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Diffstat (limited to 'src/lib/libcrypto/ec/ecp_nistputil.c')
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diff --git a/src/lib/libcrypto/ec/ecp_nistputil.c b/src/lib/libcrypto/ec/ecp_nistputil.c new file mode 100644 index 0000000000..c8140c807f --- /dev/null +++ b/src/lib/libcrypto/ec/ecp_nistputil.c | |||
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1 | /* crypto/ec/ecp_nistputil.c */ | ||
2 | /* | ||
3 | * Written by Bodo Moeller for the OpenSSL project. | ||
4 | */ | ||
5 | /* Copyright 2011 Google Inc. | ||
6 | * | ||
7 | * Licensed under the Apache License, Version 2.0 (the "License"); | ||
8 | * | ||
9 | * you may not use this file except in compliance with the License. | ||
10 | * You may obtain a copy of the License at | ||
11 | * | ||
12 | * http://www.apache.org/licenses/LICENSE-2.0 | ||
13 | * | ||
14 | * Unless required by applicable law or agreed to in writing, software | ||
15 | * distributed under the License is distributed on an "AS IS" BASIS, | ||
16 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
17 | * See the License for the specific language governing permissions and | ||
18 | * limitations under the License. | ||
19 | */ | ||
20 | |||
21 | #include <openssl/opensslconf.h> | ||
22 | #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 | ||
23 | |||
24 | /* | ||
25 | * Common utility functions for ecp_nistp224.c, ecp_nistp256.c, ecp_nistp521.c. | ||
26 | */ | ||
27 | |||
28 | #include <stddef.h> | ||
29 | #include "ec_lcl.h" | ||
30 | |||
31 | /* Convert an array of points into affine coordinates. | ||
32 | * (If the point at infinity is found (Z = 0), it remains unchanged.) | ||
33 | * This function is essentially an equivalent to EC_POINTs_make_affine(), but | ||
34 | * works with the internal representation of points as used by ecp_nistp###.c | ||
35 | * rather than with (BIGNUM-based) EC_POINT data structures. | ||
36 | * | ||
37 | * point_array is the input/output buffer ('num' points in projective form, | ||
38 | * i.e. three coordinates each), based on an internal representation of | ||
39 | * field elements of size 'felem_size'. | ||
40 | * | ||
41 | * tmp_felems needs to point to a temporary array of 'num'+1 field elements | ||
42 | * for storage of intermediate values. | ||
43 | */ | ||
44 | void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, | ||
45 | size_t felem_size, void *tmp_felems, | ||
46 | void (*felem_one)(void *out), | ||
47 | int (*felem_is_zero)(const void *in), | ||
48 | void (*felem_assign)(void *out, const void *in), | ||
49 | void (*felem_square)(void *out, const void *in), | ||
50 | void (*felem_mul)(void *out, const void *in1, const void *in2), | ||
51 | void (*felem_inv)(void *out, const void *in), | ||
52 | void (*felem_contract)(void *out, const void *in)) | ||
53 | { | ||
54 | int i = 0; | ||
55 | |||
56 | #define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) | ||
57 | #define X(I) (&((char *)point_array)[3*(I) * felem_size]) | ||
58 | #define Y(I) (&((char *)point_array)[(3*(I) + 1) * felem_size]) | ||
59 | #define Z(I) (&((char *)point_array)[(3*(I) + 2) * felem_size]) | ||
60 | |||
61 | if (!felem_is_zero(Z(0))) | ||
62 | felem_assign(tmp_felem(0), Z(0)); | ||
63 | else | ||
64 | felem_one(tmp_felem(0)); | ||
65 | for (i = 1; i < (int)num; i++) | ||
66 | { | ||
67 | if (!felem_is_zero(Z(i))) | ||
68 | felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i)); | ||
69 | else | ||
70 | felem_assign(tmp_felem(i), tmp_felem(i-1)); | ||
71 | } | ||
72 | /* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors: | ||
73 | * if Z(i) = 0, we essentially pretend that Z(i) = 1 */ | ||
74 | |||
75 | felem_inv(tmp_felem(num-1), tmp_felem(num-1)); | ||
76 | for (i = num - 1; i >= 0; i--) | ||
77 | { | ||
78 | if (i > 0) | ||
79 | /* tmp_felem(i-1) is the product of Z(0) .. Z(i-1), | ||
80 | * tmp_felem(i) is the inverse of the product of Z(0) .. Z(i) | ||
81 | */ | ||
82 | felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */ | ||
83 | else | ||
84 | felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ | ||
85 | |||
86 | if (!felem_is_zero(Z(i))) | ||
87 | { | ||
88 | if (i > 0) | ||
89 | /* For next iteration, replace tmp_felem(i-1) by its inverse */ | ||
90 | felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i)); | ||
91 | |||
92 | /* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */ | ||
93 | felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ | ||
94 | felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ | ||
95 | felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ | ||
96 | felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ | ||
97 | felem_contract(X(i), X(i)); | ||
98 | felem_contract(Y(i), Y(i)); | ||
99 | felem_one(Z(i)); | ||
100 | } | ||
101 | else | ||
102 | { | ||
103 | if (i > 0) | ||
