| /****************************************************************************** |
| * |
| * 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_t 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); |
| } |
| |
| |