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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 /* Extended euclidean algorithm of (a, b) produces |
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18 a*u1 + b*u2 = u3 |
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19 */ |
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20 int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3) |
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21 { |
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22 mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp; |
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23 int err; |
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24 |
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25 if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) { |
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26 return err; |
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27 } |
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28 |
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29 /* initialize, (u1,u2,u3) = (1,0,a) */ |
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30 mp_set(&u1, 1); |
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31 if ((err = mp_copy(a, &u3)) != MP_OKAY) { goto _ERR; } |
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32 |
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33 /* initialize, (v1,v2,v3) = (0,1,b) */ |
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34 mp_set(&v2, 1); |
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35 if ((err = mp_copy(b, &v3)) != MP_OKAY) { goto _ERR; } |
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36 |
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37 /* loop while v3 != 0 */ |
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38 while (mp_iszero(&v3) == MP_NO) { |
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39 /* q = u3/v3 */ |
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40 if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; } |
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41 |
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42 /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */ |
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43 if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; } |
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44 if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; } |
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45 if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; } |
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46 if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; } |
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47 if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; } |
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48 if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; } |
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49 |
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50 /* (u1,u2,u3) = (v1,v2,v3) */ |
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51 if ((err = mp_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; } |
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52 if ((err = mp_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; } |
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53 if ((err = mp_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; } |
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54 |
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55 /* (v1,v2,v3) = (t1,t2,t3) */ |
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56 if ((err = mp_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; } |
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57 if ((err = mp_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; } |
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58 if ((err = mp_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; } |
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59 } |
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60 |
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61 /* copy result out */ |
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62 if (U1 != NULL) { mp_exch(U1, &u1); } |
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63 if (U2 != NULL) { mp_exch(U2, &u2); } |
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64 if (U3 != NULL) { mp_exch(U3, &u3); } |
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65 |
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66 err = MP_OKAY; |
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67 _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); |
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68 return err; |
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69 } |
