1 /*
2  * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>
3  *
4  * Permission is hereby granted, free of charge, to any person obtaining
5  * a copy of this software and associated documentation files (the
6  * "Software"), to deal in the Software without restriction, including
7  * without limitation the rights to use, copy, modify, merge, publish,
8  * distribute, sublicense, and/or sell copies of the Software, and to
9  * permit persons to whom the Software is furnished to do so, subject to
10  * the following conditions:
11  *
12  * The above copyright notice and this permission notice shall be
13  * included in all copies or substantial portions of the Software.
14  *
15  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16  * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18  * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19  * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20  * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21  * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22  * SOFTWARE.
23  */
24 
25 #include "inner.h"
26 
27 /*
28  * Recompute public exponent, based on factor p and reduced private
29  * exponent dp.
30  */
31 static uint32_t
32 get_pubexp(const unsigned char *pbuf, size_t plen,
33 	const unsigned char *dpbuf, size_t dplen)
34 {
35 	/*
36 	 * dp is the inverse of e modulo p-1. If p = 3 mod 4, then
37 	 * p-1 = 2*((p-1)/2). Taken modulo 2, e is odd and has inverse 1;
38 	 * thus, dp must be odd.
39 	 *
40 	 * We compute the inverse of dp modulo (p-1)/2. This requires
41 	 * first reducing dp modulo (p-1)/2 (this can be done with a
42 	 * conditional subtract, no need to use the generic modular
43 	 * reduction function); then, we use moddiv.
44 	 */
45 
46 	uint32_t tmp[6 * ((BR_MAX_RSA_FACTOR + 61) / 31)];
47 	uint32_t *p, *dp, *x;
48 	size_t len;
49 	uint32_t e;
50 
51 	/*
52 	 * Compute actual factor length (in bytes) and check that it fits
53 	 * under our size constraints.
54 	 */
55 	while (plen > 0 && *pbuf == 0) {
56 		pbuf ++;
57 		plen --;
58 	}
59 	if (plen == 0 || plen < 5 || plen > (BR_MAX_RSA_FACTOR / 8)) {
60 		return 0;
61 	}
62 
63 	/*
64 	 * Compute actual reduced exponent length (in bytes) and check that
65 	 * it is not longer than p.
66 	 */
67 	while (dplen > 0 && *dpbuf == 0) {
68 		dpbuf ++;
69 		dplen --;
70 	}
71 	if (dplen > plen || dplen == 0
72 		|| (dplen == plen && dpbuf[0] > pbuf[0]))
73 	{
74 		return 0;
75 	}
76 
77 	/*
78 	 * Verify that p = 3 mod 4 and that dp is odd.
79 	 */
80 	if ((pbuf[plen - 1] & 3) != 3 || (dpbuf[dplen - 1] & 1) != 1) {
81 		return 0;
82 	}
83 
84 	/*
85 	 * Decode p and compute (p-1)/2.
86 	 */
87 	p = tmp;
88 	br_i31_decode(p, pbuf, plen);
89 	len = (p[0] + 63) >> 5;
90 	br_i31_rshift(p, 1);
91 
92 	/*
93 	 * Decode dp and make sure its announced bit length matches that of
94 	 * p (we already know that the size of dp, in bits, does not exceed
95 	 * the size of p, so we just have to copy the header word).
96 	 */
97 	dp = p + len;
98 	memset(dp, 0, len * sizeof *dp);
99 	br_i31_decode(dp, dpbuf, dplen);
100 	dp[0] = p[0];
101 
102 	/*
103 	 * Subtract (p-1)/2 from dp if necessary.
104 	 */
105 	br_i31_sub(dp, p, NOT(br_i31_sub(dp, p, 0)));
106 
107 	/*
108 	 * If another subtraction is needed, then this means that the
109 	 * value was invalid. We don't care to leak information about
110 	 * invalid keys.
111 	 */
112 	if (br_i31_sub(dp, p, 0) == 0) {
113 		return 0;
114 	}
115 
116 	/*
117 	 * Invert dp modulo (p-1)/2. If the inversion fails, then the
118 	 * key value was invalid.
119 	 */
120 	x = dp + len;
121 	br_i31_zero(x, p[0]);
122 	x[1] = 1;
123 	if (br_i31_moddiv(x, dp, p, br_i31_ninv31(p[1]), x + len) == 0) {
124 		return 0;
125 	}
126 
127 	/*
128 	 * We now have an inverse. We must set it to zero (error) if its
129 	 * length is greater than 32 bits and/or if it is an even integer.
130 	 * Take care that the bit_length function returns an encoded
131 	 * bit length.
132 	 */
133 	e = (uint32_t)x[1] | ((uint32_t)x[2] << 31);
134 	e &= -LT(br_i31_bit_length(x + 1, len - 1), 34);
135 	e &= -(e & 1);
136 	return e;
137 }
138 
139 /* see bearssl_rsa.h */
140 uint32_t
141 br_rsa_i31_compute_pubexp(const br_rsa_private_key *sk)
142 {
143 	/*
144 	 * Get the public exponent from both p and q. This is the right
145 	 * exponent if we get twice the same value.
146 	 */
147 	uint32_t ep, eq;
148 
149 	ep = get_pubexp(sk->p, sk->plen, sk->dp, sk->dplen);
150 	eq = get_pubexp(sk->q, sk->qlen, sk->dq, sk->dqlen);
151 	return ep & -EQ(ep, eq);
152 }
153