1 /******************************************************************************
3 * Copyright (C) 2006-2015 Broadcom Corporation
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:
9 * http://www.apache.org/licenses/LICENSE-2.0
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.
17 ******************************************************************************/
19 /******************************************************************************
21 * This file contains simple pairing algorithms using Elliptic Curve Cryptography for private public key
23 ******************************************************************************/
27 #include "p_256_ecc_pp.h"
28 #include "p_256_multprecision.h"
30 elliptic_curve_t curve;
31 elliptic_curve_t curve_p256;
33 static void p_256_init_point(Point *q)
35 memset(q, 0, sizeof(Point));
38 static void p_256_copy_point(Point *q, Point *p)
40 memcpy(q, p, sizeof(Point));
44 static void ECC_Double(Point *q, Point *p, uint32_t keyLength)
46 DWORD t1[KEY_LENGTH_DWORDS_P256];
47 DWORD t2[KEY_LENGTH_DWORDS_P256];
48 DWORD t3[KEY_LENGTH_DWORDS_P256];
56 if (multiprecision_iszero(p->z, keyLength))
58 multiprecision_init(q->z, keyLength);
59 return; // return infinity
62 x1=p->x; y1=p->y; z1=p->z;
63 x3=q->x; y3=q->y; z3=q->z;
65 multiprecision_mersenns_squa_mod(t1, z1, keyLength); // t1=z1^2
66 multiprecision_sub_mod(t2, x1, t1, keyLength); // t2=x1-t1
67 multiprecision_add_mod(t1, x1, t1, keyLength); // t1=x1+t1
68 multiprecision_mersenns_mult_mod(t2, t1, t2, keyLength); // t2=t2*t1
69 multiprecision_lshift_mod(t3, t2, keyLength);
70 multiprecision_add_mod(t2, t3, t2, keyLength); // t2=3t2
72 multiprecision_mersenns_mult_mod(z3, y1, z1, keyLength); // z3=y1*z1
73 multiprecision_lshift_mod(z3, z3, keyLength);
75 multiprecision_mersenns_squa_mod(y3, y1, keyLength); // y3=y1^2
76 multiprecision_lshift_mod(y3, y3, keyLength);
77 multiprecision_mersenns_mult_mod(t3, y3, x1, keyLength); // t3=y3*x1=x1*y1^2
78 multiprecision_lshift_mod(t3, t3, keyLength);
79 multiprecision_mersenns_squa_mod(y3, y3, keyLength); // y3=y3^2=y1^4
80 multiprecision_lshift_mod(y3, y3, keyLength);
82 multiprecision_mersenns_squa_mod(x3, t2, keyLength); // x3=t2^2
83 multiprecision_lshift_mod(t1, t3, keyLength); // t1=2t3
84 multiprecision_sub_mod(x3, x3, t1, keyLength); // x3=x3-t1
85 multiprecision_sub_mod(t1, t3, x3, keyLength); // t1=t3-x3
86 multiprecision_mersenns_mult_mod(t1, t1, t2, keyLength); // t1=t1*t2
87 multiprecision_sub_mod(y3, t1, y3, keyLength); // y3=t1-y3
90 // q=q+p, zp must be 1
91 static void ECC_Add(Point *r, Point *p, Point *q, uint32_t keyLength)
93 DWORD t1[KEY_LENGTH_DWORDS_P256];
94 DWORD t2[KEY_LENGTH_DWORDS_P256];
105 x1=p->x; y1=p->y; z1=p->z;
106 x2=q->x; y2=q->y; z2=q->z;
107 x3=r->x; y3=r->y; z3=r->z;
109 // if Q=infinity, return p
110 if (multiprecision_iszero(z2, keyLength))
112 p_256_copy_point(r, p);
116 // if P=infinity, return q
117 if (multiprecision_iszero(z1, keyLength))
119 p_256_copy_point(r, q);
