lib/mpi/mpi-mod.c

   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 }