Outline ![]()
Files ![]()
loading...
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
/******************************************************************************
*
* 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"
#include "common/bt_target.h"
#if SMP_DYNAMIC_MEMORY == FALSE
elliptic_curve_t curve;
elliptic_curve_t curve_p256;
#else
elliptic_curve_t *curve_ptr;
elliptic_curve_t *curve_p256_ptr;
#endif
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;
}
}
Details ![]()
Show: from Types: Columns: ![]( "Show Project Names")
![]( "Show Locations")
![]( "Show Referring Symbols")
![]( "Show Scope")
This file uses the notable symbols shown below. Click anywhere in the file to view more details.