esp-idf/components/bt/bluedroid/stack/smp/p_256_ecc_pp.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 using Elliptic Curve Cryptography for private public key
*
******************************************************************************/
//#include <stdio.h>
//#include <stdlib.h>
#include <string.h>
#include "p_256_ecc_pp.h"
#include "p_256_multprecision.h"
elliptic_curve_t curve;
elliptic_curve_t curve_p256;
static void p_256_init_point(Point *q)
{
memset(q, 0, sizeof(Point));
}
static void p_256_copy_point(Point *q, Point *p)
{
memcpy(q, p, sizeof(Point));
}
// q=2q
static void ECC_Double(Point *q, Point *p, uint32_t keyLength)
{
DWORD t1[KEY_LENGTH_DWORDS_P256];
DWORD t2[KEY_LENGTH_DWORDS_P256];
DWORD t3[KEY_LENGTH_DWORDS_P256];
DWORD *x1;
DWORD *x3;
DWORD *y1;
DWORD *y3;
DWORD *z1;
DWORD *z3;
if (multiprecision_iszero(p->z, keyLength)) {
multiprecision_init(q->z, keyLength);
return; // return infinity
}
x1 = p->x; y1 = p->y; z1 = p->z;
x3 = q->x; y3 = q->y; z3 = q->z;
multiprecision_mersenns_squa_mod(t1, z1, keyLength); // t1=z1^2
multiprecision_sub_mod(t2, x1, t1, keyLength); // t2=x1-t1
multiprecision_add_mod(t1, x1, t1, keyLength); // t1=x1+t1
multiprecision_mersenns_mult_mod(t2, t1, t2, keyLength); // t2=t2*t1
multiprecision_lshift_mod(t3, t2, keyLength);
multiprecision_add_mod(t2, t3, t2, keyLength); // t2=3t2
multiprecision_mersenns_mult_mod(z3, y1, z1, keyLength); // z3=y1*z1
multiprecision_lshift_mod(z3, z3, keyLength);
multiprecision_mersenns_squa_mod(y3, y1, keyLength); // y3=y1^2
multiprecision_lshift_mod(y3, y3, keyLength);
multiprecision_mersenns_mult_mod(t3, y3, x1, keyLength); // t3=y3*x1=x1*y1^2
multiprecision_lshift_mod(t3, t3, keyLength);
multiprecision_mersenns_squa_mod(y3, y3, keyLength); // y3=y3^2=y1^4
multiprecision_lshift_mod(y3, y3, keyLength);
multiprecision_mersenns_squa_mod(x3, t2, keyLength); // x3=t2^2
multiprecision_lshift_mod(t1, t3, keyLength); // t1=2t3
multiprecision_sub_mod(x3, x3, t1, keyLength); // x3=x3-t1
multiprecision_sub_mod(t1, t3, x3, keyLength); // t1=t3-x3
multiprecision_mersenns_mult_mod(t1, t1, t2, keyLength); // t1=t1*t2
multiprecision_sub_mod(y3, t1, y3, keyLength); // y3=t1-y3
}
// q=q+p, zp must be 1
static void ECC_Add(Point *r, Point *p, Point *q, uint32_t keyLength)
{
DWORD t1[KEY_LENGTH_DWORDS_P256];
DWORD t2[KEY_LENGTH_DWORDS_P256];
DWORD *x1;
DWORD *x2;
DWORD *x3;
DWORD *y1;
DWORD *y2;
DWORD *y3;
DWORD *z1;
DWORD *z2;
DWORD *z3;
x1 = p->x; y1 = p->y; z1 = p->z;
x2 = q->x; y2 = q->y; z2 = q->z;
x3 = r->x; y3 = r->y; z3 = r->z;
// if Q=infinity, return p
if (multiprecision_iszero(z2, keyLength)) {
p_256_copy_point(r, p);
return;
}
// if P=infinity, return q
if (multiprecision_iszero(z1, keyLength)) {
p_256_copy_point(r, q);
return;
}
multiprecision_mersenns_squa_mod(t1, z1, keyLength); // t1=z1^2
multiprecision_mersenns_mult_mod(t2, z1, t1, keyLength); // t2=t1*z1
multiprecision_mersenns_mult_mod(t1, x2, t1, keyLength); // t1=t1*x2
multiprecision_mersenns_mult_mod(t2, y2, t2, keyLength); // t2=t2*y2
multiprecision_sub_mod(t1, t1, x1, keyLength); // t1=t1-x1
multiprecision_sub_mod(t2, t2, y1, keyLength); // t2=t2-y1
if (multiprecision_iszero(t1, keyLength)) {
if (multiprecision_iszero(t2, keyLength)) {
ECC_Double(r, q, keyLength) ;
return;
} else {
multiprecision_init(z3, keyLength);
return; // return infinity
}
}
multiprecision_mersenns_mult_mod(z3, z1, t1, keyLength); // z3=z1*t1
multiprecision_mersenns_squa_mod(y3, t1, keyLength); // t3=t1^2
multiprecision_mersenns_mult_mod(z1, y3, t1, keyLength); // t4=t3*t1
multiprecision_mersenns_mult_mod(y3, y3, x1, keyLength); // t3=t3*x1
multiprecision_lshift_mod(t1, y3, keyLength); // t1=2*t3
