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