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1 /* LibTomMath, multiple-precision integer library -- Tom St Denis |
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2 * |
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3 * LibTomMath is a library that provides multiple-precision |
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4 * integer arithmetic as well as number theoretic functionality. |
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5 * |
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6 * The library was designed directly after the MPI library by |
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7 * Michael Fromberger but has been written from scratch with |
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8 * additional optimizations in place. |
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9 * |
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10 * The library is free for all purposes without any express |
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11 * guarantee it works. |
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12 * |
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13 * Tom St Denis, [email protected], http://math.libtomcrypt.org |
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14 */ |
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15 #include <tommath.h> |
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16 |
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17 /* reduces x mod m, assumes 0 < x < m**2, mu is |
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18 * precomputed via mp_reduce_setup. |
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19 * From HAC pp.604 Algorithm 14.42 |
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20 */ |
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21 int |
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22 mp_reduce (mp_int * x, mp_int * m, mp_int * mu) |
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23 { |
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24 mp_int q; |
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25 int res, um = m->used; |
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26 |
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27 /* q = x */ |
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28 if ((res = mp_init_copy (&q, x)) != MP_OKAY) { |
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29 return res; |
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30 } |
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31 |
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32 /* q1 = x / b**(k-1) */ |
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33 mp_rshd (&q, um - 1); |
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34 |
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35 /* according to HAC this optimization is ok */ |
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36 if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) { |
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37 if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) { |
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38 goto CLEANUP; |
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39 } |
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40 } else { |
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41 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { |
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42 goto CLEANUP; |
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43 } |
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44 } |
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45 |
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46 /* q3 = q2 / b**(k+1) */ |
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47 mp_rshd (&q, um + 1); |
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48 |
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49 /* x = x mod b**(k+1), quick (no division) */ |
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50 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) { |
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51 goto CLEANUP; |
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52 } |
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53 |
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54 /* q = q * m mod b**(k+1), quick (no division) */ |
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55 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) { |
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56 goto CLEANUP; |
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57 } |
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58 |
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59 /* x = x - q */ |
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60 if ((res = mp_sub (x, &q, x)) != MP_OKAY) { |
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61 goto CLEANUP; |
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62 } |
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63 |
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64 /* If x < 0, add b**(k+1) to it */ |
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65 if (mp_cmp_d (x, 0) == MP_LT) { |
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66 mp_set (&q, 1); |
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67 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) |
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68 goto CLEANUP; |
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69 if ((res = mp_add (x, &q, x)) != MP_OKAY) |
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70 goto CLEANUP; |
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71 } |
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72 |
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73 /* Back off if it's too big */ |
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74 while (mp_cmp (x, m) != MP_LT) { |
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75 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) { |
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76 goto CLEANUP; |
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77 } |
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78 } |
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79 |
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80 CLEANUP: |
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81 mp_clear (&q); |
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82 |
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83 return res; |
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84 } |
