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arith_tests-p751.c
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/********************************************************************************************
* SIDH: an efficient supersingular isogeny cryptography library
*
* Abstract: testing code for field arithmetic, elliptic curve and isogeny functions
*********************************************************************************************/
#include "../src/config.h"
#include "../src/P751/P751_internal.h"
#include "test_extras.h"
#include <stdio.h>
// Benchmark and test parameters
#if defined(OPTIMIZED_GENERIC_IMPLEMENTATION) || (TARGET == TARGET_ARM)
#define BENCH_LOOPS 100 // Number of iterations per bench
#define SMALL_BENCH_LOOPS 100 // Number of iterations per bench
#define TEST_LOOPS 10 // Number of iterations per test
#else
#define BENCH_LOOPS 100000
#define SMALL_BENCH_LOOPS 10000
#define TEST_LOOPS 100
#endif
bool fp_test()
{ // Tests for the field arithmetic
bool OK = true;
int n, passed;
felm_t a, b, c, d, e, f, ma, mb, mc, md, me, mf;
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
printf("Testing field arithmetic over GF(p751): \n\n");
// Field addition over the prime p751
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fprandom751_test(a); fprandom751_test(b); fprandom751_test(c); fprandom751_test(d); fprandom751_test(e); fprandom751_test(f);
fpadd751(a, b, d); fpadd751(d, c, e); // e = (a+b)+c
fpadd751(b, c, d); fpadd751(d, a, f); // f = a+(b+c)
fpcorrection751(e);
fpcorrection751(f);
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
fpadd751(a, b, d); // d = a+b
fpadd751(b, a, e); // e = b+a
fpcorrection751(d);
fpcorrection751(e);
if (compare_words(d, e, NWORDS_FIELD)!=0) { passed=0; break; }
fpzero751(b);
fpadd751(a, b, d); // d = a+0
if (compare_words(a, d, NWORDS_FIELD)!=0) { passed=0; break; }
fpzero751(b);
fpcopy751(a, d);
fpneg751(d);
fpadd751(a, d, e); // e = a+(-a)
fpcorrection751(e);
if (compare_words(e, b, NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p) addition tests ............................................ PASSED");
else { printf(" GF(p) addition tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Field subtraction over the prime p751
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fprandom751_test(a); fprandom751_test(b); fprandom751_test(c); fprandom751_test(d); fprandom751_test(e); fprandom751_test(f);
fpsub751(a, b, d); fpsub751(d, c, e); // e = (a-b)-c
fpadd751(b, c, d); fpsub751(a, d, f); // f = a-(b+c)
fpcorrection751(e);
fpcorrection751(f);
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
fpsub751(a, b, d); // d = a-b
fpsub751(b, a, e);
fpneg751(e); // e = -(b-a)
fpcorrection751(d);
fpcorrection751(e);
if (compare_words(d, e, NWORDS_FIELD)!=0) { passed=0; break; }
fpzero751(b);
fpsub751(a, b, d); // d = a-0
if (compare_words(a, d, NWORDS_FIELD)!=0) { passed=0; break; }
fpzero751(b);
fpcopy751(a, d);
fpsub751(a, d, e); // e = a+(-a)
fpcorrection751(e);
if (compare_words(e, b, NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p) subtraction tests ......................................... PASSED");
else { printf(" GF(p) subtraction tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Field multiplication over the prime p751
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fprandom751_test(a); fprandom751_test(b); fprandom751_test(c);
fprandom751_test(ma); fprandom751_test(mb); fprandom751_test(mc); fprandom751_test(md); fprandom751_test(me); fprandom751_test(mf);
to_mont(a, ma);
fpcopy751(ma, mc);
from_mont(mc, c);
if (compare_words(a, c, NWORDS_FIELD)!=0) {
passed=0; break; }
to_mont(a, ma); to_mont(b, mb); to_mont(c, mc);
fpmul751_mont(ma, mb, md); fpmul751_mont(md, mc, me); // e = (a*b)*c
fpmul751_mont(mb, mc, md); fpmul751_mont(md, ma, mf); // f = a*(b*c)
from_mont(me, e);
from_mont(mf, f);
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
to_mont(a, ma); to_mont(b, mb); to_mont(c, mc);
fpadd751(mb, mc, md); fpmul751_mont(ma, md, me); // e = a*(b+c)
fpmul751_mont(ma, mb, md); fpmul751_mont(ma, mc, mf); fpadd751(md, mf, mf); // f = a*b+a*c
from_mont(me, e);
from_mont(mf, f);
if (compare_words(e, f, NWORDS_FIELD)!=0) { passed=0; break; }
to_mont(a, ma); to_mont(b, mb);
fpmul751_mont(ma, mb, md); // d = a*b
fpmul751_mont(mb, ma, me); // e = b*a
from_mont(md, d);
from_mont(me, e);
if (compare_words(d, e, NWORDS_FIELD)!=0) { passed=0; break; }
to_mont(a, ma);
