a portable and fast pairing-based cryptography library
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mcl/test/mont_fp_test.cpp

704 lines
15 KiB

#define PUT(x) std::cout << #x "=" << (x) << std::endl
#include <cybozu/test.hpp>
#include <cybozu/benchmark.hpp>
#include <time.h>
#include <mcl/fp.hpp>
struct ZnTag;
typedef mcl::FpT<ZnTag> Zn;
typedef mcl::FpT<> Fp;
struct Montgomery {
typedef mcl::gmp::Unit Unit;
mpz_class p_;
mpz_class R_; // (1 << (pn_ * 64)) % p
mpz_class RR_; // (R * R) % p
Unit rp_; // rp * p = -1 mod M = 1 << 64
size_t pn_;
Montgomery() {}
explicit Montgomery(const mpz_class& p)
{
p_ = p;
rp_ = mcl::fp::getMontgomeryCoeff(mcl::gmp::getUnit(p, 0));
pn_ = mcl::gmp::getUnitSize(p);
R_ = 1;
R_ = (R_ << (pn_ * 64)) % p_;
RR_ = (R_ * R_) % p_;
}
void toMont(mpz_class& x) const { mul(x, x, RR_); }
void fromMont(mpz_class& x) const { mul(x, x, 1); }
void mul(mpz_class& z, const mpz_class& x, const mpz_class& y) const
{
#if 0
const size_t ySize = mcl::gmp::getUnitSize(y);
mpz_class c = x * mcl::gmp::getUnit(y, 0);
Unit q = mcl::gmp::getUnit(c, 0) * rp_;
c += p_ * q;
c >>= sizeof(Unit) * 8;
for (size_t i = 1; i < pn_; i++) {
if (i < ySize) {
c += x * mcl::gmp::getUnit(y, i);
}
Unit q = mcl::gmp::getUnit(c, 0) * rp_;
c += p_ * q;
c >>= sizeof(Unit) * 8;
}
if (c >= p_) {
c -= p_;
}
z = c;
#else
z = x * y;
for (size_t i = 0; i < pn_; i++) {
Unit q = mcl::gmp::getUnit(z, 0) * rp_;
z += p_ * (mp_limb_t)q;
z >>= sizeof(Unit) * 8;
}
if (z >= p_) {
z -= p_;
}
#endif
}
};
template<class T>
mpz_class getMpz(const T& x)
{
std::string str = x.getStr();
mpz_class t;
mcl::gmp::setStr(t, str);
return t;
}
template<class T>
std::string getStr(const T& x)
{
std::ostringstream os;
os << x;
return os.str();
}
template<class T, class U>
T castTo(const U& x)
{
T t;
t.setStr(getStr(x));
return t;
}
template<class T>
void putRaw(const T& x)
{
const uint64_t *p = x.getInnerValue();
for (size_t i = 0, n = T::BlockSize; i < n; i++) {
printf("%016llx", p[n - 1 - i]);
}
printf("\n");
}
template<size_t N>
void put(const uint64_t (&x)[N])
{
for (size_t i = 0; i < N; i++) {
printf("%016llx", x[N - 1 - i]);
}
printf("\n");
}
struct Test {
typedef mcl::FpT<> Fp;
mpz_class m;
void run(const char *p)
{
Fp::init(p);
m = p;
Zn::init(p);
edge();
cstr();
getStr();
setStr();
stream();
conv();
compare();
modulo();
ope();
pow();
mul_Unit();
pow_Zn();
setArray();
set64bit();
divBy2();
bench();
}
void cstr()
{
const struct {
const char *str;
int val;
} tbl[] = {
{ "0", 0 },
{ "1", 1 },
{ "123", 123 },
{ "0x123", 0x123 },
{ "0b10101", 21 },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
// string cstr
Fp x(tbl[i].str);
CYBOZU_TEST_EQUAL(x, tbl[i].val);
// int cstr
Fp y(tbl[i].val);
CYBOZU_TEST_EQUAL(y, x);
// copy cstr
Fp z(x);
CYBOZU_TEST_EQUAL(z, x);
