1 /******************************************************************************
2 *
3 * Copyright 2006-2015 Broadcom Corporation
4 *
5 * Licensed under the Apache License, Version 2.0 (the "License");
6 * you may not use this file except in compliance with the License.
7 * You may obtain a copy of the License at:
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 *
17 ******************************************************************************/
18
19 /*******************************************************************************
20 *
21 * This file contains simple pairing algorithms using Elliptic Curve
22 * Cryptography for private public key
23 *
24 ******************************************************************************/
25 #include "p_256_ecc_pp.h"
26
27 #include <cstdint>
28 #include <cstring>
29
30 #include "p_256_multprecision.h"
31
32 elliptic_curve_t curve;
33 elliptic_curve_t curve_p256;
34
p_256_init_point(Point * q)35 static void p_256_init_point(Point* q) { memset(q, 0, sizeof(Point)); }
36
p_256_copy_point(Point * q,Point * p)37 static void p_256_copy_point(Point* q, Point* p) {
38 memcpy(q, p, sizeof(Point));
39 }
40
41 // q=2q
ECC_Double(Point * q,Point * p)42 static void ECC_Double(Point* q, Point* p) {
43 uint32_t t1[KEY_LENGTH_DWORDS_P256];
44 uint32_t t2[KEY_LENGTH_DWORDS_P256];
45 uint32_t t3[KEY_LENGTH_DWORDS_P256];
46 uint32_t* x1;
47 uint32_t* x3;
48 uint32_t* y1;
49 uint32_t* y3;
50 uint32_t* z1;
51 uint32_t* z3;
52
53 if (multiprecision_iszero(p->z)) {
54 multiprecision_init(q->z);
55 return; // return infinity
56 }
57
58 x1 = p->x;
59 y1 = p->y;
60 z1 = p->z;
61 x3 = q->x;
62 y3 = q->y;
63 z3 = q->z;
64
65 multiprecision_mersenns_squa_mod(t1, z1); // t1=z1^2
66 multiprecision_sub_mod(t2, x1, t1); // t2=x1-t1
67 multiprecision_add_mod(t1, x1, t1); // t1=x1+t1
68 multiprecision_mersenns_mult_mod(t2, t1, t2); // t2=t2*t1
69 multiprecision_lshift_mod(t3, t2);
70 multiprecision_add_mod(t2, t3, t2); // t2=3t2
71
72 multiprecision_mersenns_mult_mod(z3, y1, z1); // z3=y1*z1
73 multiprecision_lshift_mod(z3, z3);
74
75 multiprecision_mersenns_squa_mod(y3, y1); // y3=y1^2
76 multiprecision_lshift_mod(y3, y3);
77 multiprecision_mersenns_mult_mod(t3, y3, x1); // t3=y3*x1=x1*y1^2
78 multiprecision_lshift_mod(t3, t3);
79 multiprecision_mersenns_squa_mod(y3, y3); // y3=y3^2=y1^4
80 multiprecision_lshift_mod(y3, y3);
81
82 multiprecision_mersenns_squa_mod(x3, t2); // x3=t2^2
83 multiprecision_lshift_mod(t1, t3); // t1=2t3
84 multiprecision_sub_mod(x3, x3, t1); // x3=x3-t1
85 multiprecision_sub_mod(t1, t3, x3); // t1=t3-x3
86 multiprecision_mersenns_mult_mod(t1, t1, t2); // t1=t1*t2
87 multiprecision_sub_mod(y3, t1, y3); // y3=t1-y3
88 }
89
90 // q=q+p, zp must be 1
ECC_Add(Point * r,Point * p,Point * q)91 static void ECC_Add(Point* r, Point* p, Point* q) {
92 uint32_t t1[KEY_LENGTH_DWORDS_P256];
93 uint32_t t2[KEY_LENGTH_DWORDS_P256];
94 uint32_t* x1;
95 uint32_t* x2;
96 uint32_t* x3;
97 uint32_t* y1;
98 uint32_t* y2;
99 uint32_t* y3;
100 uint32_t* z1;
101 uint32_t* z2;
102 uint32_t* z3;
103
104 x1 = p->x;
105 y1 = p->y;
106 z1 = p->z;
107 x2 = q->x;
108 y2 = q->y;
109 z2 = q->z;
110 x3 = r->x;
111 y3 = r->y;
112 z3 = r->z;
113
114 // if Q=infinity, return p
115 if (multiprecision_iszero(z2)) {
116 p_256_copy_point(r, p);
117 return;
118 }
119
120 // if P=infinity, return q
121 if (multiprecision_iszero(z1)) {
122 p_256_copy_point(r, q);
123 return;
124 }
125
126 multiprecision_mersenns_squa_mod(t1, z1); // t1=z1^2
127 multiprecision_mersenns_mult_mod(t2, z1, t1); // t2=t1*z1
128 multiprecision_mersenns_mult_mod(t1, x2, t1); // t1=t1*x2
129 multiprecision_mersenns_mult_mod(t2, y2, t2); // t2=t2*y2
130
131 multiprecision_sub_mod(t1, t1, x1); // t1=t1-x1
