75 lines
3.2 KiB
C
75 lines
3.2 KiB
C
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/* LibTomPoly, Polynomial Basis Math -- Tom St Denis
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*
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* LibTomPoly is a public domain library that provides
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* polynomial basis arithmetic support. It relies on
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* LibTomMath for large integer support.
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*
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* This library is free for all purposes without any
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* express guarantee that it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://poly.libtomcrypt.org
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*/
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#include <tompoly.h>
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/* Extended euclidean algorithm of (a, b) produces
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a*u1 + b*u2 = u3
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*/
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int pb_exteuclid(pb_poly *a, pb_poly *b, pb_poly *U1, pb_poly *U2, pb_poly *U3)
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{
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pb_poly u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
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int err;
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if ((err = pb_init_multi(&(b->characteristic),
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&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
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return err;
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}
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/* initialize, (u1,u2,u3) = (1,0,a) */
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mp_set(&(u1.terms[0]), 1); u1.used = 1;
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if ((err = pb_copy(a, &u3)) != MP_OKAY) { goto _ERR; }
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/* initialize, (v1,v2,v3) = (0,1,b) */
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mp_set(&(v2.terms[0]), 1); v2.used = 1;
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if ((err = pb_copy(b, &v3)) != MP_OKAY) { goto _ERR; }
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/* loop while v3 != 0 */
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while (v3.used > 0) {
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/* q = u3/v3 */
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if ((err = pb_div(&u3, &v3, &q, NULL)) != MP_OKAY) { goto _ERR; }
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/* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
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if ((err = pb_mul(&v1, &q, &tmp)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_sub(&u1, &tmp, &t1)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_mul(&v2, &q, &tmp)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_sub(&u2, &tmp, &t2)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_mul(&v3, &q, &tmp)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_sub(&u3, &tmp, &t3)) != MP_OKAY) { goto _ERR; }
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/* (u1,u2,u3) = (v1,v2,v3) */
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if ((err = pb_copy(&v1, &u1)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_copy(&v2, &u2)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_copy(&v3, &u3)) != MP_OKAY) { goto _ERR; }
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/* (v1,v2,v3) = (t1,t2,t3) */
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if ((err = pb_copy(&t1, &v1)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_copy(&t2, &v2)) != MP_OKAY) { goto _ERR; }
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if ((err = pb_copy(&t3, &v3)) != MP_OKAY) { goto _ERR; }
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}
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/* reduce U3 to monic but we have to mangle all three to remain consistent */
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pb_zero(&v1);
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if ((err = mp_copy(&(u3.terms[u3.used-1]), &(v1.terms[0]))) != MP_OKAY) { goto _ERR; }
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v1.used = 1;
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/* copy result out */
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if (U1 != NULL) { if ((err = pb_div(&u1, &v1, U1, NULL)) != MP_OKAY) { goto _ERR; }}
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if (U2 != NULL) { if ((err = pb_div(&u2, &v1, U2, NULL)) != MP_OKAY) { goto _ERR; }}
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if (U3 != NULL) { if ((err = pb_div(&u3, &v1, U3, NULL)) != MP_OKAY) { goto _ERR; }}
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err = MP_OKAY;
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_ERR: pb_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
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return err;
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}
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