crypto/unittest/bignum.cc

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*/
#include <crypto/bignum.h>
#include <gtest/gtest.h>
#include <iostream>
#include <string>
#include <encode/hex.h>
 
using std::cout;
using std::endl;
using std::vector;
using std::runtime_error;
using scc::encode::Hex;
using scc::crypto::Bignum;
 
TEST(bignum_test, init)
{
    Bignum n;
    cout << "Init: " << n << endl;
    ASSERT_EQ(n.str(), "0");
}
 
TEST(bignum_test, set_zero)
{
    Bignum n;
    n = 0;
    cout << "Zero: " << n << endl;
    ASSERT_EQ(n.str(), "0");
}
 
TEST(bignum_test, set_one)
{
    Bignum n;
    n = 1;
    cout << "One: " << n << endl;
    ASSERT_EQ(n.str(), "1");
}
 
TEST(bignum_test, init_ten)
{
    Bignum n(10);
    cout << "Init ten: " << n << endl;
    ASSERT_EQ(n.str(), "10");
}
 
TEST(bignum_test, copy_construct)
{
    Bignum a(10);
    Bignum b(a);
    cout << "copy_construct a=" << a << " b=" << b << endl;
    ASSERT_TRUE(a == 10);
    ASSERT_TRUE(b == 10);
}
 
TEST(bignum_test, copy_op)
{
    Bignum a(10);
    Bignum b;
    b = a;
    cout << "copy_op a=" << a << " b=" << b << endl;
    ASSERT_TRUE(a == 10);
    ASSERT_TRUE(b == 10);
}
 
TEST(bignum_test, move_construct)
{
    Bignum a(10);
    Bignum b = std::move(a);
    cout << "move_construct a=" << a << " b=" << b << endl;
    ASSERT_TRUE(b == 10);
    ASSERT_FALSE(a == 10);
}
 
TEST(bignum_test, move_opt)
{
    Bignum a(10);
    Bignum b;
    b = std::move(a);
    cout << "move_op a=" << a << " b=" << b << endl;
    ASSERT_TRUE(b == 10);
    ASSERT_FALSE(a == 10);
}
 
TEST(bignum_test, print_hex)
{
    Bignum a(1 << 20);
    a += 15*16;
    a = -a;
    cout << "print_hex " << std::hex << a << std::dec << endl;
    ASSERT_EQ(a.str(true), "-1000f0");
    
}
 
TEST(bignum_test, print_dec)
{
    Bignum a(1 << 20);
    a = -a;
    cout << "print_dec " << a << endl;
    ASSERT_EQ(a.str(), "-1048576");
}
 
TEST(bignum_test, compare)
{
    Bignum one(1), ten(10);
    ASSERT_TRUE(one == one);
    ASSERT_TRUE(one >= one);
    ASSERT_TRUE(one <= one);
    ASSERT_FALSE(one < one);
    ASSERT_FALSE(one > one);
    ASSERT_TRUE(one != ten);
    ASSERT_TRUE(one < ten);
    ASSERT_TRUE(one <= ten);
    ASSERT_TRUE(ten > one);
    ASSERT_TRUE(ten >= one);
    ASSERT_TRUE(one == 1);
    ASSERT_TRUE(one >= 1);
    ASSERT_TRUE(one <= 1);
    ASSERT_FALSE(one < 1);
    ASSERT_FALSE(one > 1);
    ASSERT_TRUE(one != 10);
    ASSERT_TRUE(one < 10);
    ASSERT_TRUE(one <= 10);
    ASSERT_TRUE(ten > 1);
    ASSERT_TRUE(ten >= 1);
}
 
 
TEST(bignum_test, shift)
{
    Bignum one(1);
    Bignum sft(1<<7);
    Bignum a(1);
 
    a <<= 7;
    ASSERT_EQ(a, sft);
    Bignum b = one << 7;
    ASSERT_EQ(b, sft);
    Bignum c(sft);
    c >>= 7;
    ASSERT_EQ(c, one);
    Bignum d = sft >> 7;
    ASSERT_EQ(d, one);
    Bignum shiftaway(123456);
    shiftaway >>= shiftaway.width();
    ASSERT_EQ(shiftaway, 0);
}
 