fpzero751(b); b[0] = 1; to_mont(b, mb);
fpmul751_mont(ma, mb, md); // d = a*1
from_mont(ma, a);
from_mont(md, d);
if (compare_words(a, d, NWORDS_FIELD)!=0) { passed=0; break; }
fpzero751(b); to_mont(b, mb);
fpmul751_mont(ma, mb, md); // d = a*0
from_mont(mb, b);
from_mont(md, d);
if (compare_words(b, d, NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p) multiplication tests ...................................... PASSED");
else { printf(" GF(p) multiplication tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Field squaring over the prime p751
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fprandom751_test(a);
to_mont(a, ma);
fpsqr751_mont(ma, mb); // b = a^2
fpmul751_mont(ma, ma, mc); // c = a*a
if (compare_words(mb, mc, NWORDS_FIELD)!=0) { passed=0; break; }
fpzero751(a); to_mont(a, ma);
fpsqr751_mont(ma, md); // d = 0^2
if (compare_words(ma, md, NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p) squaring tests............................................. PASSED");
else { printf(" GF(p) squaring tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Field inversion over the prime p751
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fprandom751_test(a);
to_mont(a, ma);
fpzero751(d); d[0]=1; to_mont(d, md);
fpcopy751(ma, mb);
fpinv751_mont(ma);
fpmul751_mont(ma, mb, mc); // c = a*a^-1
if (compare_words(mc, md, NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p) inversion tests............................................ PASSED");
else { printf(" GF(p) inversion tests... FAILED"); printf("\n"); return false; }
printf("\n");
return OK;
}
bool fp2_test()
{ // Tests for the quadratic extension field arithmetic
bool OK = true;
int n, passed;
f2elm_t a, b, c, d, e, f, ma, mb, mc, md, me, mf;
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
printf("Testing quadratic extension arithmetic over GF(p751^2): \n\n");
// Addition over GF(p751^2)
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fp2random751_test((digit_t*)a); fp2random751_test((digit_t*)b); fp2random751_test((digit_t*)c); fp2random751_test((digit_t*)d); fp2random751_test((digit_t*)e); fp2random751_test((digit_t*)f);
fp2add751(a, b, d); fp2add751(d, c, e); // e = (a+b)+c
fp2add751(b, c, d); fp2add751(d, a, f); // f = a+(b+c)
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2add751(a, b, d); // d = a+b
fp2add751(b, a, e); // e = b+a
if (compare_words((digit_t*)d, (digit_t*)e, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2zero751(b);
fp2add751(a, b, d); // d = a+0
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2zero751(b);
fp2copy751(a, d);
fp2neg751(d);
fp2add751(a, d, e); // e = a+(-a)
if (compare_words((digit_t*)e, (digit_t*)b, 2*NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p^2) addition tests .......................................... PASSED");
else { printf(" GF(p^2) addition tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Subtraction over GF(p751^2)
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fp2random751_test((digit_t*)a); fp2random751_test((digit_t*)b); fp2random751_test((digit_t*)c); fp2random751_test((digit_t*)d); fp2random751_test((digit_t*)e); fp2random751_test((digit_t*)f);
fp2sub751(a, b, d); fp2sub751(d, c, e); // e = (a-b)-c
fp2add751(b, c, d); fp2sub751(a, d, f); // f = a-(b+c)
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2sub751(a, b, d); // d = a-b
fp2sub751(b, a, e);
fp2neg751(e); // e = -(b-a)
if (compare_words((digit_t*)d, (digit_t*)e, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2zero751(b);
fp2sub751(a, b, d); // d = a-0
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2zero751(b);
fp2copy751(a, d);
fp2sub751(a, d, e); // e = a+(-a)
if (compare_words((digit_t*)e, (digit_t*)b, 2*NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p^2) subtraction tests ....................................... PASSED");
else { printf(" GF(p^2) subtraction tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Multiplication over GF(p751^2)
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fp2random751_test((digit_t*)a); fp2random751_test((digit_t*)b); fp2random751_test((digit_t*)c);
fp2random751_test((digit_t*)ma); fp2random751_test((digit_t*)mb); fp2random751_test((digit_t*)mc); fp2random751_test((digit_t*)md); fp2random751_test((digit_t*)me); fp2random751_test((digit_t*)mf);
to_fp2mont(a, ma);
fp2copy751(ma, mc);
from_fp2mont(mc, c);
if (compare_words((digit_t*)a, (digit_t*)c, 2*NWORDS_FIELD)!=0) { passed=0; break; }
