written to
|
|
// be portable 32-bit, although it's still constant-time.
|
|
//
|
|
// WARNING: Implementing these functions in a constant-time manner is far from
|
|
// obvious. Be careful when touching this code.
|
|
//
|
|
// See http://www.imperialviolet.org/2010/12/04/ecc.html ([1]) for background.
|
|
|
|
#include <assert.h>
|
|
#include <stdint.h>
|
|
#include <string.h>
|
|
#include <stdio.h>
|
|
|
|
#include "mincrypt/p256.h"
|
|
|
|
const p256_int SECP256r1_n = // curve order
|
|
{{0xfc632551, 0xf3b9cac2, 0xa7179e84, 0xbce6faad, -1, -1, 0, -1}};
|
|
|
|
const p256_int SECP256r1_p = // curve field size
|
|
{{-1, -1, -1, 0, 0, 0, 1, -1 }};
|
|
|
|
const p256_int SECP256r1_b = // curve b
|
|
{{0x27d2604b, 0x3bce3c3e, 0xcc53b0f6, 0x651d06b0,
|
|
0x769886bc, 0xb3ebbd55, 0xaa3a93e7, 0x5ac635d8}};
|
|
|
|
void p256_init(p256_int* a) {
|
|
memset(a, 0, sizeof(*a));
|
|
}
|
|
|
|
void p256_clear(p256_int* a) { p256_init(a); }
|
|
|
|
int p256_get_bit(const p256_int* scalar, int bit) {
|
|
return (P256_DIGIT(scalar, bit / P256_BITSPERDIGIT)
|
|
>> (bit & (P256_BITSPERDIGIT - 1))) & 1;
|
|
}
|
|
|
|
int p256_is_zero(const p256_int* a) {
|
|
int i, result = 0;
|
|
for (i = 0; i < P256_NDIGITS; ++i) result |= P256_DIGIT(a, i);
|
|
return !result;
|
|
}
|
|
|
|
// top, c[] += a[] * b
|
|
// Returns new top
|
|
static p256_digit mulAdd(const p256_int* a,
|
|
p256_digit b,
|
|
p256_digit top,
|
|
p256_digit* c) {
|
|
int i;
|
|
p256_ddigit carry = 0;
|
|
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
carry += *c;
|
|
carry += (p256_ddigit)P256_DIGIT(a, i) * b;
|
|
*c++ = (p256_digit)carry;
|
|
carry >>= P256_BITSPERDIGIT;
|
|
}
|
|
return top + (p256_digit)carry;
|
|
}
|
|
|
|
// top, c[] -= top_a, a[]
|
|
static p256_digit subTop(p256_digit top_a,
|
|
const p256_digit* a,
|
|
p256_digit top_c,
|
|
p256_digit* c) {
|
|
int i;
|
|
p256_sddigit borrow = 0;
|
|
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
borrow += *c;
|
|
borrow -= *a++;
|
|
*c++ = (p256_digit)borrow;
|
|
borrow >>= P256_BITSPERDIGIT;
|
|
}
|
|
borrow += top_c;
|
|
borrow -= top_a;
|
|
top_c = (p256_digit)borrow;
|
|
assert((borrow >> P256_BITSPERDIGIT) == 0);
|
|
return top_c;
|
|
}
|
|
|
|
// top, c[] -= MOD[] & mask (0 or -1)
|
|
// returns new top.
|
|
static p256_digit subM(const p256_int* MOD,
|
|
p256_digit top,
|
|
p256_digit* c,
|
|
p256_digit mask) {
|
|
int i;
|
|
p256_sddigit borrow = 0;
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
borrow += *c;
|
|
borrow -= P256_DIGIT(MOD, i) & mask;
|
|
*c++ = (p256_digit)borrow;
|
|
borrow >>= P256_BITSPERDIGIT;
|
|
}
|
|
return top + (p256_digit)borrow;
|
|
}
|
|
|
|
// top, c[] += MOD[] & mask (0 or -1)
|
|
// returns new top.
