//============================================ // 楕円曲線の演算テスト //============================================ void test_arithmetic_operation(const EC_GROUP ec) { int i; unsigned long long int t1, t2; EC_POINT a, b, c, d; Element dx, dy; mpz_t scalar; //------------------- // init //------------------- point_init(a, ec); point_init(b, ec); point_init(c, ec); point_init(d, ec); //------------------- // random //------------------- point_random(a); assert(point_is_on_curve(a)); t1 = rdtsc(); for (i = 0; i < M; i++) { point_random(a); } t2 = rdtsc(); printf("point random: %.2lf [clock]\n", (double)(t2 - t1) / M); //------------------- // add/dob //------------------- point_add(b, b, a); point_add(c, b, c); assert(point_cmp(b, a) == 0); assert(point_cmp(c, b) == 0); point_set_infinity(d); point_dob(d, d); assert(point_is_infinity(d)); point_set_str(a, "[6D2E4115FA177379A504A0EE4EF53767DE51C6364AAB69D4064529EC1FD047A 635B2C858AA4F4A3DB8AA17A588B037CAFFD36678F76E3F3369DFC90C6878C7,193E877C82EFCA81EC2815906630B837BBC6976CC8A7958E6A40D1B190FF2E5F E8A77E88AFCEE9F806DC15BF50EADD138320F1A5A87E78DDE86FA7A867300D]"); point_set_str(b, "[1A8F5DAB09EE4290F95FE4C824C153E355D55B6CF94B998C6203FEC3D81377CF 15A19F2704C4BDBAAE39A5E26772A3E4E7EC7A9E205651F8822298766DE044FF,1C566EB3917F06B05E0A786BD8030CAFCCDB62864DD0E2A22A9B6817B310FD53 6A0927BB33EB263F45CAB921A20E67A1BD8A791D6EB0415AC92C9B1F74D16D1]"); point_set_str(d, "[143D414F99AA18C844B331064C9DD66363EBA3D852250CBCF8C9D4B33E0C4C1C 225865D85EC7A34647CA55E026BD1FA201E0C4E8C66F7A43E69AF708F410A0FF,FACA1388C034CF614A72E06EE60DEDC4880CDBD368E5BEC2795130B266FFB9E 1681217E50705AB9A21FEB62E0BF9A5657EB27C3AED3323FE9C57058358735A9]"); point_add(c, a, b); assert(point_cmp(c, d) == 0); t1 = rdtsc(); for (i = 0; i < N; i++) { point_add(c, a, b); } t2 = rdtsc(); printf("point add: %.2lf [clock]\n", (double)(t2 - t1) / N); element_init(dx, ec->field); element_init(dy, ec->field); element_set_str(dx, "33F550F9A63EF53C786BF7BDFDAB1538CD76A3FCED3C9DBC3307DD4F354775A C814AE99C91C71845F0B51E4349520908E48C70181313D70C05F6ED24EC1F36"); element_set_str(dy, "3766ED0DD7C988DB76770081A298DAA924D0E3279726F9B5504129AFA3E57B9 520CE8A563F88AF882AB99086BFDBBDCEF9DE65879AB234DFF5AAFD5BEE7E4F"); point_set_xy(d, dx, dy); point_dob(c, a); assert(point_cmp(c, d) == 0); t1 = rdtsc(); for (i = 0; i < N; i++) { point_dob(c, a); } t2 = rdtsc(); printf("point dob: %.2lf [clock]\n", (double)(t2 - t1) / N); element_clear(dx); element_clear(dy); //------------------ // neg/sub //------------------ point_neg(c, a); point_add(d, a, c); point_sub(b, a, a); assert(point_is_infinity(d)); assert(point_is_infinity(b)); //------------------- // mul //------------------- mpz_init(scalar); mpz_set(scalar, ec->order); for (i = 0; i < 100; i++) { point_random(a); point_mul(b, scalar, a); ec_bn254_fp2_mul_end(c, scalar, a); assert(point_is_infinity(b)); assert(point_cmp(c, b) == 0); } t1 = rdtsc(); for (i = 0; i < M; i++) { point_mul(b, scalar, a); } t2 = rdtsc(); printf("point mul with endomorphism: %.2lf [clock]\n", (double)(t2 - t1) / M); t1 = rdtsc(); for (i = 0; i < M; i++) { ec_bn254_fp2_mul(b, scalar, a); } t2 = rdtsc(); printf("point mul with binary method: %.2lf [clock]\n", (double)(t2 - t1) / M); mpz_clear(scalar); //------------------- // clear //------------------- point_clear(a); point_clear(b); point_clear(c); point_clear(d); }
