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/*
Hess ID-based signature.
Based on papers "F. Hess. Efficient Identity Based Signature Schemes Based on Pairings. SAC 2002, LNCS 2595, Springer-Verlag, 2000"
Contributed by Dmitry Kosolapov.
*/
#include <pbc.h>
#include <pbc_test.h>
int main(int argc, char **argv) {
pairing_t pairing;
double time1, time2;
pbc_demo_pairing_init(pairing, argc, argv);
element_t Qid, P, P1, Ppub, s, k, Did, r, v, u, t1, t3, t4, t5, t6, t7, t8;
mpz_t t2;
if (!pairing_is_symmetric(pairing)) pbc_die("pairing must be symmetric");
mpz_init(t2);
element_init_G1(P, pairing);
element_init_G1(P1, pairing);
element_init_G1(Qid, pairing);
element_init_G1(Did, pairing);
element_init_G1(Ppub, pairing);
element_init_G1(t4, pairing);
element_init_G1(t5, pairing);
element_init_G1(u, pairing);
element_init_Zr(s, pairing);
element_init_Zr(k, pairing);
element_init_Zr(v, pairing);
element_init_Zr(t3, pairing);
element_init_Zr(t8, pairing);
element_init_GT(r, pairing);
element_init_GT(t1, pairing);
element_init_GT(t6, pairing);
element_init_GT(t7, pairing);
time1 = pbc_get_time();
printf("Hess ID-based signature protocol\n");
printf("KEYGEN\n");
element_random(P);
element_random(s);
element_random(Qid);
element_mul_zn(Ppub, P, s);
element_mul_zn(Did, Qid, s);
element_printf("Qid = %B\n", Qid);
element_printf("P = %B\n", P);
element_printf("Ppub = %B\n", Ppub);
printf("SIGN\n");
element_random(P1);
element_random(k);
element_pairing(t1, P1, P);
element_pow_zn(r, t1, k);
element_to_mpz(t2, r);
//h3=h(m)*mpz(r);
element_from_hash(t3, "Message", 7);
element_mul_mpz(v, t3, t2);
element_mul_zn(t4, Did, v);
element_mul_zn(t5, P1, k);
element_add(u, t4, t5);
printf("Signature of message \"Message\" is:\n");
element_printf("u = %B\n", u);
element_printf("v = %B\n", v);
printf("VERIFY\n");
element_pairing(t6, u, P);
element_neg(Ppub, Ppub);
element_pairing(t7, Qid, Ppub);
element_pow_zn(t7, t7, v);
element_mul(r, t6, t7);
element_to_mpz(t2, r);
element_from_hash(t3, "Message", 7);
element_mul_mpz(t8, t3, t2);
element_printf("h3(m,r) = %B\n", t8);
element_printf("v = %B\n", v);
if (!element_cmp(t8, v)) {
printf("Signature is valid!\n");
} else {
printf("Signature is invalid!\n");
}
time2 = pbc_get_time();
printf("All time = %fs\n", time2 - time1);
element_clear(P);
element_clear(P1);
element_clear(Qid);
element_clear(Did);
element_clear(Ppub);
element_clear(t4);
element_clear(t5);
element_clear(u);
element_clear(s);
element_clear(k);
element_clear(v);
element_clear(t3);
element_clear(t8);
element_clear(r);
element_clear(t1);
element_clear(t6);
element_clear(t7);
pairing_clear(pairing);
return 0;
}
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