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esp-idf/components/bt/host/bluedroid/stack/smp/p_256_multprecision.c
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/******************************************************************************
*
* Copyright (C) 2006-2015 Broadcom Corporation
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at:
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
******************************************************************************/
/******************************************************************************
*
* This file contains simple pairing algorithms
*
******************************************************************************/
#include <string.h>
#include "common/bt_target.h"
#include "p_256_ecc_pp.h"
#include "p_256_multprecision.h"
void multiprecision_init(DWORD *c, uint32_t keyLength)
{
for (uint32_t i = 0; i < keyLength; i++) {
c[i] = 0;
}
}
void multiprecision_copy(DWORD *c, DWORD *a, uint32_t keyLength)
{
for (uint32_t i = 0; i < keyLength; i++) {
c[i] = a[i];
}
}
int multiprecision_compare(DWORD *a, DWORD *b, uint32_t keyLength)
{
for (int i = keyLength - 1; i >= 0; i--) {
if (a[i] > b[i]) {
return 1;
}
if (a[i] < b[i]) {
return -1;
}
}
return 0;
}
int multiprecision_iszero(DWORD *a, uint32_t keyLength)
{
for (uint32_t i = 0; i < keyLength; i++)
if (a[i]) {
return 0;
}
return 1;
}
UINT32 multiprecision_dword_bits(DWORD a)
{
uint32_t i;
for (i = 0; i < DWORD_BITS; i++, a >>= 1)
if (a == 0) {
break;
}
return i;
}
UINT32 multiprecision_most_signdwords(DWORD *a, uint32_t keyLength)
{
int i;
for (i = keyLength - 1; i >= 0; i--)
if (a[i]) {
break;
}
return (i + 1);
}
UINT32 multiprecision_most_signbits(DWORD *a, uint32_t keyLength)
{
int aMostSignDWORDs;
aMostSignDWORDs = multiprecision_most_signdwords(a, keyLength);
if (aMostSignDWORDs == 0) {
return 0;
}
return (((aMostSignDWORDs - 1) << DWORD_BITS_SHIFT) +
multiprecision_dword_bits(a[aMostSignDWORDs - 1]) );
}
DWORD multiprecision_add(DWORD *c, DWORD *a, DWORD *b, uint32_t keyLength)
{
DWORD carrier;
DWORD temp;
carrier = 0;
for (uint32_t i = 0; i < keyLength; i++) {
temp = a[i] + carrier;
carrier = (temp < carrier);
temp += b[i];
carrier |= (temp < b[i]);
c[i] = temp;
}
return carrier;
}
//c=a-b
DWORD multiprecision_sub(DWORD *c, DWORD *a, DWORD *b, uint32_t keyLength)
{
DWORD borrow;
DWORD temp;
borrow = 0;
for (uint32_t i = 0; i < keyLength; i++) {
temp = a[i] - borrow;
borrow = (temp > a[i]);
c[i] = temp - b[i];
borrow |= (c[i] > temp);
}
return borrow;
}
// c = a << 1
void multiprecision_lshift_mod(DWORD *c, DWORD *a, uint32_t keyLength)
{
DWORD carrier;
DWORD *modp;
if (keyLength == KEY_LENGTH_DWORDS_P192) {
modp = curve.p;
} else if (keyLength == KEY_LENGTH_DWORDS_P256) {
modp = curve_p256.p;
} else {
return;
}
carrier = multiprecision_lshift(c, a, keyLength);
if (carrier) {
multiprecision_sub(c, c, modp, keyLength);