TEST(bignum_test, big_shift)
{
    Bignum n(0xffff0000);
    cout << "bigshift in  : " << std::hex << n << std::dec << " width: " << n.width() << endl;
    n <<= 47;
    auto hx = n.str(true);
    cout << "bigshift <<47: " << std::hex << hx << std::dec << " width: " << n.width() << endl;
    ASSERT_EQ(n.width(), 32+47);
    ASSERT_EQ(hx, "7fff8000000000000000");
    n >>= 9;
    hx = n.str(true);
    cout << "bigshift >>9: " << std::hex << hx << std::dec << " width: " << n.width() << endl;
    ASSERT_EQ(hx, "3fffc0000000000000");
    ASSERT_EQ(n.width(), 32+47-9);
}
 
TEST(bignum_test, incdec)
{
    Bignum a;
    a = 1;
    ASSERT_EQ(++a, 2);
    ASSERT_EQ(a, 2);
    ASSERT_EQ(a++, 2);
    ASSERT_EQ(a, 3);
    ASSERT_EQ(--a, 2);
    ASSERT_EQ(a, 2);
    ASSERT_EQ(a--, 2);
    ASSERT_EQ(a, 1);
}
 
TEST(bignum_test, arith)
{
    Bignum zero, one(1), two(2), three(3), nine(9), ten(10), eleven(11), twelve(12), hund(100);
 
    Bignum a = one * ten;
    ASSERT_EQ(a, ten);
    a /= ten;
    ASSERT_EQ(a, one);
 
    a = nine / three;
    ASSERT_EQ(a, three);
    a *= three;
    ASSERT_EQ(a, nine);
 
    a = nine + one;
    ASSERT_EQ(a, ten);
    a -= one;
    ASSERT_EQ(a, nine);
 
    a = ten - one;
    ASSERT_EQ(a, nine);
    a += one;
    ASSERT_EQ(a, ten);
 
    a = hund % nine;
    ASSERT_EQ(a, one);
 
    a = hund;
    Bignum rem;
    a.div(nine, &rem);
    ASSERT_EQ(a, eleven);
    ASSERT_EQ(rem, one);
 
    a = exp(nine, zero);
    ASSERT_EQ(a, one);
 
    a = exp(ten, two);
    ASSERT_EQ(a, hund);
    a = ten;
    a.exp(two);
    ASSERT_EQ(a, hund);
 
    a = gcd(nine, twelve);
    ASSERT_EQ(a, three);
    a = nine;
    a.gcd(twelve);
    ASSERT_EQ(a, three);
}
 
TEST(bignum_test, arith_num)
{
    Bignum one(1), two(2), three(3), nine(9), ten(10), eleven(11), twelve(12), hund(100);
 
    Bignum a = one * 10;
    ASSERT_EQ(a, 10);
    a /= 10;
    ASSERT_EQ(a, 1);
 
    a = nine / 3;
    ASSERT_EQ(a, 3);
    a *= 3;
    ASSERT_EQ(a, 9);
 
    a = nine + 1;
    ASSERT_EQ(a, 10);
    a -= 1;
    ASSERT_EQ(a, 9);
 
    a = ten - 1;
    ASSERT_EQ(a, 9);
    a += 1;
    ASSERT_EQ(a, 10);
 
    a = hund % 9;
    ASSERT_EQ(a, 1);
 
    a = hund;
    Bignum rem;
    a.div(nine, &rem);
    ASSERT_EQ(a, 11);
    ASSERT_EQ(rem, 1);
 
    a = exp(nine, 0);
    ASSERT_EQ(a, 1);
 
    a = exp(ten, 2);
    ASSERT_EQ(a, 100);
    a = ten;
    a.exp(2);
    ASSERT_EQ(a, 100);
 
    a = gcd(nine, 12);
    ASSERT_EQ(a, 3);
    a = nine;
    a.gcd(12);
    ASSERT_EQ(a, 3);
}
 
TEST(bignum_test, prime)
{
    Bignum p1(217645177);
    Bignum p2(236887691);
    ASSERT_TRUE(p1.is_prime());
    ASSERT_TRUE(p2.is_prime());
    Bignum c = p1*p2;
    ASSERT_FALSE(c.is_prime());
    cout << "Prime 1:   " << p1 << endl;
    cout << "Prime 2:   " << p2 << endl;
    cout << "Composite: " << c << endl;
 
    // find the first hundred primes (see primes.utm.edu)
    int count = 0;
    Bignum b;
    for (int t = 2; t <= 541; t++)
    {
        b = t;
        if (b.is_prime())
            count++;
    }
    cout << "First hundred primes found: " << count << endl;
    EXPECT_EQ(count, 100);
}
 