// assign int
Fp w;
w = tbl[i].val;
CYBOZU_TEST_EQUAL(w, x);
// assign self
Fp u;
u = w;
CYBOZU_TEST_EQUAL(u, x);
// conv
std::ostringstream os;
os << tbl[i].val;
std::string str;
x.getStr(str);
CYBOZU_TEST_EQUAL(str, os.str());
}
const struct {
const char *str;
int val;
} tbl2[] = {
{ "-123", 123 },
{ "-0x123", 0x123 },
{ "-0b10101", 21 },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl2); i++) {
Fp x(tbl2[i].str);
x = -x;
CYBOZU_TEST_EQUAL(x, tbl2[i].val);
}
}
void getStr()
{
Fp x(0);
std::string str;
str = x.getStr();
CYBOZU_TEST_EQUAL(str, "0");
str = x.getStr(2, true);
CYBOZU_TEST_EQUAL(str, "0b0");
str = x.getStr(2, false);
CYBOZU_TEST_EQUAL(str, "0");
str = x.getStr(16, true);
CYBOZU_TEST_EQUAL(str, "0x0");
str = x.getStr(16, false);
CYBOZU_TEST_EQUAL(str, "0");
x = 123;
str = x.getStr();
CYBOZU_TEST_EQUAL(str, "123");
str = x.getStr(2, true);
CYBOZU_TEST_EQUAL(str, "0b1111011");
str = x.getStr(2, false);
CYBOZU_TEST_EQUAL(str, "1111011");
str = x.getStr(16, true);
CYBOZU_TEST_EQUAL(str, "0x7b");
str = x.getStr(16, false);
CYBOZU_TEST_EQUAL(str, "7b");
{
std::ostringstream os;
os << x;
CYBOZU_TEST_EQUAL(os.str(), "123");
}
{
std::ostringstream os;
os << std::hex << std::showbase << x;
CYBOZU_TEST_EQUAL(os.str(), "0x7b");
}
{
std::ostringstream os;
os << std::hex << x;
CYBOZU_TEST_EQUAL(os.str(), "7b");
}
}
void setStr()
{
const struct {
const char *in;
int out;
int base;
} tbl[] = {
{ "100", 100, 0 }, // set base = 10 if base = 0
{ "100", 4, 2 },
{ "100", 256, 16 },
{ "0b100", 4, 0 },
{ "0b100", 4, 2 },
{ "0x100", 256, 0 },
{ "0x100", 256, 16 },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
Fp x;
x.setStr(tbl[i].in, tbl[i].base);
CYBOZU_TEST_EQUAL(x, tbl[i].out);
}
// conflict prefix with base
Fp x;
CYBOZU_TEST_EXCEPTION(x.setStr("0b100", 16), cybozu::Exception);
CYBOZU_TEST_EXCEPTION(x.setStr("0x100", 2), cybozu::Exception);
}
void stream()
{
const struct {
const char *in;
int out10;
int out16;
} tbl[] = {
{ "100", 100, 256 }, // set base = 10 if base = 0
{ "0x100", 256, 256 },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
{
std::istringstream is(tbl[i].in);
Fp x;
is >> x;
CYBOZU_TEST_EQUAL(x, tbl[i].out10);
}
{
std::istringstream is(tbl[i].in);
Fp x;
is >> std::hex >> x;
CYBOZU_TEST_EQUAL(x, tbl[i].out16);
}
}
std::istringstream is("0b100");
Fp x;
CYBOZU_TEST_EXCEPTION(is >> std::hex >> x, cybozu::Exception);
}
void edge()
{
std::cout << std::hex;
/*
real mont
0 0
1 R^-1
R 1
-1 -R^-1
-R -1
*/
mpz_class t = 1;
const size_t N = Fp::getUnitSize();
const mpz_class R = (t << (N * mcl::fp::UnitBitSize)) % m;
const mpz_class tbl[] = {
0, 1, R, m - 1, m - R
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
const mpz_class& x = tbl[i];
for (size_t j = i; j < CYBOZU_NUM_OF_ARRAY(tbl); j++) {