void IBE_setup(params_t params, byte_string_t master, int k, int qk, char *id) /* generate system parameters * k = number of bits in p (should be at least 512) * qk = number of bits in q (size of subgroup, 160 is typical) * id = system ID */ { mpz_t p, q, r; mpz_t x; point_ptr P; int solinasa, solinasb; int kqk = k - qk - 4; //lose 4 bits since 12 is a 4-bit no. unsigned int seed; mpz_init(p); mpz_init(q); mpz_init(r); mpz_init(x); //find random k-bit prime p such that //p = 2 mod 3 and q = (p+1)/12r is prime as well for some r //now also want q to be a Solinas prime //we use rand() to help us find one: should be ok crypto_rand_bytes((unsigned char *) &seed, sizeof(int)); srand(seed); for(;;) { //once q was just a random qk-bit prime //now it must be a Solinas one mpz_set_ui(q, 0); solinasa = qk - 1; mpz_setbit(q, solinasa); mpz_set_ui(r, 0); solinasb = rand() % qk; mpz_setbit(r, solinasb); if (rand() % 2) { mpz_add(q, q, r); } else { mpz_sub(q, q, r); solinasb = -solinasb; } mpz_set_ui(r, 1); if (rand() % 2) { mpz_add(q, q, r); } else { mpz_sub(q, q, r); solinasa = -solinasa; } if (!mpz_probab_prime_p(q, 10)) continue; mympz_randomb(r, kqk); //p = q * r mpz_mul(p, q, r); //r = (((p << 1) + p) << 2) (= 12p) mpz_mul_2exp(r, p, 1); mpz_add(r, r, p); mpz_mul_2exp(r, r, 2); //p = r - 1 mpz_set_ui(p, 1); mpz_sub(p, r, p); if (mpz_probab_prime_p(p, 10)) break; } //pick master key x from F_q mympz_randomm(x, q); byte_string_set_mpz(master, x); mpz_init(params->p); mpz_init(params->q); mpz_set(params->p, p); mpz_set(params->q, q); initpq(params); //pick random point P of order q from E/F_p point_init(params->P); P = params->P; do { point_random(P, params->curve); point_make_order_q(P, params); } while (P->infinity); point_init(params->Ppub); point_mul(params->Ppub, x, P, params->curve); point_mul_preprocess(P, params->curve); miller_cache_init(params->Ppub_mc, params->curve); tate_preprocess(params->Ppub_mc, params->Ppub, params->curve); point_init(params->PhiPpub); point_Phi(params->PhiPpub, params->Ppub, params); params->id = (char *) malloc(strlen(id) + 1); strcpy(params->id, id); params->sharet = params->sharen = 0; params->version = (char *) malloc(strlen(IBE_VERSION) + 1); strcpy(params->version, IBE_VERSION); mpz_clear(p); mpz_clear(q); mpz_clear(r); mpz_clear(x); }
//============================================ // 楕円曲線の入出力テスト //============================================ void test_io(const EC_GROUP ec) { int i; unsigned long long int t1, t2; EC_POINT P, Q, R; size_t osize; unsigned char os[130]; char str[262]; point_init(P, ec); point_init(Q, ec); point_init(R, ec); //--------------------- // octet string //--------------------- point_set_infinity(R); point_to_oct(os, &osize, R); point_from_oct(Q, os, osize); assert(point_is_infinity(Q)); for (i = 0; i < 100; i++) { point_random(P); point_to_oct(os, &osize, P); point_from_oct(Q, os, osize); assert(point_cmp(P, Q) == 0); } t1 = rdtsc(); for (i = 0; i < N; i++) { point_to_oct(os, &osize, P); } t2 = rdtsc(); printf("point to octet string: %.2lf [clock]\n", (double)(t2 - t1) / N); t1 = rdtsc(); for (i = 0; i < N; i++) { point_from_oct(Q, os, osize); } t2 = rdtsc(); printf("point from octet string: %.2lf [clock]\n", (double)(t2 - t1) / N); //--------------------- // string //--------------------- point_set_infinity(R); point_get_str(str, R); point_set_str(Q, str); assert(point_is_infinity(Q)); for (i = 0; i < 100; i++) { point_get_str(str, P); point_set_str(Q, str); assert(point_cmp(P, Q) == 0); } t1 = rdtsc(); for (i = 0; i < N; i++) { point_get_str(str, P); } t2 = rdtsc(); printf("point get string: %.2lf [clock]\n", (double)(t2 - t1) / N); t1 = rdtsc(); for (i = 0; i < N; i++) { point_set_str(Q, str); } t2 = rdtsc(); printf("point set string: %.2lf [clock]\n", (double)(t2 - t1) / N); point_clear(P); point_clear(Q); point_clear(R); }