|
|
static p256_digit addM(const p256_int* MOD,
|
|
p256_digit top,
|
|
p256_digit* c,
|
|
p256_digit mask) {
|
|
int i;
|
|
p256_ddigit carry = 0;
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
carry += *c;
|
|
carry += P256_DIGIT(MOD, i) & mask;
|
|
*c++ = (p256_digit)carry;
|
|
carry >>= P256_BITSPERDIGIT;
|
|
}
|
|
return top + (p256_digit)carry;
|
|
}
|
|
|
|
// c = a * b mod MOD. c can be a and/or b.
|
|
void p256_modmul(const p256_int* MOD,
|
|
const p256_int* a,
|
|
const p256_digit top_b,
|
|
const p256_int* b,
|
|
p256_int* c) {
|
|
p256_digit tmp[P256_NDIGITS * 2 + 1] = { 0 };
|
|
p256_digit top = 0;
|
|
int i;
|
|
|
|
// Multiply/add into tmp.
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
if (i) tmp[i + P256_NDIGITS - 1] = top;
|
|
top = mulAdd(a, P256_DIGIT(b, i), 0, tmp + i);
|
|
}
|
|
|
|
// Multiply/add top digit
|
|
tmp[i + P256_NDIGITS - 1] = top;
|
|
top = mulAdd(a, top_b, 0, tmp + i);
|
|
|
|
// Reduce tmp, digit by digit.
|
|
for (; i >= 0; --i) {
|
|
p256_digit reducer[P256_NDIGITS] = { 0 };
|
|
p256_digit top_reducer;
|
|
|
|
// top can be any value at this point.
|
|
// Guestimate reducer as top * MOD, since msw of MOD is -1.
|
|
top_reducer = mulAdd(MOD, top, 0, reducer);
|
|
|
|
// Subtract reducer from top | tmp.
|
|
top = subTop(top_reducer, reducer, top, tmp + i);
|
|
|
|
// top is now either 0 or 1. Make it 0, fixed-timing.
|
|
assert(top <= 1);
|
|
|
|
top = subM(MOD, top, tmp + i, ~(top - 1));
|
|
|
|
assert(top == 0);
|
|
|
|
// We have now reduced the top digit off tmp. Fetch new top digit.
|
|
top = tmp[i + P256_NDIGITS - 1];
|
|
}
|
|
|
|
// tmp might still be larger than MOD, yet same bit length.
|
|
// Make sure it is less, fixed-timing.
|
|
addM(MOD, 0, tmp, subM(MOD, 0, tmp, -1));
|
|
|
|
memcpy(c, tmp, P256_NBYTES);
|
|
}
|
|
int p256_is_odd(const p256_int* a) { return P256_DIGIT(a, 0) & 1; }
|
|
int p256_is_even(const p256_int* a) { return !(P256_DIGIT(a, 0) & 1); }
|
|
|
|
p256_digit p256_shl(const p256_int* a, int n, p256_int* b) {
|
|
int i;
|
|
p256_digit top = P256_DIGIT(a, P256_NDIGITS - 1);
|
|
|
|
n %= P256_BITSPERDIGIT;
|
|
for (i = P256_NDIGITS - 1; i > 0; --i) {
|
|
p256_digit accu = (P256_DIGIT(a, i) << n);
|
|
accu |= (P256_DIGIT(a, i - 1) >> (P256_BITSPERDIGIT - n));
|
|
P256_DIGIT(b, i) = accu;
|
|
}
|
|
P256_DIGIT(b, i) = (P256_DIGIT(a, i) << n);
|
|
|
|
top = (p256_digit)((((p256_ddigit)top) << n) >> P256_BITSPERDIGIT);
|
|
|
|
return top;
|
|
}
|
|
|