const mpz_class& y = tbl[j];
mpz_class z = (x * y) % m;
Fp xx, yy;
xx.setMpz(x);
yy.setMpz(y);
Fp zz = xx * yy;
mpz_class t;
zz.getMpz(t);
CYBOZU_TEST_EQUAL(z, t);
}
}
t = Fp::getOp().mp;
t /= 2;
Fp x;
x.setMpz(t);
CYBOZU_TEST_EQUAL(x * 2, -1);
t += 1;
x.setMpz(t);
CYBOZU_TEST_EQUAL(x * 2, 1);
}
void conv()
{
const char *bin, *hex, *dec;
if (Fp::getBitSize() <= 117) {
bin = "0b1000000000000000000000000000000000000000000000000000000000001110";
hex = "0x800000000000000e";
dec = "9223372036854775822";
} else {
bin = "0b100100011010001010110011110001001000000010010001101000101011001111000100100000001001000110100010101100111100010010000";
hex = "0x123456789012345678901234567890";
dec = "94522879687365475552814062743484560";
}
Fp b(bin);
Fp h(hex);
Fp d(dec);
CYBOZU_TEST_EQUAL(b, h);
CYBOZU_TEST_EQUAL(b, d);
std::string str;
b.getStr(str, 2, true);
CYBOZU_TEST_EQUAL(str, bin);
b.getStr(str);
CYBOZU_TEST_EQUAL(str, dec);
b.getStr(str, 16, true);
CYBOZU_TEST_EQUAL(str, hex);
}
void compare()
{
const struct {
int lhs;
int rhs;
int cmp;
} tbl[] = {
{ 0, 0, 0 },
{ 1, 0, 1 },
{ 0, 1, -1 },
{ -1, 0, 1 }, // m-1, 0
{ 0, -1, -1 }, // 0, m-1
{ 123, 456, -1 },
{ 456, 123, 1 },
{ 5, 5, 0 },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
const Fp x(tbl[i].lhs);
const Fp y(tbl[i].rhs);
const int cmp = tbl[i].cmp;
if (cmp == 0) {
CYBOZU_TEST_EQUAL(x, y);
} else {
CYBOZU_TEST_ASSERT(x != y);
}
}
{
Fp x(1);
CYBOZU_TEST_ASSERT(x.isOne());
x = 2;
CYBOZU_TEST_ASSERT(!x.isOne());
}
{
const struct {
int v;
bool expected;
} tbl[] = {
{ 0, false },
{ 1, false },
{ -1, true },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
Fp x = tbl[i].v;
PUT(x);
CYBOZU_TEST_EQUAL(x.isNegative(), tbl[i].expected);
}
std::string str;
Fp::getModulo(str);
mpz_class half(str);
half = (half - 1) / 2;
Fp x;
x.setMpz(half - 1);
CYBOZU_TEST_ASSERT(!x.isNegative());
x.setMpz(half);
CYBOZU_TEST_ASSERT(!x.isNegative());
x.setMpz(half + 1);
CYBOZU_TEST_ASSERT(x.isNegative());
}
}
void modulo()
{
std::ostringstream ms;
ms << m;
std::string str;
Fp::getModulo(str);
CYBOZU_TEST_EQUAL(str, ms.str());
}
void ope()
{
const struct {
Zn x;
Zn y;
Zn add; // x + y
Zn sub; // x - y
Zn mul; // x * y
Zn sqr; // x * x
} tbl[] = {
{ 0, 1, 1, -1, 0, 0 },
{ 9, 7, 16, 2, 63, 81 },
{ 10, 13, 23, -3, 130, 100 },
{ 2000, -1000, 1000, 3000, -2000000, 4000000 },
{ -12345, -9999, -(12345 + 9999), - 12345 + 9999, 12345 * 9999, 12345 * 12345 },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
const Fp x(castTo<Fp>(tbl[i].x));
const Fp y(castTo<Fp>(tbl[i].y));
Fp z;
Fp::add(z, x, y);
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].add));
Fp::sub(z, x, y);
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].sub));
Fp::mul(z, x, y);
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].mul));