to_fp2mont(a, ma); to_fp2mont(b, mb); to_fp2mont(c, mc);
fp2mul751_mont(ma, mb, md); fp2mul751_mont(md, mc, me); // e = (a*b)*c
fp2mul751_mont(mb, mc, md); fp2mul751_mont(md, ma, mf); // f = a*(b*c)
from_fp2mont(me, e);
from_fp2mont(mf, f);
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
to_fp2mont(a, ma); to_fp2mont(b, mb); to_fp2mont(c, mc);
fp2add751(mb, mc, md); fp2mul751_mont(ma, md, me); // e = a*(b+c)
fp2mul751_mont(ma, mb, md); fp2mul751_mont(ma, mc, mf); fp2add751(md, mf, mf); // f = a*b+a*c
from_fp2mont(me, e);
from_fp2mont(mf, f);
if (compare_words((digit_t*)e, (digit_t*)f, 2*NWORDS_FIELD)!=0) { passed=0; break; }
to_fp2mont(a, ma); to_fp2mont(b, mb);
fp2mul751_mont(ma, mb, md); // d = a*b
fp2mul751_mont(mb, ma, me); // e = b*a
from_fp2mont(md, d);
from_fp2mont(me, e);
if (compare_words((digit_t*)d, (digit_t*)e, 2*NWORDS_FIELD)!=0) { passed=0; break; }
to_fp2mont(a, ma);
fp2zero751(b); b[0][0] = 1; to_fp2mont(b, mb);
fp2mul751_mont(ma, mb, md); // d = a*1
from_fp2mont(md, d);
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2zero751(b); to_fp2mont(b, mb);
fp2mul751_mont(ma, mb, md); // d = a*0
from_fp2mont(md, d);
if (compare_words((digit_t*)b, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p^2) multiplication tests .................................... PASSED");
else { printf(" GF(p^2) multiplication tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Squaring over GF(p751^2)
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fp2random751_test((digit_t*)a);
to_fp2mont(a, ma);
fp2sqr751_mont(ma, mb); // b = a^2
fp2mul751_mont(ma, ma, mc); // c = a*a
from_fp2mont(mb, b);
from_fp2mont(mc, c);
if (compare_words((digit_t*)b, (digit_t*)c, 2*NWORDS_FIELD)!=0) { passed=0; break; }
fp2zero751(a); to_fp2mont(a, ma);
fp2sqr751_mont(ma, md); // d = 0^2
from_fp2mont(md, d);
if (compare_words((digit_t*)a, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p^2) squaring tests........................................... PASSED");
else { printf(" GF(p^2) squaring tests... FAILED"); printf("\n"); return false; }
printf("\n");
// Inversion over GF(p751^2)
passed = 1;
for (n=0; n<TEST_LOOPS; n++)
{
fp2random751_test((digit_t*)a);
to_fp2mont(a, ma);
fp2zero751(d); d[0][0]=1; to_fp2mont(d, md);
fp2copy751(ma, mb);
fp2inv751_mont(ma);
fp2mul751_mont(ma, mb, mc); // c = a*a^-1
from_fp2mont(mc, c);
if (compare_words((digit_t*)c, (digit_t*)d, 2*NWORDS_FIELD)!=0) { passed=0; break; }
}
if (passed==1) printf(" GF(p^2) inversion tests.......................................... PASSED");
else { printf(" GF(p^2) inversion tests... FAILED"); printf("\n"); return false; }
printf("\n");
return OK;
}
bool fp_run()
{
bool OK = true;
int n;
unsigned long long cycles, cycles1, cycles2;
felm_t a, b, c;
dfelm_t aa;
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
printf("Benchmarking field arithmetic over GF(p751): \n\n");
fprandom751_test(a); fprandom751_test(b); fprandom751_test(c);
// GF(p) addition using p751
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fpadd751(a, b, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p) addition runs in .......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p) subtraction using p751
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fpsub751(a, b, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p) subtraction runs in ....................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p) multiplication using p751
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fpmul751_mont(a, b, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p) multiplication runs in .................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p) reduction using p751
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
mp_mul(a, b, aa, NWORDS_FIELD);
cycles1 = cpucycles();
rdc_mont(aa, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p) reduction runs in ......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p) inversion
cycles = 0;
for (n=0; n<SMALL_BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fpinv751_mont(a);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p) inversion (exponentiation) runs in ........................ %7lld ", cycles/SMALL_BENCH_LOOPS); print_unit;
printf("\n");
return OK;
}
bool fp2_run()
{
bool OK = true;
int n;
unsigned long long cycles, cycles1, cycles2;
f2elm_t a, b, c;
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
printf("Benchmarking quadratic extension arithmetic over GF(p751^2): \n\n");
