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a8ea8bdd TZ |
1 | /* mpi-mod.c - Modular reduction |
2 | * Copyright (C) 1998, 1999, 2001, 2002, 2003, | |
3 | * 2007 Free Software Foundation, Inc. | |
4 | * | |
5 | * This file is part of Libgcrypt. | |
6 | */ | |
7 | ||
8 | ||
9 | #include "mpi-internal.h" | |
10 | #include "longlong.h" | |
11 | ||
12 | /* Context used with Barrett reduction. */ | |
13 | struct barrett_ctx_s { | |
14 | MPI m; /* The modulus - may not be modified. */ | |
15 | int m_copied; /* If true, M needs to be released. */ | |
16 | int k; | |
17 | MPI y; | |
18 | MPI r1; /* Helper MPI. */ | |
19 | MPI r2; /* Helper MPI. */ | |
20 | MPI r3; /* Helper MPI allocated on demand. */ | |
21 | }; | |
22 | ||
23 | ||
24 | ||
25 | void mpi_mod(MPI rem, MPI dividend, MPI divisor) | |
26 | { | |
27 | mpi_fdiv_r(rem, dividend, divisor); | |
28 | } | |
29 | ||
30 | /* This function returns a new context for Barrett based operations on | |
31 | * the modulus M. This context needs to be released using | |
32 | * _gcry_mpi_barrett_free. If COPY is true M will be transferred to | |
33 | * the context and the user may change M. If COPY is false, M may not | |
34 | * be changed until gcry_mpi_barrett_free has been called. | |
35 | */ | |
36 | mpi_barrett_t mpi_barrett_init(MPI m, int copy) | |
37 | { | |
38 | mpi_barrett_t ctx; | |
39 | MPI tmp; | |
40 | ||
41 | mpi_normalize(m); | |
42 | ctx = kcalloc(1, sizeof(*ctx), GFP_KERNEL); | |
43 | ||
44 | if (copy) { | |
45 | ctx->m = mpi_copy(m); | |
46 | ctx->m_copied = 1; | |
47 | } else | |
48 | ctx->m = m; | |
49 | ||
50 | ctx->k = mpi_get_nlimbs(m); | |
51 | tmp = mpi_alloc(ctx->k + 1); | |
52 | ||
53 | /* Barrett precalculation: y = floor(b^(2k) / m). */ | |
54 | mpi_set_ui(tmp, 1); | |
55 | mpi_lshift_limbs(tmp, 2 * ctx->k); | |
56 | mpi_fdiv_q(tmp, tmp, m); | |
57 | ||
58 | ctx->y = tmp; | |
59 | ctx->r1 = mpi_alloc(2 * ctx->k + 1); | |
60 | ctx->r2 = mpi_alloc(2 * ctx->k + 1); | |
61 | ||
62 | return ctx; | |
63 | } | |
64 | ||
65 | void mpi_barrett_free(mpi_barrett_t ctx) | |
66 | { | |
67 | if (ctx) { | |
68 | mpi_free(ctx->y); | |
69 | mpi_free(ctx->r1); | |
70 | mpi_free(ctx->r2); | |
71 | if (ctx->r3) | |
72 | mpi_free(ctx->r3); | |
73 | if (ctx->m_copied) | |
74 | mpi_free(ctx->m); | |
75 | kfree(ctx); | |
76 | } | |
77 | } | |
78 | ||
79 | ||
80 | /* R = X mod M | |
81 | * | |
82 | * Using Barrett reduction. Before using this function | |
83 | * _gcry_mpi_barrett_init must have been called to do the | |
84 | * precalculations. CTX is the context created by this precalculation | |
85 | * and also conveys M. If the Barret reduction could no be done a | |
86 | * straightforward reduction method is used. | |
87 | * | |
88 | * We assume that these conditions are met: | |
89 | * Input: x =(x_2k-1 ...x_0)_b | |
90 | * m =(m_k-1 ....m_0)_b with m_k-1 != 0 | |
91 | * Output: r = x mod m | |
92 | */ | |
93 | void mpi_mod_barrett(MPI r, MPI x, mpi_barrett_t ctx) | |
94 | { | |
95 | MPI m = ctx->m; | |
96 | int k = ctx->k; | |
97 | MPI y = ctx->y; | |
98 | MPI r1 = ctx->r1; | |
99 | MPI r2 = ctx->r2; | |
100 | int sign; | |
101 | ||
102 | mpi_normalize(x); | |
103 | if (mpi_get_nlimbs(x) > 2*k) { | |
104 | mpi_mod(r, x, m); | |
105 | return; | |
106 | } | |
107 | ||
108 | sign = x->sign; | |
109 | x->sign = 0; | |
110 | ||
111 | /* 1. q1 = floor( x / b^k-1) | |
112 | * q2 = q1 * y | |
113 | * q3 = floor( q2 / b^k+1 ) | |
114 | * Actually, we don't need qx, we can work direct on r2 | |
115 | */ | |
116 | mpi_set(r2, x); | |
117 | mpi_rshift_limbs(r2, k-1); | |
118 | mpi_mul(r2, r2, y); | |
119 | mpi_rshift_limbs(r2, k+1); | |
120 | ||
121 | /* 2. r1 = x mod b^k+1 | |
122 | * r2 = q3 * m mod b^k+1 | |
123 | * r = r1 - r2 | |
124 | * 3. if r < 0 then r = r + b^k+1 | |
125 | */ | |
126 | mpi_set(r1, x); | |
127 | if (r1->nlimbs > k+1) /* Quick modulo operation. */ | |
128 | r1->nlimbs = k+1; | |
129 | mpi_mul(r2, r2, m); | |
130 | if (r2->nlimbs > k+1) /* Quick modulo operation. */ | |
131 | r2->nlimbs = k+1; | |
132 | mpi_sub(r, r1, r2); | |
133 | ||
134 | if (mpi_has_sign(r)) { | |
135 | if (!ctx->r3) { | |
136 | ctx->r3 = mpi_alloc(k + 2); | |
137 | mpi_set_ui(ctx->r3, 1); | |
138 | mpi_lshift_limbs(ctx->r3, k + 1); | |
139 | } | |
140 | mpi_add(r, r, ctx->r3); | |
141 | } | |
142 | ||
143 | /* 4. while r >= m do r = r - m */ | |
144 | while (mpi_cmp(r, m) >= 0) | |
145 | mpi_sub(r, r, m); | |
146 | ||
147 | x->sign = sign; | |
148 | } | |
149 | ||
150 | ||
151 | void mpi_mul_barrett(MPI w, MPI u, MPI v, mpi_barrett_t ctx) | |
152 | { | |
153 | mpi_mul(w, u, v); | |
154 | mpi_mod_barrett(w, w, ctx); | |
155 | } |