Fp r;
Fp::inv(r, y);
Zn rr = 1 / tbl[i].y;
CYBOZU_TEST_EQUAL(r, castTo<Fp>(rr));
Fp::mul(z, z, r);
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].x));
z = x + y;
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].add));
z = x - y;
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].sub));
z = x * y;
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].mul));
Fp::sqr(z, x);
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].sqr));
z = x / y;
z *= y;
CYBOZU_TEST_EQUAL(z, castTo<Fp>(tbl[i].x));
}
{
Fp x(5), y(3), z;
Fp::addNC(z, x, y);
if (Fp::compareRaw(z, Fp::getP()) >= 0) {
Fp::subNC(z, z, Fp::getP());
}
CYBOZU_TEST_EQUAL(z, Fp(8));
if (Fp::compareRaw(x, y) < 0) {
Fp::addNC(x, x, Fp::getP());
}
Fp::subNC(x, x, y);
CYBOZU_TEST_EQUAL(x, Fp(2));
}
}
void pow()
{
Fp x, y, z;
x = 12345;
z = 1;
for (int i = 0; i < 100; i++) {
Fp::pow(y, x, i);
CYBOZU_TEST_EQUAL(y, z);
z *= x;
}
x = z;
Fp::pow(z, x, Fp::getOp().mp - 1);
CYBOZU_TEST_EQUAL(z, 1);
Fp::pow(z, x, Fp::getOp().mp);
CYBOZU_TEST_EQUAL(z, x);
}
void mul_Unit()
{
Fp x(-1), y, z;
for (unsigned int u = 0; u < 20; u++) {
Fp::mul(y, x, u);
Fp::mul_Unit(z, x, u);
CYBOZU_TEST_EQUAL(y, z);
}
}
void pow_Zn()
{
Fp x, y, z;
x = 12345;
z = 1;
for (int i = 0; i < 100; i++) {
Fp::pow(y, x, Zn(i));
CYBOZU_TEST_EQUAL(y, z);
z *= x;
}
}
void setArray()
{
// QQQ
#if 0
char b1[] = { 0x56, 0x34, 0x12 };
Fp x;
x.setArray(b1, 3);
CYBOZU_TEST_EQUAL(x, 0x123456);
int b2[] = { 0x12, 0x34 };
x.setArray(b2, 2);
CYBOZU_TEST_EQUAL(x, Fp("0x3400000012"));
#endif
}
void set64bit()
{
const struct {
const char *p;
int64_t i;
} tbl[] = {
{ "0x1234567812345678", uint64_t(0x1234567812345678ull) },
{ "0x1234567812345678", int64_t(0x1234567812345678ll) },
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
Fp x(tbl[i].p);
Fp y(tbl[i].i);
if (tbl[i].i < 0) x = -x;
CYBOZU_TEST_EQUAL(x, y);
}
}
void divBy2()
{
const int tbl[] = { -4, -3, -2, -1, 0, 1, 2, 3 };
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
Fp x(tbl[i]), y;
Fp::divBy2(y, x);
y *= 2;
CYBOZU_TEST_EQUAL(y, x);
y = x;
Fp::divBy2(y, y);
y *= 2;
CYBOZU_TEST_EQUAL(y, x);
}
}
void bench()
{
Fp x("-123456789");
Fp y("-0x7ffffffff");
CYBOZU_BENCH("add", operator+, x, x);
CYBOZU_BENCH("sub", operator-, x, y);
CYBOZU_BENCH("mul", operator*, x, x);
CYBOZU_BENCH("sqr", Fp::sqr, x, x);
CYBOZU_BENCH("div", y += x; operator/, x, y);
}
};
void customTest(const char *pStr, const char *xStr, const char *yStr)
{
#if 0
{
pStr = "0xfffffffffffffffffffffffffffffffffffffffeffffee37",
Fp::init(pStr);
static uint64_t x[3] = { 1, 0, 0 };
uint64_t z[3];
std::cout<<std::hex;
Fp::inv(*(Fp*)z, *(const Fp*)x);
put(z);
exit(1);
}
#endif
#if 0
std::cout << std::hex;
uint64_t x[9] = { 0xff7fffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0x1ff };