} else if (multiprecision_compare(c, modp, keyLength) >= 0) {
multiprecision_sub(c, c, modp, keyLength);
}
}
// c=a>>1
void multiprecision_rshift(DWORD *c, DWORD *a, uint32_t keyLength)
{
int j;
DWORD b = 1;
j = DWORD_BITS - b;
DWORD carrier = 0;
DWORD temp;
for (int i = keyLength - 1; i >= 0; i--) {
temp = a[i]; // in case of c==a
c[i] = (temp >> b) | carrier;
carrier = temp << j;
}
}
// Curve specific optimization when p is a pseudo-Mersenns prime, p=2^(KEY_LENGTH_BITS)-omega
void multiprecision_mersenns_mult_mod(DWORD *c, DWORD *a, DWORD *b, uint32_t keyLength)
{
DWORD cc[2 * KEY_LENGTH_DWORDS_P256];
multiprecision_mult(cc, a, b, keyLength);
if (keyLength == 6) {
multiprecision_fast_mod(c, cc);
} else if (keyLength == 8) {
multiprecision_fast_mod_P256(c, cc);
}
}
// Curve specific optimization when p is a pseudo-Mersenns prime
void multiprecision_mersenns_squa_mod(DWORD *c, DWORD *a, uint32_t keyLength)
{
multiprecision_mersenns_mult_mod(c, a, a, keyLength);
}
// c=(a+b) mod p, b<p, a<p
void multiprecision_add_mod(DWORD *c, DWORD *a, DWORD *b, uint32_t keyLength)
{
DWORD carrier;
DWORD *modp;
if (keyLength == KEY_LENGTH_DWORDS_P192) {
modp = curve.p;
} else if (keyLength == KEY_LENGTH_DWORDS_P256) {
modp = curve_p256.p;
} else {
return;
}
carrier = multiprecision_add(c, a, b, keyLength);
if (carrier) {
multiprecision_sub(c, c, modp, keyLength);
} else if (multiprecision_compare(c, modp, keyLength) >= 0) {
multiprecision_sub(c, c, modp, keyLength);
}
}
// c=(a-b) mod p, a<p, b<p
void multiprecision_sub_mod(DWORD *c, DWORD *a, DWORD *b, uint32_t keyLength)
{
DWORD borrow;
DWORD *modp;
if (keyLength == KEY_LENGTH_DWORDS_P192) {
modp = curve.p;
} else if (keyLength == KEY_LENGTH_DWORDS_P256) {
modp = curve_p256.p;
} else {
return;
}
borrow = multiprecision_sub(c, a, b, keyLength);
if (borrow) {
multiprecision_add(c, c, modp, keyLength);
}
}
// c=a<<b, b<DWORD_BITS, c has a buffer size of NumDWORDs+1
DWORD multiprecision_lshift(DWORD *c, DWORD *a, uint32_t keyLength)
{
int j;
uint32_t b = 1;
j = DWORD_BITS - b;
DWORD carrier = 0;
DWORD temp;
for (uint32_t i = 0; i < keyLength; i++) {
temp = a[i]; // in case c==a
c[i] = (temp << b) | carrier;
carrier = temp >> j;
}
return carrier;
}
// c=a*b; c must have a buffer of 2*Key_LENGTH_DWORDS, c != a != b
void multiprecision_mult(DWORD *c, DWORD *a, DWORD *b, uint32_t keyLength)
{
DWORD W;
DWORD U;
DWORD V;
U = V = W = 0;
multiprecision_init(c, keyLength);
//assume little endian right now
for (uint32_t i = 0; i < keyLength; i++) {
U = 0;
for (uint32_t j = 0; j < keyLength; j++) {
uint64_t result;
result = ((UINT64)a[i]) * ((uint64_t) b[j]);
W = result >> 32;
V = a[i] * b[j];
V = V + U;
U = (V < U);
U += W;
V = V + c[i + j];
U += (V < c[i + j]);
c[i + j] = V;
}
c[i + keyLength] = U;
}
}
void multiprecision_fast_mod(DWORD *c, DWORD *a)
{
DWORD U;
DWORD V;
DWORD *modp = curve.p;