132 multiprecision_sub_mod(t2, t2, y1); // t2=t2-y1
133
134 if (multiprecision_iszero(t1)) {
135 if (multiprecision_iszero(t2)) {
136 ECC_Double(r, q);
137 return;
138 } else {
139 multiprecision_init(z3);
140 return; // return infinity
141 }
142 }
143
144 multiprecision_mersenns_mult_mod(z3, z1, t1); // z3=z1*t1
145 multiprecision_mersenns_squa_mod(y3, t1); // t3=t1^2
146 multiprecision_mersenns_mult_mod(z1, y3, t1); // t4=t3*t1
147 multiprecision_mersenns_mult_mod(y3, y3, x1); // t3=t3*x1
148 multiprecision_lshift_mod(t1, y3); // t1=2*t3
149 multiprecision_mersenns_squa_mod(x3, t2); // x3=t2^2
150 multiprecision_sub_mod(x3, x3, t1); // x3=x3-t1
151 multiprecision_sub_mod(x3, x3, z1); // x3=x3-t4
152 multiprecision_sub_mod(y3, y3, x3); // t3=t3-x3
153 multiprecision_mersenns_mult_mod(y3, y3, t2); // t3=t3*t2
154 multiprecision_mersenns_mult_mod(z1, z1, y1); // t4=t4*t1
155 multiprecision_sub_mod(y3, y3, z1);
156 }
157
158 // Computing the Non-Adjacent Form of a positive integer
ECC_NAF(uint8_t * naf,uint32_t * NumNAF,uint32_t * k)159 static void ECC_NAF(uint8_t* naf, uint32_t* NumNAF, uint32_t* k) {
160 uint32_t sign;
161 int i = 0;
162 int j;
163 uint32_t var;
164
165 while ((var = multiprecision_most_signbits(k)) >= 1) {
166 if (k[0] & 0x01) // k is odd
167 {
168 sign = (k[0] & 0x03); // 1 or 3
169
170 // k = k-naf[i]
171 if (sign == 1)
172 k[0] = k[0] & 0xFFFFFFFE;
173 else {
174 k[0] = k[0] + 1;
175 if (k[0] == 0) // overflow
176 {
177 j = 1;
178 do {
179 k[j]++;
180 } while (k[j++] == 0); // overflow
181 }
182 }
183 } else
184 sign = 0;
185
186 multiprecision_rshift(k, k);
187 naf[i / 4] |= (sign) << ((i % 4) * 2);
188 i++;
189 }
190
191 *NumNAF = i;
192 }
193
194 // Binary Non-Adjacent Form for point multiplication
ECC_PointMult_Bin_NAF(Point * q,Point * p,uint32_t * n)195 void ECC_PointMult_Bin_NAF(Point* q, Point* p, uint32_t* n) {
196 uint32_t sign;
197 uint8_t naf[256 / 4 + 1];
198 uint32_t NumNaf;
199 Point minus_p;
200 Point r;
201 uint32_t* modp;
202
203 modp = curve_p256.p;
204
205 p_256_init_point(&r);
206 multiprecision_init(p->z);
207 p->z[0] = 1;
208
209 // initialization
210 p_256_init_point(q);
211
212 // -p
213 multiprecision_copy(minus_p.x, p->x);
214 multiprecision_sub(minus_p.y, modp, p->y);
215
216 multiprecision_init(minus_p.z);
217 minus_p.z[0] = 1;
218
219 // NAF
220 memset(naf, 0, sizeof(naf));
221 ECC_NAF(naf, &NumNaf, n);
222
223 for (int i = NumNaf - 1; i >= 0; i--) {
224 p_256_copy_point(&r, q);
225 ECC_Double(q, &r);
226 sign = (naf[i / 4] >> ((i % 4) * 2)) & 0x03;
227
228 if (sign == 1) {
229 p_256_copy_point(&r, q);
230 ECC_Add(q, &r, p);
231 } else if (sign == 3) {
232 p_256_copy_point(&r, q);
233 ECC_Add(q, &r, &minus_p);
234 }
235 }
236
237 multiprecision_inv_mod(minus_p.x, q->z);
238 multiprecision_mersenns_squa_mod(q->z, minus_p.x);
239 multiprecision_mersenns_mult_mod(q->x, q->x, q->z);
240 multiprecision_mersenns_mult_mod(q->z, q->z, minus_p.x);
241 multiprecision_mersenns_mult_mod(q->y, q->y, q->z);
242 }
243
ECC_ValidatePoint(const Point & pt)244 bool ECC_ValidatePoint(const Point& pt) {
245 p_256_init_curve();
246
247 // Ensure y^2 = x^3 + a*x + b (mod p); a = -3
248
249 // y^2 mod p
250 uint32_t y2_mod[KEY_LENGTH_DWORDS_P256] = {0};
251 multiprecision_mersenns_squa_mod(y2_mod, (uint32_t*)pt.y);
252
253 // Right hand side calculation
254 uint32_t rhs[KEY_LENGTH_DWORDS_P256] = {0};
255 multiprecision_mersenns_squa_mod(rhs, (uint32_t*)pt.x);
256 uint32_t three[KEY_LENGTH_DWORDS_P256] = {0};
257 three[0] = 3;
258 multiprecision_sub_mod(rhs, rhs, three);
259 multiprecision_mersenns_mult_mod(rhs, rhs, (uint32_t*)pt.x);
260 multiprecision_add_mod(rhs, rhs, curve_p256.b);
261
262 return multiprecision_compare(rhs, y2_mod) == 0;
263 }
264