123 multiprecision_mersenns_squa_mod(t1, z1, keyLength); // t1=z1^2
124 multiprecision_mersenns_mult_mod(t2, z1, t1, keyLength); // t2=t1*z1
125 multiprecision_mersenns_mult_mod(t1, x2, t1, keyLength); // t1=t1*x2
126 multiprecision_mersenns_mult_mod(t2, y2, t2, keyLength); // t2=t2*y2
128 multiprecision_sub_mod(t1, t1, x1, keyLength); // t1=t1-x1
129 multiprecision_sub_mod(t2, t2, y1, keyLength); // t2=t2-y1
131 if (multiprecision_iszero(t1, keyLength))
133 if (multiprecision_iszero(t2, keyLength))
135 ECC_Double(r, q, keyLength) ;
140 multiprecision_init(z3, keyLength);
141 return; // return infinity
145 multiprecision_mersenns_mult_mod(z3, z1, t1, keyLength); // z3=z1*t1
146 multiprecision_mersenns_squa_mod(y3, t1, keyLength); // t3=t1^2
147 multiprecision_mersenns_mult_mod(z1, y3, t1, keyLength); // t4=t3*t1
148 multiprecision_mersenns_mult_mod(y3, y3, x1, keyLength); // t3=t3*x1
149 multiprecision_lshift_mod(t1, y3, keyLength); // t1=2*t3
150 multiprecision_mersenns_squa_mod(x3, t2, keyLength); // x3=t2^2
151 multiprecision_sub_mod(x3, x3, t1, keyLength); // x3=x3-t1
152 multiprecision_sub_mod(x3, x3, z1, keyLength); // x3=x3-t4
153 multiprecision_sub_mod(y3, y3, x3, keyLength); // t3=t3-x3
154 multiprecision_mersenns_mult_mod(y3, y3, t2, keyLength); // t3=t3*t2
155 multiprecision_mersenns_mult_mod(z1, z1, y1, keyLength); // t4=t4*t1
156 multiprecision_sub_mod(y3, y3, z1, keyLength);
159 // Computing the Non-Adjacent Form of a positive integer
160 static void ECC_NAF(uint8_t *naf, uint32_t *NumNAF, DWORD *k, uint32_t keyLength)
167 while ((var = multiprecision_most_signbits(k, keyLength))>=1)
169 if (k[0] & 0x01) // k is odd
171 sign = (k[0] & 0x03); // 1 or 3
175 k[0] = k[0] & 0xFFFFFFFE;
179 if (k[0] == 0) //overflow
185 } while (k[j++]==0); //overflow
192 multiprecision_rshift(k, k, keyLength);
193 naf[i / 4] |= (sign) << ((i % 4) * 2);
200 // Binary Non-Adjacent Form for point multiplication
201 void ECC_PointMult_Bin_NAF(Point *q, Point *p, DWORD *n, uint32_t keyLength)
204 UINT8 naf[256 / 4 +1];
210 if (keyLength == KEY_LENGTH_DWORDS_P256)
219 p_256_init_point(&r);
220 multiprecision_init(p->z, keyLength);
227 multiprecision_copy(minus_p.x, p->x, keyLength);
228 multiprecision_sub(minus_p.y, modp, p->y, keyLength);
230 multiprecision_init(minus_p.z, keyLength);
234 memset(naf, 0, sizeof(naf));
235 ECC_NAF(naf, &NumNaf, n, keyLength);
237 for (int i = NumNaf - 1; i >= 0; i--)
239 p_256_copy_point(&r, q);
240 ECC_Double(q, &r, keyLength);
241 sign = (naf[i / 4] >> ((i % 4) * 2)) & 0x03;
245 p_256_copy_point(&r, q);
246 ECC_Add(q, &r, p, keyLength);
250 p_256_copy_point(&r, q);
251 ECC_Add(q, &r, &minus_p, keyLength);
255 multiprecision_inv_mod(minus_p.x, q->z, keyLength);
256 multiprecision_mersenns_squa_mod(q->z, minus_p.x, keyLength);
257 multiprecision_mersenns_mult_mod(q->x, q->x, q->z, keyLength);
258 multiprecision_mersenns_mult_mod(q->z, q->z, minus_p.x, keyLength);
259 multiprecision_mersenns_mult_mod(q->y, q->y, q->z, keyLength);