c[0] = a[0] + a[6];
U = c[0] < a[0];
c[0] += a[10];
U += c[0] < a[10];
c[1] = a[1] + U;
U = c[1] < a[1];
c[1] += a[7];
U += c[1] < a[7];
c[1] += a[11];
U += c[1] < a[11];
c[2] = a[2] + U;
U = c[2] < a[2];
c[2] += a[6];
U += c[2] < a[6];
c[2] += a[8];
U += c[2] < a[8];
c[2] += a[10];
U += c[2] < a[10];
c[3] = a[3] + U;
U = c[3] < a[3];
c[3] += a[7];
U += c[3] < a[7];
c[3] += a[9];
U += c[3] < a[9];
c[3] += a[11];
U += c[3] < a[11];
c[4] = a[4] + U;
U = c[4] < a[4];
c[4] += a[8];
U += c[4] < a[8];
c[4] += a[10];
U += c[4] < a[10];
c[5] = a[5] + U;
U = c[5] < a[5];
c[5] += a[9];
U += c[5] < a[9];
c[5] += a[11];
U += c[5] < a[11];
c[0] += U;
V = c[0] < U;
c[1] += V;
V = c[1] < V;
c[2] += V;
V = c[2] < V;
c[2] += U;
V = c[2] < U;
c[3] += V;
V = c[3] < V;
c[4] += V;
V = c[4] < V;
c[5] += V;
V = c[5] < V;
if (V) {
multiprecision_sub(c, c, modp, KEY_LENGTH_DWORDS_P192);
} else if (multiprecision_compare(c, modp, KEY_LENGTH_DWORDS_P192) >= 0) {
multiprecision_sub(c, c, modp, KEY_LENGTH_DWORDS_P192);
}
}
void multiprecision_fast_mod_P256(DWORD *c, DWORD *a)
{
DWORD A;
DWORD B;
DWORD C;
DWORD D;
DWORD E;
DWORD F;
DWORD G;
uint8_t UA;
uint8_t UB;
uint8_t UC;
uint8_t UD;
uint8_t UE;
uint8_t UF;
uint8_t UG;
DWORD U;
DWORD *modp = curve_p256.p;
// C = a[13] + a[14] + a[15];
C = a[13];
C += a[14];
UC = (C < a[14]);
C += a[15];
UC += (C < a[15]);
// E = a[8] + a[9];
E = a[8];
E += a[9];
UE = (E < a[9]);
// F = a[9] + a[10];
F = a[9];
F += a[10];
UF = (F < a[10]);
// G = a[10] + a[11]
G = a[10];
G += a[11];
UG = (G < a[11]);
// B = a[12] + a[13] + a[14] + a[15] == C + a[12]
B = C;
UB = UC;
B += a[12];
UB += (B < a[12]);
// A = a[11] + a[12] + a[13] + a[14] == B + a[11] - a[15]
A = B;
UA = UB;
A += a[11];
UA += (A < a[11]);
UA -= (A < a[15]);
A -= a[15];
// D = a[10] + a[11] + a[12] + a[13] == A + a[10] - a[14]
D = A;
UD = UA;
D += a[10];
UD += (D < a[10]);
UD -= (D < a[14]);
D -= a[14];
c[0] = a[0];
c[0] += E;
U = (c[0] < E);
U += UE;
U -= (c[0] < A);
U -= UA;
c[0] -= A;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[1] < UU);
c[1] = a[1] - UU;
} else {
c[1] = a[1] + U;
U = (c[1] < a[1]);
}
c[1] += F;
U += (c[1] < F);
U += UF;
U -= (c[1] < B);
U -= UB;
c[1] -= B;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[2] < UU);
c[2] = a[2] - UU;
} else {
c[2] = a[2] + U;
U = (c[2] < a[2]);
}
c[2] += G;
U += (c[2] < G);
U += UG;
U -= (c[2] < C);
U -= UC;
c[2] -= C;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[3] < UU);
c[3] = a[3] - UU;
} else {
c[3] = a[3] + U;
U = (c[3] < a[3]);
}
c[3] += A;
U += (c[3] < A);
U += UA;
c[3] += a[11];
U += (c[3] < a[11]);
c[3] += a[12];
U += (c[3] < a[12]);
U -= (c[3] < a[14]);
c[3] -= a[14];
U -= (c[3] < a[15]);
c[3] -= a[15];
U -= (c[3] < E);
U -= UE;
c[3] -= E;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[4] < UU);
c[4] = a[4] - UU;
} else {
c[4] = a[4] + U;
U = (c[4] < a[4]);
}
c[4] += B;
U += (c[4] < B);
