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
 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
 65void 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 */
 93void 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
151void 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}