TEST(bignum_test, gcd)
{
    Bignum p1(2829604451);
    cout << "p1: " << std::hex << p1 << endl;
    ASSERT_TRUE(p1.is_prime());
    Bignum p2(1787494861);
    cout << "p2: " << std::hex << p2 << endl;
    ASSERT_TRUE(p2.is_prime());
    Bignum p3(3954380029);
    cout << "p3: " << std::hex << p3 << endl;
    ASSERT_TRUE(p3.is_prime());
    Bignum p12 = p1 * p2;
    cout << "p1 * p2: " << std::hex << p12 << endl;
    Bignum p13 = p1 * p3;
    cout << "p1 * p3: " << std::hex << p13 << endl;
    Bignum gcd(p12);
    gcd.gcd(p13);
    cout << "gcd: " << std::hex << gcd << endl;
    ASSERT_EQ(p1, gcd);
}
 
TEST(bignum_test, bintest)
{
    uint8_t octval[] = "\x12\x34\x56\x78\x9a\xbc\xde\xf0"
        "\xcc";
 
    Bignum b(octval, sizeof(octval));
    cout << "bin: " << std::hex << b << " " << std::dec << b << endl;
    Bignum t;
    t = 0x12345678;
    t <<= 32;
    t += 0x9abcdef0;
    t <<= 16;
    t += 0xcc00;
    cout << "tst: " << std::hex << t << " " << std::dec << t << endl;
    ASSERT_EQ(b, t);
}
 
TEST(bignum_test, generate_rand)
{
    auto gen = [](int w, bool s=false, bool o=false)
    {
        Bignum p;
        p.gen_rand(w, s, o);
        cout << "genrand request width="<<w<<" strong="<<s<<" odd="<<o<<": " << std::hex << p << std::dec << " width: " << p.width() << endl;
        ASSERT_LE(p.width(), w);
        if (s)
        {
            ASSERT_TRUE(p.is_bit_set(w-1));
            ASSERT_TRUE(p.is_bit_set(w-2));
        }
        if (o)
        {
            // must be odd
            ASSERT_TRUE(p.is_bit_set(0));
        }
 
    };
    for (int i = 1; i <= 128; i++)      gen(i);
    for (int i = 1; i <= 128; i++)      gen(i, false, true);
    for (int i = 2; i <= 128; i++)      gen(i, true, false);
    for (int i = 2; i <= 128; i++)      gen(i, true, true);
}
 
// https://prime-numbers.info/list/first-1000-primes
// https://prime-numbers.info/list/safe-primes (this library does not generate them, but will check here)
TEST(bignum_test, generate_primes)
{
    auto gen = [](int w)
    {
        Bignum p;
        p.gen_prime(w);
        cout << "genprime width=" << p.width() << ": " << p;
        ASSERT_TRUE(p.is_prime());
        ASSERT_EQ(p.width(), w);
 
        p -= 1;
        p /= 2;
        if (p.is_prime())
        {
            cout << " SAFE";
        }
        cout << endl;
    };
    for (int i = 2; i <= 128; i++)      gen(i);
}
 
TEST(bignum_test, bit_test_set_clear)
{
    Bignum w32(3);
    cout << "init w32     n="<<std::hex<<w32<<std::dec<<" width: "<< w32.width()<<std::endl;
    ASSERT_EQ(w32.width(), 2);
    ASSERT_TRUE(w32.is_bit_set(0));
    ASSERT_TRUE(w32.is_bit_set(1));
    ASSERT_FALSE(w32.is_bit_set(2));
    w32.set_bit(30);
    w32.set_bit(31);
    cout << "set bit 30-31 n="<<std::hex<<w32<<std::dec<<" width: "<< w32.width()<<std::endl;
    ASSERT_EQ(w32, 0xc0000003);
    ASSERT_EQ(w32.width(), 32);
    ASSERT_TRUE(w32.is_bit_set(0));
    ASSERT_TRUE(w32.is_bit_set(1));
    ASSERT_FALSE(w32.is_bit_set(2));
    ASSERT_TRUE(w32.is_bit_set(30));
    ASSERT_TRUE(w32.is_bit_set(31));
    ASSERT_FALSE(w32.is_bit_set(32));
    w32.clear_bit(30);
    w32.clear_bit(31);
    cout << "clr w32 30-31 n="<<std::hex<<w32<<std::dec<<" width: "<< w32.width()<<std::endl;
    ASSERT_EQ(w32, 0x3);
    ASSERT_EQ(w32.width(), 2);
    ASSERT_TRUE(w32.is_bit_set(0));
    ASSERT_TRUE(w32.is_bit_set(1));
    ASSERT_FALSE(w32.is_bit_set(2));
    ASSERT_FALSE(w32.is_bit_set(30));
    ASSERT_FALSE(w32.is_bit_set(31));
    ASSERT_FALSE(w32.is_bit_set(32));
 