fp2random751_test((digit_t*)a); fp2random751_test((digit_t*)b); fp2random751_test((digit_t*)c);
// GF(p^2) addition
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fp2add751(a, b, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p^2) addition runs in ........................................ %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p^2) subtraction
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fp2sub751(a, b, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p^2) subtraction runs in ..................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p^2) multiplication
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fp2mul751_mont(a, b, c);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p^2) multiplication runs in .................................. %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p^2) squaring
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fp2sqr751_mont(a, b);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p^2) squaring runs in ........................................ %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// GF(p^2) inversion
cycles = 0;
for (n=0; n<SMALL_BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
fp2inv751_mont(a);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" GF(p^2) inversion (exponentiation) runs in ...................... %7lld ", cycles/SMALL_BENCH_LOOPS); print_unit;
printf("\n");
return OK;
}
bool ecisog_run()
{
bool OK = true;
int n;
unsigned long long cycles, cycles1, cycles2;
f2elm_t A24, C24, A4, A, C, coeff[5];
point_proj_t P, Q;
printf("\n--------------------------------------------------------------------------------------------------------\n\n");
printf("Benchmarking elliptic curve and isogeny functions: \n\n");
// Point doubling
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
fp2random751_test((digit_t*)A24); fp2random751_test((digit_t*)C24);
cycles1 = cpucycles();
xDBL(P, Q, A24, C24);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" Point doubling runs in .......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// 4-isogeny of a projective point
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
fp2random751_test((digit_t*)A); fp2random751_test((digit_t*)coeff[0]); fp2random751_test((digit_t*)coeff[1]); fp2random751_test((digit_t*)coeff[2]);
cycles1 = cpucycles();
get_4_isog(P, A, C, coeff);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" 4-isogeny of projective point runs in ........................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// 4-isogeny evaluation at projective point
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
fp2random751_test((digit_t*)A); fp2random751_test((digit_t*)coeff[0]); fp2random751_test((digit_t*)coeff[1]); fp2random751_test((digit_t*)coeff[2]);
cycles1 = cpucycles();
eval_4_isog(P, coeff);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" 4-isogeny evaluation at projective point runs in ................ %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// Point tripling
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
fp2random751_test((digit_t*)A4); fp2random751_test((digit_t*)C);
cycles1 = cpucycles();
xTPL(P, Q, A4, C);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" Point tripling runs in .......................................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// 3-isogeny of a projective point
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
fp2random751_test((digit_t*)A); fp2random751_test((digit_t*)C);
cycles1 = cpucycles();
get_3_isog(P, A, C, coeff);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" 3-isogeny of projective point runs in ........................... %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
// 3-isogeny evaluation at projective point
cycles = 0;
for (n=0; n<BENCH_LOOPS; n++)
{
cycles1 = cpucycles();
eval_3_isog(Q, coeff);
cycles2 = cpucycles();
cycles = cycles+(cycles2-cycles1);
}
printf(" 3-isogeny evaluation at projective point runs in ................ %7lld ", cycles/BENCH_LOOPS); print_unit;
printf("\n");
return OK;
}
int main()
{
bool OK = true;
OK = OK && fp_test(); // Test field operations using p751
OK = OK && fp_run(); // Benchmark field operations using p751
OK = OK && fp2_test(); // Test arithmetic functions over GF(p751^2)
OK = OK && fp2_run(); // Benchmark arithmetic functions over GF(p751^2)
OK = OK && ecisog_run(); // Benchmark elliptic curve and isogeny functions
return OK;
}