inline long long test(Object* (*make)(int), int (*match)(Object*))
{
size_t a = 0; // Accumulator to make sure compiler doesn't take some loop invariants out
size_t j = 0; // Incremental number for the current path/object combination. Ensures all path get tested.
std::vector<long long> medians(K); // Final verdict of medians for each of the K experiments
std::vector<Object*> objects(N);
std::vector<long long> timings(M);
for (size_t k = 0; k < K; ++k)
{
for (size_t n = 0; n < N; ++n)
objects[n] = make(j++);
for (size_t m = 0; m < M; ++m)
{
time_stamp liStart = get_time_stamp();
for (size_t i = 0; i < N; ++i)
a += match(objects[i]);
time_stamp liFinish = get_time_stamp();
timings[m] = liFinish-liStart;
}
for (size_t n = 0; n < N; ++n)
delete objects[n];
medians[k] = display("test", timings); // We are looking for a median per N iterations
}
std::sort(medians.begin(), medians.end());
return cycles(medians[K/2])/N;
}
LookupTable* Timer::to_ruby(VM* state) {
LookupTable* tbl = LookupTable::create(state);
tbl->store(state, stats::total(state), Integer::from(state, total()));
tbl->store(state, stats::timings(state), Integer::from(state, timings()));
tbl->store(state, stats::max(state), Integer::from(state, max()));
tbl->store(state, stats::min(state), Integer::from(state, min()));
tbl->store(state, stats::average(state), Float::create(state, moving_average()));
return tbl;
}
int main()
{
typedef LaplaceSpherical kernel_type;
kernel_type K(5);
typedef kernel_type::point_type point_type;
typedef kernel_type::charge_type charge_type;
typedef kernel_type::result_type result_type;
FMMOptions opts;
opts.set_mac_theta(.5);
opts.set_max_per_box(125); // optimal ncrit
std::vector<std::pair<unsigned,double>> times;
double tic, toc;
int numBodies = 1000000;
// initialize points
std::vector<point_type> points(numBodies);
for (int k=0; k<numBodies; ++k){
points[k] = point_type(drand(), drand(), drand());
}
// initialize charges
std::vector<charge_type> charges(numBodies);
for (int k=0; k<numBodies; ++k){
charges[k] = drand();
}
// loop in ncrit
for (int ncrit=50; ncrit<=400; ncrit+=50){
opts.set_max_per_box(ncrit);
// create FMM plan
FMM_plan<kernel_type> plan = FMM_plan<kernel_type>(K, points, opts);
// execute FMM
// run 3 times and make an average
int nt = 3; // number of identical runs for timing
std::vector<double> timings(nt);
std::vector<result_type> result(numBodies);
for (int i=0; i<nt; i++){
tic = get_time();
result = plan.execute(charges);
toc = get_time();
timings[i] = toc-tic;
}
double FMM_time = std::accumulate(timings.begin(), timings.end(), 0.0) / timings.size();
std::cout << ncrit << " " << FMM_time << std::endl;
}
return 0;
}
ImbalanceTimings measure_imbalance(MPI_Comm communicator, FUNCTION do_work)
{
enum {CHILDMASK1 = 1};
stk::diag::TimerSet enabledTimerSet(CHILDMASK1);
stk::diag::Timer rootTimer = createRootTimer("totalTestRuntime", enabledTimerSet);
rootTimer.start();
stk::diag::Timer childTimer1("childTimer1", CHILDMASK1, rootTimer);
{
stk::diag::TimeBlockSynchronized timerStartSynchronizedAcrossProcessors(childTimer1, communicator);
do_work();
}
float time = childTimer1.getMetric<stk::diag::WallTime>().getAccumulatedLap(false);
ImbalanceTimings timings(communicator, time);
stk::diag::deleteRootTimer(rootTimer);
return timings;
}
int main(int argc, char **argv)
{
// function pointer via which worker routine is called
double (*worker)(double*, std::size_t) = compute_sum;
std::cout << "# N Time GB/sec" << std::endl;
for (std::size_t N=42; N<1e6; N = (3*N) / 2)
{
std::vector<double> x(N);
for (std::size_t i=0; i<N; ++i)
x[i] = i;
if (argc < 0) // make sure compiler doesn't inline function call
worker = compute_sum2;
double sum = 0;
Timer timer;
std::vector<double> timings(10);
for (std::size_t i=0; i<timings.size(); ++i)
{
timer.start();
for (std::size_t j=0; j<timings.size(); ++j)
{
sum = worker(&(x[0]), N);
if (sum < 0)
std::cerr << "Error: Computed sum negative!" << std::endl;
}
timings[i] = timer.get() / timings.size();