U += UB;
U -= (c[4] < a[15]);
c[4] -= a[15];
c[4] += a[12];
U += (c[4] < a[12]);
c[4] += a[13];
U += (c[4] < a[13]);
U -= (c[4] < F);
U -= UF;
c[4] -= F;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[5] < UU);
c[5] = a[5] - UU;
} else {
c[5] = a[5] + U;
U = (c[5] < a[5]);
}
c[5] += C;
U += (c[5] < C);
U += UC;
c[5] += a[13];
U += (c[5] < a[13]);
c[5] += a[14];
U += (c[5] < a[14]);
U -= (c[5] < G);
U -= UG;
c[5] -= G;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[6] < UU);
c[6] = a[6] - UU;
} else {
c[6] = a[6] + U;
U = (c[6] < a[6]);
}
c[6] += C;
U += (c[6] < C);
U += UC;
c[6] += a[14];
U += (c[6] < a[14]);
c[6] += a[14];
U += (c[6] < a[14]);
c[6] += a[15];
U += (c[6] < a[15]);
U -= (c[6] < E);
U -= UE;
c[6] -= E;
if (U & 0x80000000) {
DWORD UU;
UU = 0 - U;
U = (a[7] < UU);
c[7] = a[7] - UU;
} else {
c[7] = a[7] + U;
U = (c[7] < a[7]);
}
c[7] += a[15];
U += (c[7] < a[15]);
c[7] += a[15];
U += (c[7] < a[15]);
c[7] += a[15];
U += (c[7] < a[15]);
c[7] += a[8];
U += (c[7] < a[8]);
U -= (c[7] < D);
U -= UD;
c[7] -= D;
if (U & 0x80000000) {
while (U) {
multiprecision_add(c, c, modp, KEY_LENGTH_DWORDS_P256);
U++;
}
} else if (U) {
while (U) {
multiprecision_sub(c, c, modp, KEY_LENGTH_DWORDS_P256);
U--;
}
}
if (multiprecision_compare(c, modp, KEY_LENGTH_DWORDS_P256) >= 0) {
multiprecision_sub(c, c, modp, KEY_LENGTH_DWORDS_P256);
}
}
void multiprecision_inv_mod(DWORD *aminus, DWORD *u, uint32_t keyLength)
{
DWORD v[KEY_LENGTH_DWORDS_P256];
DWORD A[KEY_LENGTH_DWORDS_P256 + 1];
DWORD C[KEY_LENGTH_DWORDS_P256 + 1];
DWORD *modp;
if (keyLength == KEY_LENGTH_DWORDS_P256) {
modp = curve_p256.p;
} else {
modp = curve.p;
}
multiprecision_copy(v, modp, keyLength);
multiprecision_init(A, keyLength);
multiprecision_init(C, keyLength);
A[0] = 1;
while (!multiprecision_iszero(u, keyLength)) {
while (!(u[0] & 0x01)) { // u is even
multiprecision_rshift(u, u, keyLength);
if (!(A[0] & 0x01)) { // A is even
multiprecision_rshift(A, A, keyLength);
} else {
A[keyLength] = multiprecision_add(A, A, modp, keyLength); // A =A+p
multiprecision_rshift(A, A, keyLength);
A[keyLength - 1] |= (A[keyLength] << 31);
}
}
while (!(v[0] & 0x01)) { // v is even
multiprecision_rshift(v, v, keyLength);
if (!(C[0] & 0x01)) { // C is even
multiprecision_rshift(C, C, keyLength);
} else {
C[keyLength] = multiprecision_add(C, C, modp, keyLength); // C =C+p
multiprecision_rshift(C, C, keyLength);
C[keyLength - 1] |= (C[keyLength] << 31);
}
}
if (multiprecision_compare(u, v, keyLength) >= 0) {
multiprecision_sub(u, u, v, keyLength);
multiprecision_sub_mod(A, A, C, keyLength);
} else {
multiprecision_sub(v, v, u, keyLength);
multiprecision_sub_mod(C, C, A, keyLength);
}
}
if (multiprecision_compare(C, modp, keyLength) >= 0) {
multiprecision_sub(aminus, C, modp, keyLength);
} else {
multiprecision_copy(aminus, C, keyLength);
}
}
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