|
void p256_shr(const p256_int* a, int n, p256_int* b) {
|
|
int i;
|
|
|
|
n %= P256_BITSPERDIGIT;
|
|
for (i = 0; i < P256_NDIGITS - 1; ++i) {
|
|
p256_digit accu = (P256_DIGIT(a, i) >> n);
|
|
accu |= (P256_DIGIT(a, i + 1) << (P256_BITSPERDIGIT - n));
|
|
P256_DIGIT(b, i) = accu;
|
|
}
|
|
P256_DIGIT(b, i) = (P256_DIGIT(a, i) >> n);
|
|
}
|
|
|
|
static void p256_shr1(const p256_int* a, int highbit, p256_int* b) {
|
|
int i;
|
|
|
|
for (i = 0; i < P256_NDIGITS - 1; ++i) {
|
|
p256_digit accu = (P256_DIGIT(a, i) >> 1);
|
|
accu |= (P256_DIGIT(a, i + 1) << (P256_BITSPERDIGIT - 1));
|
|
P256_DIGIT(b, i) = accu;
|
|
}
|
|
P256_DIGIT(b, i) = (P256_DIGIT(a, i) >> 1) |
|
|
(highbit << (P256_BITSPERDIGIT - 1));
|
|
}
|
|
|
|
// Return -1, 0, 1 for a < b, a == b or a > b respectively.
|
|
int p256_cmp(const p256_int* a, const p256_int* b) {
|
|
int i;
|
|
p256_sddigit borrow = 0;
|
|
p256_digit notzero = 0;
|
|
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
borrow += (p256_sddigit)P256_DIGIT(a, i) - P256_DIGIT(b, i);
|
|
// Track whether any result digit is ever not zero.
|
|
// Relies on !!(non-zero) evaluating to 1, e.g., !!(-1) evaluating to 1.
|
|
notzero |= !!((p256_digit)borrow);
|
|
borrow >>= P256_BITSPERDIGIT;
|
|
}
|
|
return (int)borrow | notzero;
|
|
}
|
|
|
|
// c = a - b. Returns borrow: 0 or -1.
|
|
int p256_sub(const p256_int* a, const p256_int* b, p256_int* c) {
|
|
int i;
|
|
p256_sddigit borrow = 0;
|
|
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
borrow += (p256_sddigit)P256_DIGIT(a, i) - P256_DIGIT(b, i);
|
|
if (c) P256_DIGIT(c, i) = (p256_digit)borrow;
|
|
borrow >>= P256_BITSPERDIGIT;
|
|
}
|
|
return (int)borrow;
|
|
}
|
|
|
|
// c = a + b. Returns carry: 0 or 1.
|
|
int p256_add(const p256_int* a, const p256_int* b, p256_int* c) {
|
|
int i;
|
|
p256_ddigit carry = 0;
|
|
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
carry += (p256_ddigit)P256_DIGIT(a, i) + P256_DIGIT(b, i);
|
|
if (c) P256_DIGIT(c, i) = (p256_digit)carry;
|
|
carry >>= P256_BITSPERDIGIT;
|
|
}
|
|
return (int)carry;
|
|
}
|
|
|
|
// b = a + d. Returns carry, 0 or 1.
|
|
int p256_add_d(const p256_int* a, p256_digit d, p256_int* b) {
|
|
int i;
|
|
p256_ddigit carry = d;
|
|
|
|
for (i = 0; i < P256_NDIGITS; ++i) {
|
|
carry += (p256_ddigit)P256_DIGIT(a, i);
|
|
if (b) P256_DIGIT(b, i) = (p256_digit)carry;
|
|
carry >>= P256_BITSPERDIGIT;
|
|
}
|
|
return (int)carry;
|
|
}
|
|
|
|
// b = 1/a mod MOD, binary euclid.