uint64_t y[9] = { 0xff7fffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0x1ff };
uint64_t z1[9], z2[9];
Fp::init(pStr);
Fp::fg_.mul_(z2, x, y);
put(z2);
{
puts("C");
mpz_class p(pStr);
Montgomery mont(p);
mpz_class xx, yy;
mcl::gmp::setArray(xx, x, CYBOZU_NUM_OF_ARRAY(x));
mcl::gmp::setArray(yy, y, CYBOZU_NUM_OF_ARRAY(y));
mpz_class z;
mont.mul(z, xx, yy);
std::cout << std::hex << z << std::endl;
}
exit(1);
#else
std::string rOrg, rC, rAsm;
Zn::init(pStr);
Zn s(xStr), t(yStr);
s *= t;
rOrg = getStr(s);
{
puts("C");
mpz_class p(pStr);
Montgomery mont(p);
mpz_class x(xStr), y(yStr);
mont.toMont(x);
mont.toMont(y);
mpz_class z;
mont.mul(z, x, y);
mont.fromMont(z);
rC = getStr(z);
}
puts("asm");
Fp::init(pStr);
Fp x(xStr), y(yStr);
x *= y;
rAsm = getStr(x);
CYBOZU_TEST_EQUAL(rOrg, rC);
CYBOZU_TEST_EQUAL(rOrg, rAsm);
#endif
}
CYBOZU_TEST_AUTO(customTest)
{
const struct {
const char *p;
const char *x;
const char *y;
} tbl[] = {
{
"0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
// "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff",
// "0xfffffffffffffffffffffffffffffffffffffffeffffee37",
"0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
"0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
},
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
customTest(tbl[i].p, tbl[i].x, tbl[i].y);
}
}
CYBOZU_TEST_AUTO(test)
{
Test test;
const char *tbl[] = {
// N = 2
"0x0000000000000001000000000000000d",
"0x7fffffffffffffffffffffffffffffff",
"0x8000000000000000000000000000001d",
"0xffffffffffffffffffffffffffffff61",
// N = 3
"0x000000000000000100000000000000000000000000000033", // min prime
"0x00000000fffffffffffffffffffffffffffffffeffffac73",
"0x0000000100000000000000000001b8fa16dfab9aca16b6b3",
"0x000000010000000000000000000000000000000000000007",
"0x30000000000000000000000000000000000000000000002b",
"0x70000000000000000000000000000000000000000000001f",
"0x800000000000000000000000000000000000000000000005",
"0xfffffffffffffffffffffffffffffffffffffffeffffee37",
"0xfffffffffffffffffffffffe26f2fc170f69466a74defd8d",
"0xffffffffffffffffffffffffffffffffffffffffffffff13", // max prime
// N = 4
"0x0000000000000001000000000000000000000000000000000000000000000085", // min prime
"0x2523648240000001ba344d80000000086121000000000013a700000000000013",
"0x7523648240000001ba344d80000000086121000000000013a700000000000017",
"0x800000000000000000000000000000000000000000000000000000000000005f",
"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff43", // max prime
// N = 6
"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff",
// N = 9
"0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
};
for (size_t i = 0; i < CYBOZU_NUM_OF_ARRAY(tbl); i++) {
printf("prime=%s\n", tbl[i]);
test.run(tbl[i]);
}
}