multiprecision_mersenns_squa_mod(x3, t2, keyLength); // x3=t2^2
multiprecision_sub_mod(x3, x3, t1, keyLength); // x3=x3-t1
multiprecision_sub_mod(x3, x3, z1, keyLength); // x3=x3-t4
multiprecision_sub_mod(y3, y3, x3, keyLength); // t3=t3-x3
multiprecision_mersenns_mult_mod(y3, y3, t2, keyLength); // t3=t3*t2
multiprecision_mersenns_mult_mod(z1, z1, y1, keyLength); // t4=t4*t1
multiprecision_sub_mod(y3, y3, z1, keyLength);
}
// Computing the Non-Adjacent Form of a positive integer
static void ECC_NAF(uint8_t *naf, uint32_t *NumNAF, DWORD *k, uint32_t keyLength)
{
uint32_t sign;
int i = 0;
int j;
uint32_t var;
while ((var = multiprecision_most_signbits(k, keyLength)) >= 1) {
if (k[0] & 0x01) { // k is odd
sign = (k[0] & 0x03); // 1 or 3
// k = k-naf[i]
if (sign == 1) {
k[0] = k[0] & 0xFFFFFFFE;
} else {
k[0] = k[0] + 1;
if (k[0] == 0) { //overflow
j = 1;
do {
k[j]++;
} while (k[j++] == 0); //overflow
}
}
} else {
sign = 0;
}
multiprecision_rshift(k, k, keyLength);
naf[i / 4] |= (sign) << ((i % 4) * 2);
i++;
}
*NumNAF = i;
}
// Binary Non-Adjacent Form for point multiplication
void ECC_PointMult_Bin_NAF(Point *q, Point *p, DWORD *n, uint32_t keyLength)
{
uint32_t sign;
UINT8 naf[256 / 4 + 1];
uint32_t NumNaf;
Point minus_p;
Point r;
DWORD *modp;
if (keyLength == KEY_LENGTH_DWORDS_P256) {
modp = curve_p256.p;
} else {
modp = curve.p;
}
p_256_init_point(&r);
multiprecision_init(p->z, keyLength);
p->z[0] = 1;
// initialization
p_256_init_point(q);
// -p
multiprecision_copy(minus_p.x, p->x, keyLength);
multiprecision_sub(minus_p.y, modp, p->y, keyLength);
multiprecision_init(minus_p.z, keyLength);
minus_p.z[0] = 1;
// NAF
memset(naf, 0, sizeof(naf));
ECC_NAF(naf, &NumNaf, n, keyLength);
for (int i = NumNaf - 1; i >= 0; i--) {
p_256_copy_point(&r, q);
ECC_Double(q, &r, keyLength);
sign = (naf[i / 4] >> ((i % 4) * 2)) & 0x03;
if (sign == 1) {
p_256_copy_point(&r, q);
ECC_Add(q, &r, p, keyLength);
} else if (sign == 3) {
p_256_copy_point(&r, q);
ECC_Add(q, &r, &minus_p, keyLength);
}
}
multiprecision_inv_mod(minus_p.x, q->z, keyLength);
multiprecision_mersenns_squa_mod(q->z, minus_p.x, keyLength);
multiprecision_mersenns_mult_mod(q->x, q->x, q->z, keyLength);
multiprecision_mersenns_mult_mod(q->z, q->z, minus_p.x, keyLength);
multiprecision_mersenns_mult_mod(q->y, q->y, q->z, keyLength);
}
bool ECC_CheckPointIsInElliCur_P256(Point *p)
{
/* y^2 % q */
DWORD y_y_q[KEY_LENGTH_DWORDS_P256] = {0x0};
/* x^2 % q */
DWORD x_x_q[KEY_LENGTH_DWORDS_P256] = {0x0};
/* x % q */
DWORD x_q[KEY_LENGTH_DWORDS_P256] = {0x0};
/* x^2, To prevent overflow, the length of the x square here needs to
be expanded to two times the original one. */
DWORD x_x[2*KEY_LENGTH_DWORDS_P256] = {0x0};
/* y_y_q =(p->y)^2(mod q) */
multiprecision_mersenns_squa_mod(y_y_q, p->y, KEY_LENGTH_DWORDS_P256);
/* Calculate the value of p->x square, x_x = (p->x)^2 */
multiprecision_mult(x_x, p->x, p->x, KEY_LENGTH_DWORDS_P256);
/* The function of the elliptic curve is y^2 = x^3 - 3x + b (mod q) ==>
y^2 = (x^2 - 3)*x + b (mod q),
so we calculate the x^2 - 3 value here */
x_x[0] -= 3;
/* Using math relations. (a*b) % q = ((a%q)*(b%q)) % q ==>
(x^2 - 3)*x = (((x^2 - 3) % q) * x % q) % q */
multiprecision_fast_mod_P256(x_x_q, x_x);
/* x_x = x_x_q * x_q */
multiprecision_mult(x_x, x_x_q, p->x, KEY_LENGTH_DWORDS_P256);
/* x_q = x_x % q */
multiprecision_fast_mod_P256(x_q, x_x);
/* Save the result in x_x_q */
multiprecision_add_mod(x_x_q, x_q, curve_p256.b, KEY_LENGTH_DWORDS_P256);
/* compare the y_y_q and x_x_q, see if they are on a given elliptic curve. */
if (multiprecision_compare(y_y_q, x_x_q, KEY_LENGTH_DWORDS_P256)) {
return false;
} else {
return true;
}
}