|
|
void p256_modinv_vartime(const p256_int* MOD,
|
|
const p256_int* a,
|
|
p256_int* b) {
|
|
p256_int R = P256_ZERO;
|
|
p256_int S = P256_ONE;
|
|
p256_int U = *MOD;
|
|
p256_int V = *a;
|
|
|
|
for (;;) {
|
|
if (p256_is_even(&U)) {
|
|
p256_shr1(&U, 0, &U);
|
|
if (p256_is_even(&R)) {
|
|
p256_shr1(&R, 0, &R);
|
|
} else {
|
|
// R = (R+MOD)/2
|
|
p256_shr1(&R, p256_add(&R, MOD, &R), &R);
|
|
}
|
|
} else if (p256_is_even(&V)) {
|
|
p256_shr1(&V, 0, &V);
|
|
if (p256_is_even(&S)) {
|
|
p256_shr1(&S, 0, &S);
|
|
} else {
|
|
// S = (S+MOD)/2
|
|
p256_shr1(&S, p256_add(&S, MOD, &S) , &S);
|
|
}
|
|
} else { // U,V both odd.
|
|
if (!p256_sub(&V, &U, NULL)) {
|
|
p256_sub(&V, &U, &V);
|
|
if (p256_sub(&S, &R, &S)) p256_add(&S, MOD, &S);
|
|
if (p256_is_zero(&V)) break; // done.
|
|
} else {
|
|
p256_sub(&U, &V, &U);
|
|
if (p256_sub(&R, &S, &R)) p256_add(&R, MOD, &R);
|
|
}
|
|
}
|
|
}
|
|
|
|
p256_mod(MOD, &R, b);
|
|
}
|
|
|
|
void p256_mod(const p256_int* MOD,
|
|
const p256_int* in,
|
|
p256_int* out) {
|
|
if (out != in) *out = *in;
|
|
addM(MOD, 0, P256_DIGITS(out), subM(MOD, 0, P256_DIGITS(out), -1));
|
|
}
|
|
|
|
// Verify y^2 == x^3 - 3x + b mod p
|
|
// and 0 < x < p and 0 < y < p
|
|
int p256_is_valid_point(const p256_int* x, const p256_int* y) {
|
|
p256_int y2, x3;
|
|
|
|
if (p256_cmp(&SECP256r1_p, x) <= 0 ||
|
|
p256_cmp(&SECP256r1_p, y) <= 0 ||
|
|
p256_is_zero(x) ||
|
|
p256_is_zero(y)) return 0;
|
|
|
|
p256_modmul(&SECP256r1_p, y, 0, y, &y2); // y^2
|
|
|
|
p256_modmul(&SECP256r1_p, x, 0, x, &x3); // x^2
|
|
p256_modmul(&SECP256r1_p, x, 0, &x3, &x3); // x^3
|
|
if (p256_sub(&x3, x, &x3)) p256_add(&x3, &SECP256r1_p, &x3); // x^3 - x
|
|
if (p256_sub(&x3, x, &x3)) p256_add(&x3, &SECP256r1_p, &x3); // x^3 - 2x
|
|
if (p256_sub(&x3, x, &x3)) p256_add(&x3, &SECP256r1_p, &x3); // x^3 - 3x
|
|
if (p256_add(&x3, &SECP256r1_b, &x3)) // x^3 - 3x + b
|
|
p256_sub(&x3, &SECP256r1_p, &x3);
|
|
|
|
return p256_cmp(&y2, &x3) == 0;
|
|
}
|
|
|
|
void p256_from_bin(const uint8_t src[P256_NBYTES], p256_int* dst) {
|
|
int i;
|
|
const uint8_t* p = &src[0];
|
|
|
|
for (i = P256_NDIGITS - 1; i >= 0; --i) {
|
|
P256_DIGIT(dst, i) =
|
|
(p[0] << 24) |
|
|
(p[1] << 16) |
|
|
(p[2] << 8) |
|
|
p[3];
|
|
p += 4;
|
|
}
|
|
}
|