}
std::sort(timings.begin(), timings.end());
double median_time = timings[timings.size()/2];
std::cout << N << " "
<< median_time << " "
<< N * sizeof(double) / median_time / 1e9 << std::endl;
}
return EXIT_SUCCESS;
}
int main(int argc, char**argv) {
assert(argc == 2);
ifstream f(argv[1]);
InstanceData instance = readInstance(f);
cout << "Problem is " << instance.A.nrow << " by " << instance.A.ncol << " with " << instance.A.nzval.size() << " nonzeros\n";
vector<BenchmarkOperation> benchmarks{
{ doPrice, "Matrix-transpose-vector product with non-basic columns" },
{ doPriceHypersparse, "Hyper-sparse matrix-transpose-vector product" },
{ doTwoPassRatioTest, "Two-pass dual ratio test" },
{ doTwoPassRatioTestHypersparse, "Hyper-sparse two-pass dual ratio test" },
{ doUpdateDuals, "Update dual iterate with cost shifting" },
{ doUpdateDualsHypersparse, "Hyper-sparse update dual iterate with cost shifting" },
};
vector<chrono::nanoseconds> timings(benchmarks.size(), chrono::nanoseconds::zero());
int nruns = 0;
while (true) {
IterationData dat = readIteration(f,instance);
if (!dat.valid) break;
for (size_t i = 0; i < benchmarks.size(); i++) {
timings[i] += benchmarks[i].func(instance,dat);
}
nruns++;
}
cout << nruns << " simulated iterations\n";
for (size_t i = 0; i < benchmarks.size(); i++) {
cout << benchmarks[i].name << ": " << timings[i].count()/1000000000. << " sec\n";
}
return 0;
}
void char2_field_tests()
{
BN_CTX *ctx = NULL;
BIGNUM *p, *a, *b;
EC_GROUP *group;
EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
EC_POINT *P, *Q, *R;
BIGNUM *x, *y, *z, *cof;
unsigned char buf[100];
size_t i, len;
int k;
#if 1 /* optional */
ctx = BN_CTX_new();
if (!ctx) ABORT;
#endif
p = BN_new();
a = BN_new();
b = BN_new();
if (!p || !a || !b) ABORT;
if (!BN_hex2bn(&p, "13")) ABORT;
if (!BN_hex2bn(&a, "3")) ABORT;
if (!BN_hex2bn(&b, "1")) ABORT;
group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
* so that the library gets to choose the EC_METHOD */
if (!group) ABORT;
if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT;
{
EC_GROUP *tmp;
tmp = EC_GROUP_new(EC_GROUP_method_of(group));
if (!tmp) ABORT;
if (!EC_GROUP_copy(tmp, group)) ABORT;
EC_GROUP_free(group);
group = tmp;
}
if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
BN_print_fp(stdout, p);
fprintf(stdout, ")\n a = 0x");
BN_print_fp(stdout, a);
fprintf(stdout, "\n b = 0x");
BN_print_fp(stdout, b);
fprintf(stdout, "\n(0x... means binary polynomial)\n");
P = EC_POINT_new(group);
Q = EC_POINT_new(group);
R = EC_POINT_new(group);
if (!P || !Q || !R) ABORT;
if (!EC_POINT_set_to_infinity(group, P)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
buf[0] = 0;
if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
x = BN_new();
y = BN_new();
z = BN_new();
cof = BN_new();
if (!x || !y || !z || !cof) ABORT;
if (!BN_hex2bn(&x, "6")) ABORT;
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
#else
if (!BN_hex2bn(&y, "8")) ABORT;
if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
#endif
if (!EC_POINT_is_on_curve(group, Q, ctx))
{
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
#endif
fprintf(stderr, "Point is not on curve: x = 0x");
BN_print_fp(stderr, x);
fprintf(stderr, ", y = 0x");
BN_print_fp(stderr, y);
fprintf(stderr, "\n");
ABORT;
}
fprintf(stdout, "A cyclic subgroup:\n");
k = 100;
do
{
if (k-- == 0) ABORT;
if (EC_POINT_is_at_infinity(group, P))
fprintf(stdout, " point at infinity\n");
else
{
if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
fprintf(stdout, " x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, ", y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
}
if (!EC_POINT_copy(R, P)) ABORT;
if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
}
while (!EC_POINT_is_at_infinity(group, P));
if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
fprintf(stdout, "Generator as octet string, compressed form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
#endif
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
