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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 /* Karatsuba squaring, computes b = a*a using three |
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18 * half size squarings |
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19 * |
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20 * See comments of mp_karatsuba_mul for details. It |
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21 * is essentially the same algorithm but merely |
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22 * tuned to perform recursive squarings. |
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23 */ |
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24 int mp_karatsuba_sqr (mp_int * a, mp_int * b) |
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25 { |
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26 mp_int x0, x1, t1, t2, x0x0, x1x1; |
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27 int B, err; |
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28 |
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29 err = MP_MEM; |
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30 |
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31 /* min # of digits */ |
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32 B = a->used; |
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33 |
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34 /* now divide in two */ |
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35 B = B >> 1; |
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36 |
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37 /* init copy all the temps */ |
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38 if (mp_init_size (&x0, B) != MP_OKAY) |
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39 goto ERR; |
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40 if (mp_init_size (&x1, a->used - B) != MP_OKAY) |
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41 goto X0; |
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42 |
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43 /* init temps */ |
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44 if (mp_init_size (&t1, a->used * 2) != MP_OKAY) |
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45 goto X1; |
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46 if (mp_init_size (&t2, a->used * 2) != MP_OKAY) |
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47 goto T1; |
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48 if (mp_init_size (&x0x0, B * 2) != MP_OKAY) |
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49 goto T2; |
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50 if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY) |
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51 goto X0X0; |
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52 |
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53 { |
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54 register int x; |
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55 register mp_digit *dst, *src; |
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56 |
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57 src = a->dp; |
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58 |
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59 /* now shift the digits */ |
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60 dst = x0.dp; |
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61 for (x = 0; x < B; x++) { |
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62 *dst++ = *src++; |
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63 } |
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64 |
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65 dst = x1.dp; |
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66 for (x = B; x < a->used; x++) { |
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67 *dst++ = *src++; |
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68 } |
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69 } |
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70 |
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71 x0.used = B; |
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72 x1.used = a->used - B; |
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73 |
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74 mp_clamp (&x0); |
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75 |
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76 /* now calc the products x0*x0 and x1*x1 */ |
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77 if (mp_sqr (&x0, &x0x0) != MP_OKAY) |
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78 goto X1X1; /* x0x0 = x0*x0 */ |
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79 if (mp_sqr (&x1, &x1x1) != MP_OKAY) |
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80 goto X1X1; /* x1x1 = x1*x1 */ |
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81 |
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82 /* now calc (x1-x0)**2 */ |
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83 if (mp_sub (&x1, &x0, &t1) != MP_OKAY) |
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84 goto X1X1; /* t1 = x1 - x0 */ |
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85 if (mp_sqr (&t1, &t1) != MP_OKAY) |
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86 goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ |
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87 |
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88 /* add x0y0 */ |
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89 if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) |
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90 goto X1X1; /* t2 = x0x0 + x1x1 */ |
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91 if (mp_sub (&t2, &t1, &t1) != MP_OKAY) |
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92 goto X1X1; /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */ |
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93 |
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94 /* shift by B */ |
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95 if (mp_lshd (&t1, B) != MP_OKAY) |
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96 goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */ |
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97 if (mp_lshd (&x1x1, B * 2) != MP_OKAY) |
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98 goto X1X1; /* x1x1 = x1x1 << 2*B */ |
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99 |
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100 if (mp_add (&x0x0, &t1, &t1) != MP_OKAY) |
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101 goto X1X1; /* t1 = x0x0 + t1 */ |
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102 if (mp_add (&t1, &x1x1, b) != MP_OKAY) |
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103 goto X1X1; /* t1 = x0x0 + t1 + x1x1 */ |
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104 |
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105 err = MP_OKAY; |
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106 |
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107 X1X1:mp_clear (&x1x1); |
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108 X0X0:mp_clear (&x0x0); |
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109 T2:mp_clear (&t2); |
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110 T1:mp_clear (&t1); |
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111 X1:mp_clear (&x1); |
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112 X0:mp_clear (&x0); |
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113 ERR: |
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114 return err; |
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115 } |