104 | /* For next iteration, replace tmp_felem(i-1) by its inverse */ | ||
105 | felem_assign(tmp_felem(i-1), tmp_felem(i)); | ||
106 | } | ||
107 | } | ||
108 | } | ||
109 | |||
110 | /* | ||
111 | * This function looks at 5+1 scalar bits (5 current, 1 adjacent less | ||
112 | * significant bit), and recodes them into a signed digit for use in fast point | ||
113 | * multiplication: the use of signed rather than unsigned digits means that | ||
114 | * fewer points need to be precomputed, given that point inversion is easy | ||
115 | * (a precomputed point dP makes -dP available as well). | ||
116 | * | ||
117 | * BACKGROUND: | ||
118 | * | ||
119 | * Signed digits for multiplication were introduced by Booth ("A signed binary | ||
120 | * multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV, | ||
121 | * pt. 2 (1951), pp. 236-240), in that case for multiplication of integers. | ||
122 | * Booth's original encoding did not generally improve the density of nonzero | ||
123 | * digits over the binary representation, and was merely meant to simplify the | ||
124 | * handling of signed factors given in two's complement; but it has since been | ||
125 | * shown to be the basis of various signed-digit representations that do have | ||
126 | * further advantages, including the wNAF, using the following general approach: | ||
127 | * | ||
128 | * (1) Given a binary representation | ||
129 | * | ||
130 | * b_k ... b_2 b_1 b_0, | ||
131 | * | ||
132 | * of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1 | ||
133 | * by using bit-wise subtraction as follows: | ||
134 | * | ||
135 | * b_k b_(k-1) ... b_2 b_1 b_0 | ||
136 | * - b_k ... b_3 b_2 b_1 b_0 | ||
137 | * ------------------------------------- | ||
138 | * s_k b_(k-1) ... s_3 s_2 s_1 s_0 | ||
139 | * | ||
140 | * A left-shift followed by subtraction of the original value yields a new | ||
141 | * representation of the same value, using signed bits s_i = b_(i+1) - b_i. | ||
142 | * This representation from Booth's paper has since appeared in the | ||
143 | * literature under a variety of different names including "reversed binary | ||
144 | * form", "alternating greedy expansion", "mutual opposite form", and | ||
145 | * "sign-alternating {+-1}-representation". | ||
146 | * | ||
147 | * An interesting property is that among the nonzero bits, values 1 and -1 | ||
148 | * strictly alternate. | ||
149 | * | ||
150 | * (2) Various window schemes can be applied to the Booth representation of | ||
151 | * integers: for example, right-to-left sliding windows yield the wNAF | ||
152 | * (a signed-digit encoding independently discovered by various researchers | ||
153 | * in the 1990s), and left-to-right sliding windows yield a left-to-right | ||
154 | * equivalent of the wNAF (independently discovered by various researchers | ||
155 | * around 2004). | ||
156 | * | ||
157 | * To prevent leaking information through side channels in point multiplication, | ||
158 | * we need to recode the given integer into a regular pattern: sliding windows | ||
159 | * as in wNAFs won't do, we need their fixed-window equivalent -- which is a few | ||
160 | * decades older: we'll be using the so-called "modified Booth encoding" due to | ||
161 | * MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49 | ||
162 | * (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five | ||
163 | * signed bits into a signed digit: | ||
164 | * | ||
165 | * s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j) | ||
166 | * | ||
167 | * The sign-alternating property implies that the resulting digit values are | ||
168 | * integers from -16 to 16. | ||
169 | * | ||
170 | * Of course, we don't actually need to compute the signed digits s_i as an | ||
171 | * intermediate step (that's just a nice way to see how this scheme relates | ||
172 | * to the wNAF): a direct computation obtains the recoded digit from the | ||
173 | * six bits b_(4j + 4) ... b_(4j - 1). | ||
174 | * | ||
175 | * This function takes those five bits as an integer (0 .. 63), writing the | ||
176 | * recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute | ||
177 | * value, in the range 0 .. 8). Note that this integer essentially provides the | ||
178 | * input bits "shifted to the left" by one position: for example, the input to | ||
179 | * compute the least significant recoded digit, given that there's no bit b_-1, | ||
180 | * has to be b_4 b_3 b_2 b_1 b_0 0. | ||
181 | * | ||
182 | */ | ||
183 | void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) | ||
184 | { | ||
185 | unsigned char s, d; | ||
186 | |||
187 | s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */ | ||
188 | d = (1 << 6) - in - 1; | ||
189 | d = (d & s) | (in & ~s); | ||
190 | d = (d >> 1) + (d & 1); | ||
191 | |||
192 | *sign = s & 1; | ||
193 | *digit = d; | ||
194 | } | ||
195 | #else | ||
196 | static void *dummy=&dummy; | ||
197 | #endif | ||