/* Change test based on whether binary point compression is enabled or not. */
#ifdef OPENSSL_EC_BIN_PT_COMP
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
#endif
fprintf(stdout, "\n");
if (!EC_POINT_invert(group, P, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
/* Curve K-163 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve K-163",
"0800000000000000000000000000000000000000C9",
"1",
"1",
"02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
"0289070FB05D38FF58321F2E800536D538CCDAA3D9",
1,
"04000000000000000000020108A2E0CC0D99F8A5EF",
"2",
163,
C2_K163
);
/* Curve B-163 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve B-163",
"0800000000000000000000000000000000000000C9",
"1",
"020A601907B8C953CA1481EB10512F78744A3205FD",
"03F0EBA16286A2D57EA0991168D4994637E8343E36",
"00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
1,
"040000000000000000000292FE77E70C12A4234C33",
"2",
163,
C2_B163
);
/* Curve K-233 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve K-233",
"020000000000000000000000000000000000000004000000000000000001",
"0",
"1",
"017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
"01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
0,
"008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
"4",
233,
C2_K233
);
/* Curve B-233 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve B-233",
"020000000000000000000000000000000000000004000000000000000001",
"000000000000000000000000000000000000000000000000000000000001",
"0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
"00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
"01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
1,
"01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
"2",
233,
C2_B233
);
/* Curve K-283 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve K-283",
"0800000000000000000000000000000000000000000000000000000000000000000010A1",
"0",
"1",
"0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
"01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
0,
"01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
"4",
283,
C2_K283
);
/* Curve B-283 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve B-283",
"0800000000000000000000000000000000000000000000000000000000000000000010A1",
"000000000000000000000000000000000000000000000000000000000000000000000001",
"027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
"05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
"03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
1,
"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
"2",
283,
C2_B283
);
/* Curve K-409 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve K-409",
"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
"0",
"1",
"0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
"01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
1,
"007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
"4",
409,
C2_K409
);
/* Curve B-409 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve B-409",
"02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
"015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
"0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
1,
"010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
"2",
409,
C2_B409
);
/* Curve K-571 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve K-571",
"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
"0",
"1",
"026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
"0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
0,
"020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
"4",
571,
C2_K571
);
/* Curve B-571 (FIPS PUB 186-2, App. 6) */
CHAR2_CURVE_TEST
(
"NIST curve B-571",
"80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
"0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
"037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
1,
"03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
"2",
571,
C2_B571
);
/* more tests using the last curve */
