/****************************************************************************** * * 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 "p_256_ecc_pp.h" #include <stdio.h> #include <stdlib.h> #include <string.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) { uint32_t t1[KEY_LENGTH_DWORDS_P256]; uint32_t t2[KEY_LENGTH_DWORDS_P256]; uint32_t t3[KEY_LENGTH_DWORDS_P256]; uint32_t* x1; uint32_t* x3; uint32_t* y1; uint32_t* y3; uint32_t* z1; uint32_t* 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) { uint32_t t1[KEY_LENGTH_DWORDS_P256]; uint32_t t2[KEY_LENGTH_DWORDS_P256]; uint32_t* x1; uint32_t* x2; uint32_t* x3; uint32_t* y1; uint32_t* y2; uint32_t* y3; uint32_t* z1; uint32_t* z2; uint32_t* 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, uint32_t* 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, uint32_t* n, uint32_t keyLength) { uint32_t sign; uint8_t naf[256 / 4 + 1]; uint32_t NumNaf; Point minus_p; Point r; uint32_t* 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); }