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.  */
13struct 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
25void 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 */
36mpi_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	if (!ctx)
44		return NULL;
45
46	if (copy) {
47		ctx->m = mpi_copy(m);
48		ctx->m_copied = 1;
49	} else
50		ctx->m = m;
51
52	ctx->k = mpi_get_nlimbs(m);
53	tmp = mpi_alloc(ctx->k + 1);
54
55	/* Barrett precalculation: y = floor(b^(2k) / m). */
56	mpi_set_ui(tmp, 1);
57	mpi_lshift_limbs(tmp, 2 * ctx->k);
58	mpi_fdiv_q(tmp, tmp, m);
59
60	ctx->y  = tmp;
61	ctx->r1 = mpi_alloc(2 * ctx->k + 1);
62	ctx->r2 = mpi_alloc(2 * ctx->k + 1);
63
64	return ctx;
65}
66
67void mpi_barrett_free(mpi_barrett_t ctx)
68{
69	if (ctx) {
70		mpi_free(ctx->y);
71		mpi_free(ctx->r1);
72		mpi_free(ctx->r2);
73		if (ctx->r3)
74			mpi_free(ctx->r3);
75		if (ctx->m_copied)
76			mpi_free(ctx->m);
77		kfree(ctx);
78	}
79}
80
81
82/* R = X mod M
83 *
84 * Using Barrett reduction.  Before using this function
85 * _gcry_mpi_barrett_init must have been called to do the
86 * precalculations.  CTX is the context created by this precalculation
87 * and also conveys M.  If the Barret reduction could no be done a
88 * straightforward reduction method is used.
89 *
90 * We assume that these conditions are met:
91 * Input:  x =(x_2k-1 ...x_0)_b
92 *     m =(m_k-1 ....m_0)_b	  with m_k-1 != 0
93 * Output: r = x mod m
94 */
95void mpi_mod_barrett(MPI r, MPI x, mpi_barrett_t ctx)
96{
97	MPI m = ctx->m;
98	int k = ctx->k;
99	MPI y = ctx->y;
100	MPI r1 = ctx->r1;
101	MPI r2 = ctx->r2;
102	int sign;
103
104	mpi_normalize(x);
105	if (mpi_get_nlimbs(x) > 2*k) {
106		mpi_mod(r, x, m);
107		return;
108	}
109
110	sign = x->sign;
111	x->sign = 0;
112
113	/* 1. q1 = floor( x / b^k-1)
114	 *    q2 = q1 * y
115	 *    q3 = floor( q2 / b^k+1 )
116	 * Actually, we don't need qx, we can work direct on r2
117	 */
118	mpi_set(r2, x);
119	mpi_rshift_limbs(r2, k-1);
120	mpi_mul(r2, r2, y);
121	mpi_rshift_limbs(r2, k+1);
122
123	/* 2. r1 = x mod b^k+1
124	 *	r2 = q3 * m mod b^k+1
125	 *	r  = r1 - r2
126	 * 3. if r < 0 then  r = r + b^k+1
127	 */
128	mpi_set(r1, x);
129	if (r1->nlimbs > k+1) /* Quick modulo operation.  */
130		r1->nlimbs = k+1;
131	mpi_mul(r2, r2, m);
132	if (r2->nlimbs > k+1) /* Quick modulo operation. */
133		r2->nlimbs = k+1;
134	mpi_sub(r, r1, r2);
135
136	if (mpi_has_sign(r)) {
137		if (!ctx->r3) {
138			ctx->r3 = mpi_alloc(k + 2);
139			mpi_set_ui(ctx->r3, 1);
140			mpi_lshift_limbs(ctx->r3, k + 1);
141		}
142		mpi_add(r, r, ctx->r3);
143	}
144
145	/* 4. while r >= m do r = r - m */
146	while (mpi_cmp(r, m) >= 0)
147		mpi_sub(r, r, m);
148
149	x->sign = sign;
150}
151
152
153void mpi_mul_barrett(MPI w, MPI u, MPI v, mpi_barrett_t ctx)
154{
155	mpi_mul(w, u, v);
156	mpi_mod_barrett(w, w, ctx);
157}
158