if (!EC_POINT_copy(Q, P)) ABORT;
if (EC_POINT_is_at_infinity(group, Q)) ABORT;
if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
{
const EC_POINT *points[3];
const BIGNUM *scalars[3];
if (EC_POINT_is_at_infinity(group, Q)) ABORT;
points[0] = Q;
points[1] = Q;
points[2] = Q;
if (!BN_add(y, z, BN_value_one())) ABORT;
if (BN_is_odd(y)) ABORT;
if (!BN_rshift1(y, y)) ABORT;
scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
scalars[1] = y;
fprintf(stdout, "combined multiplication ...");
fflush(stdout);
/* z is still the group order */
if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
if (!BN_add(z, z, y)) ABORT;
BN_set_negative(z, 1);
scalars[0] = y;
scalars[1] = z; /* z = -(order + y) */
if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
if (!BN_add(z, x, y)) ABORT;
BN_set_negative(z, 1);
scalars[0] = x;
scalars[1] = y;
scalars[2] = z; /* z = -(x+y) */
if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
fprintf(stdout, " ok\n\n");
}
#if 0
timings(C2_K163, TIMING_BASE_PT, ctx);
timings(C2_K163, TIMING_RAND_PT, ctx);
timings(C2_K163, TIMING_SIMUL, ctx);
timings(C2_B163, TIMING_BASE_PT, ctx);
timings(C2_B163, TIMING_RAND_PT, ctx);
timings(C2_B163, TIMING_SIMUL, ctx);
timings(C2_K233, TIMING_BASE_PT, ctx);
timings(C2_K233, TIMING_RAND_PT, ctx);
timings(C2_K233, TIMING_SIMUL, ctx);
timings(C2_B233, TIMING_BASE_PT, ctx);
timings(C2_B233, TIMING_RAND_PT, ctx);
timings(C2_B233, TIMING_SIMUL, ctx);
timings(C2_K283, TIMING_BASE_PT, ctx);
timings(C2_K283, TIMING_RAND_PT, ctx);
timings(C2_K283, TIMING_SIMUL, ctx);
timings(C2_B283, TIMING_BASE_PT, ctx);
timings(C2_B283, TIMING_RAND_PT, ctx);
timings(C2_B283, TIMING_SIMUL, ctx);
timings(C2_K409, TIMING_BASE_PT, ctx);
timings(C2_K409, TIMING_RAND_PT, ctx);
timings(C2_K409, TIMING_SIMUL, ctx);
timings(C2_B409, TIMING_BASE_PT, ctx);
timings(C2_B409, TIMING_RAND_PT, ctx);
timings(C2_B409, TIMING_SIMUL, ctx);
timings(C2_K571, TIMING_BASE_PT, ctx);
timings(C2_K571, TIMING_RAND_PT, ctx);
timings(C2_K571, TIMING_SIMUL, ctx);
timings(C2_B571, TIMING_BASE_PT, ctx);
timings(C2_B571, TIMING_RAND_PT, ctx);
timings(C2_B571, TIMING_SIMUL, ctx);
#endif
if (ctx)
BN_CTX_free(ctx);
BN_free(p); BN_free(a); BN_free(b);
EC_GROUP_free(group);
EC_POINT_free(P);
EC_POINT_free(Q);
EC_POINT_free(R);
BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
if (C2_K163) EC_GROUP_free(C2_K163);
if (C2_B163) EC_GROUP_free(C2_B163);
if (C2_K233) EC_GROUP_free(C2_K233);
if (C2_B233) EC_GROUP_free(C2_B233);
if (C2_K283) EC_GROUP_free(C2_K283);
if (C2_B283) EC_GROUP_free(C2_B283);
if (C2_K409) EC_GROUP_free(C2_K409);
if (C2_B409) EC_GROUP_free(C2_B409);
if (C2_K571) EC_GROUP_free(C2_K571);
if (C2_B571) EC_GROUP_free(C2_B571);
}
void prime_field_tests()
{
BN_CTX *ctx = NULL;
BIGNUM *p, *a, *b;
EC_GROUP *group;
EC_GROUP *P_160 = NULL, *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
EC_POINT *P, *Q, *R;
BIGNUM *x, *y, *z;
unsigned char buf[100];
size_t i, len;
int k;
#if 1 /* optional */
ctx = BN_CTX_new();
if (!ctx) ABORT;
#endif
p = BN_new();
a = BN_new();
b = BN_new();
if (!p || !a || !b) ABORT;
if (!BN_hex2bn(&p, "17")) ABORT;
if (!BN_hex2bn(&a, "1")) ABORT;
if (!BN_hex2bn(&b, "1")) ABORT;
group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
* so that the library gets to choose the EC_METHOD */
if (!group) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
{
EC_GROUP *tmp;
tmp = EC_GROUP_new(EC_GROUP_method_of(group));
if (!tmp) ABORT;
if (!EC_GROUP_copy(tmp, group)) ABORT;
EC_GROUP_free(group);
group = tmp;
}
if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
BN_print_fp(stdout, p);
fprintf(stdout, ")\n a = 0x");
BN_print_fp(stdout, a);
fprintf(stdout, "\n b = 0x");
BN_print_fp(stdout, b);
fprintf(stdout, "\n");
P = EC_POINT_new(group);
Q = EC_POINT_new(group);
R = EC_POINT_new(group);
if (!P || !Q || !R) ABORT;
if (!EC_POINT_set_to_infinity(group, P)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
buf[0] = 0;
if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
x = BN_new();
