/******************************************************************************
*
* 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);
}