y = BN_new();
z = BN_new();
if (!x || !y || !z) ABORT;
if (!BN_hex2bn(&x, "D")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, Q, ctx))
{
if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
fprintf(stderr, "Point is not on curve: x = 0x");
BN_print_fp(stderr, x);
fprintf(stderr, ", y = 0x");
BN_print_fp(stderr, y);
fprintf(stderr, "\n");
ABORT;
}
fprintf(stdout, "A cyclic subgroup:\n");
k = 100;
do
{
if (k-- == 0) ABORT;
if (EC_POINT_is_at_infinity(group, P))
fprintf(stdout, " point at infinity\n");
else
{
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, " x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, ", y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
}
if (!EC_POINT_copy(R, P)) ABORT;
if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
#if 0 /* optional */
{
EC_POINT *points[3];
points[0] = R;
points[1] = Q;
points[2] = P;
if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
}
#endif
}
while (!EC_POINT_is_at_infinity(group, P));
if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
fprintf(stdout, "Generator as octect string, compressed form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, ", Y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, ", Z = 0x");
BN_print_fp(stdout, z);
fprintf(stdout, "\n");
if (!EC_POINT_invert(group, P, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
/* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
* -- not a NIST curve, but commonly used */
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, "\nSEC2 curve secp160r1 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
if (0 != BN_cmp(y, z)) ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 160) ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, " ok\n");
if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
if (!EC_GROUP_copy(P_160, group)) ABORT;
/* Curve P-192 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
if (0 != BN_cmp(y, z)) ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 192) ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
#if 0
if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, " ok\n");
if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
if (!EC_GROUP_copy(P_192, group)) ABORT;
/* Curve P-224 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
if (0 != BN_cmp(y, z)) ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 224) ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
#if 0
if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, " ok\n");
if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
if (!EC_GROUP_copy(P_224, group)) ABORT;
/* Curve P-256 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
"84F3B9CAC2FC632551")) ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
if (0 != BN_cmp(y, z)) ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 256) ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
#if 0
if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, " ok\n");
if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
if (!EC_GROUP_copy(P_256, group)) ABORT;
/* Curve P-384 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
"120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
"9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
"7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
if (0 != BN_cmp(y, z)) ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 384) ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
#if 0
if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, " ok\n");
if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
if (!EC_GROUP_copy(P_384, group)) ABORT;
/* Curve P-521 (FIPS PUB 186-2, App. 6) */
if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
"315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
"DF883D2C34F1EF451FD46B503F00")) ABORT;
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
"B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
"3C1856A429BF97E7E31C2E5BD66")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
"FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
"C9B8899C47AEBB6FB71E91386409")) ABORT;
if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
BN_print_fp(stdout, x);
fprintf(stdout, "\n y = 0x");
BN_print_fp(stdout, y);
fprintf(stdout, "\n");
/* G_y value taken from the standard: */
if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
"B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
"7086A272C24088BE94769FD16650")) ABORT;
if (0 != BN_cmp(y, z)) ABORT;
fprintf(stdout, "verify degree ...");
if (EC_GROUP_get_degree(group) != 521) ABORT;
fprintf(stdout, " ok\n");
fprintf(stdout, "verify group order ...");
fflush(stdout);
if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
#if 0
if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
fprintf(stdout, " ok\n");
if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
if (!EC_GROUP_copy(P_521, group)) ABORT;
/* more tests using the last curve */
if (!EC_POINT_copy(Q, P)) ABORT;
if (EC_POINT_is_at_infinity(group, Q)) ABORT;
if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
{
const EC_POINT *points[3];
const BIGNUM *scalars[3];
if (EC_POINT_is_at_infinity(group, Q)) ABORT;
points[0] = Q;
points[1] = Q;
points[2] = Q;
if (!BN_add(y, z, BN_value_one())) ABORT;
if (BN_is_odd(y)) ABORT;
if (!BN_rshift1(y, y)) ABORT;
scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
scalars[1] = y;
fprintf(stdout, "combined multiplication ...");
fflush(stdout);
/* z is still the group order */
if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
if (!BN_add(z, z, y)) ABORT;
BN_set_negative(z, 1);
scalars[0] = y;
scalars[1] = z; /* z = -(order + y) */
if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
fprintf(stdout, ".");
fflush(stdout);
if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
if (!BN_add(z, x, y)) ABORT;
BN_set_negative(z, 1);
scalars[0] = x;
scalars[1] = y;
scalars[2] = z; /* z = -(x+y) */
if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
if (!EC_POINT_is_at_infinity(group, P)) ABORT;
fprintf(stdout, " ok\n\n");
}
#if 0
timings(P_160, TIMING_BASE_PT, ctx);
timings(P_160, TIMING_RAND_PT, ctx);
timings(P_160, TIMING_SIMUL, ctx);
timings(P_192, TIMING_BASE_PT, ctx);
timings(P_192, TIMING_RAND_PT, ctx);
timings(P_192, TIMING_SIMUL, ctx);
timings(P_224, TIMING_BASE_PT, ctx);
timings(P_224, TIMING_RAND_PT, ctx);
timings(P_224, TIMING_SIMUL, ctx);
timings(P_256, TIMING_BASE_PT, ctx);
timings(P_256, TIMING_RAND_PT, ctx);
timings(P_256, TIMING_SIMUL, ctx);
timings(P_384, TIMING_BASE_PT, ctx);
timings(P_384, TIMING_RAND_PT, ctx);
timings(P_384, TIMING_SIMUL, ctx);
timings(P_521, TIMING_BASE_PT, ctx);
timings(P_521, TIMING_RAND_PT, ctx);
timings(P_521, TIMING_SIMUL, ctx);
#endif
if (ctx)
BN_CTX_free(ctx);
BN_free(p); BN_free(a); BN_free(b);
EC_GROUP_free(group);
EC_POINT_free(P);
EC_POINT_free(Q);
EC_POINT_free(R);
BN_free(x); BN_free(y); BN_free(z);
if (P_160) EC_GROUP_free(P_160);
if (P_192) EC_GROUP_free(P_192);
if (P_224) EC_GROUP_free(P_224);
if (P_256) EC_GROUP_free(P_256);
if (P_384) EC_GROUP_free(P_384);
if (P_521) EC_GROUP_free(P_521);
}
int main() {
std::vector< std::vector<double> > timings(17);
for (size_t r=0 ; r<R ; ++r) {
OneBase a;
OneLevel1 b;
OneLevel2 c;
OneLevel3 d;
OneBase* ones[] = {&a, &b, &c, &d};
ticks start, end;
double timed = 0.0;
size_t res = 0;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel3 *a = reinterpret_cast<OneLevel3*>(ones[3]);
res += a->getType();
}
end = getticks();
timed = elapsed(end, start);
timings[0].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
if (ones[2]->getType() == T_ONE_LEVEL2) {
OneLevel2 *a = reinterpret_cast<OneLevel2*>(ones[2]);
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[1].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneBase *a = dynamic_cast<OneBase*>(ones[0]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[2].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel1 *a = dynamic_cast<OneLevel1*>(ones[1]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[3].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel2 *a = dynamic_cast<OneLevel2*>(ones[2]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[4].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel3 *a = dynamic_cast<OneLevel3*>(ones[3]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[5].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneBase *a = dynamic_cast<OneBase*>(ones[1]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[6].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneBase *a = dynamic_cast<OneBase*>(ones[2]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[7].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneBase *a = dynamic_cast<OneBase*>(ones[3]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[8].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel1 *a = dynamic_cast<OneLevel1*>(ones[2]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[9].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel1 *a = dynamic_cast<OneLevel1*>(ones[3]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[10].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
OneLevel2 *a = dynamic_cast<OneLevel2*>(ones[3]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[11].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
TwoBase *a = dynamic_cast<TwoBase*>(ones[0]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[12].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
TwoBase *a = dynamic_cast<TwoBase*>(ones[1]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[13].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
TwoBase *a = dynamic_cast<TwoBase*>(ones[2]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[14].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
TwoBase *a = dynamic_cast<TwoBase*>(ones[3]);
if (a) {
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[15].push_back(timed);
std::cerr << res << std::endl;
res = 0;
start = getticks();
for (size_t i=0 ; i<N ; ++i) {
if (ones[3]->type == T_ONE_LEVEL3) {
OneLevel3 *a = reinterpret_cast<OneLevel3*>(ones[3]);
res += a->getType();
}
}
end = getticks();
timed = elapsed(end, start);
timings[16].push_back(timed);
std::cerr << res << std::endl;
std::cerr << std::endl;
}
std::cout << "reinterpret_cast known-type: ";
PrintStats(timings[0]);
std::cout << std::endl;
std::cout << "virtual function + reinterpret_cast: ";
PrintStats(timings[1]);
std::cout << std::endl;
std::cout << "member variable + reinterpret_cast: ";
PrintStats(timings[16]);
std::cout << std::endl;
std::cout << "dynamic_cast same-type-base success: ";
PrintStats(timings[2]);
std::cout << std::endl;
std::cout << "dynamic_cast same-type-level1 success: ";
PrintStats(timings[3]);
std::cout << std::endl;
std::cout << "dynamic_cast same-type-level2 success: ";
PrintStats(timings[4]);
std::cout << std::endl;
std::cout << "dynamic_cast same-type-level3 success: ";
PrintStats(timings[5]);
std::cout << std::endl;
std::cout << "dynamic_cast level1-to-base success: ";
PrintStats(timings[6]);
std::cout << std::endl;
std::cout << "dynamic_cast level2-to-base success: ";
PrintStats(timings[7]);
std::cout << std::endl;
std::cout << "dynamic_cast level3-to-base success: ";
PrintStats(timings[8]);
std::cout << std::endl;
std::cout << "dynamic_cast level2-to-level1 success: ";
PrintStats(timings[9]);
std::cout << std::endl;
std::cout << "dynamic_cast level3-to-level1 success: ";
PrintStats(timings[10]);
std::cout << std::endl;
std::cout << "dynamic_cast level3-to-level2 success: ";
PrintStats(timings[11]);
std::cout << std::endl;
std::cout << "dynamic_cast onebase-to-twobase fail: ";
PrintStats(timings[12]);
std::cout << std::endl;
std::cout << "dynamic_cast onelevel1-to-twobase fail: ";
PrintStats(timings[13]);
std::cout << std::endl;
std::cout << "dynamic_cast onelevel2-to-twobase fail: ";
PrintStats(timings[14]);
std::cout << std::endl;
std::cout << "dynamic_cast onelevel3-to-twobase fail: ";
PrintStats(timings[15]);
std::cout << std::endl;
std::cout << std::endl;
}