    Bignum w64(3);
    w64 <<= 32;
    cout << "init w64     n="<<std::hex<<w64<<std::dec<<" width: "<< w64.width()<<std::endl;
    ASSERT_EQ(w64.width(), 34);
    ASSERT_TRUE(w64.is_bit_set(32));
    ASSERT_TRUE(w64.is_bit_set(33));
    ASSERT_FALSE(w64.is_bit_set(34));
    w64.set_bit(62);
    w64.set_bit(63);
    cout << "set bit 62-63 n="<<std::hex<<w64<<std::dec<<" width: "<< w64.width()<<std::endl;
    ASSERT_EQ(w64.width(), 64);
    ASSERT_TRUE(w64.is_bit_set(32));
    ASSERT_TRUE(w64.is_bit_set(33));
    ASSERT_FALSE(w64.is_bit_set(34));
    ASSERT_TRUE(w64.is_bit_set(62));
    ASSERT_TRUE(w64.is_bit_set(63));
    ASSERT_FALSE(w64.is_bit_set(64));
    w64.clear_bit(62);
    w64.clear_bit(63);
    cout << "clr bit 62-63 n="<<std::hex<<w64<<std::dec<<" width: "<< w64.width()<<std::endl;
    ASSERT_EQ(w64.width(), 34);
    ASSERT_TRUE(w64.is_bit_set(32));
    ASSERT_TRUE(w64.is_bit_set(33));
    ASSERT_FALSE(w64.is_bit_set(34));
    ASSERT_FALSE(w64.is_bit_set(62));
    ASSERT_FALSE(w64.is_bit_set(63));
    ASSERT_FALSE(w64.is_bit_set(64));
}
 
TEST(bignum_test, bit_ops_and)
{
    auto doit = [](int wa, int wb){
        Bignum a(1);
        a <<= wa-1;
        cout << "bit ops   a="<<a.str(true)<<" width: "<< a.width()<<std::endl;
        Bignum b(1);
        b <<= wb-1;
        cout << "bit ops   b="<<b.str(true)<<" width: "<< b.width()<<std::endl;
        Bignum c;
        c = a + b;
        cout << "bit ops   c="<<c.str(true)<<" width: "<< c.width()<<std::endl;
        Bignum x;
        x = a & b;
        cout << "bit ops a&b="<<x.str(true)<<" width: "<< x.width()<<std::endl;
        ASSERT_EQ(x, 0);
        x = a & c;
        cout << "bit ops a&c="<<x.str(true)<<" width: "<< x.width()<<std::endl;
        ASSERT_EQ(x, a);
        x = b & c;
        cout << "bit ops b&c="<<x.str(true)<<" width: "<< x.width()<<std::endl;
        ASSERT_EQ(x, b);
        x = c;
        x &= a;
        ASSERT_EQ(x, a);
        x = c;
        x &= b;
        ASSERT_EQ(x, b);
    };
    doit(1, 2);
    doit(30, 31);
    doit(31, 32);
    doit(32, 33);
 
    Bignum a(1), b(2);
    ASSERT_EQ(a&3, 1);
    ASSERT_EQ(b&3, 2);
    Bignum x = a&3;
    ASSERT_EQ(x, 1);
    x = b&3;
    ASSERT_EQ(x, 2);
}
 
TEST(bignum_test, bit_ops_or)
{
    auto doit = [](int wa, int wb){
        Bignum a(1);
        a <<= wa-1;
        Bignum b(1);
        b <<= wb-1;
        Bignum c;
        c = a + b;
        Bignum x;
        x = a | b;
        ASSERT_EQ(x, c);
        x = a | c;
        ASSERT_EQ(x, c);
        x = b | c;
        ASSERT_EQ(x, c);
        x = c;
        x |= a;
        ASSERT_EQ(x, c);
        x = c;
        x |= b;
        ASSERT_EQ(x, c);
    };
    doit(1, 2);
    doit(30, 31);
    doit(31, 32);
    doit(32, 33);
 
    Bignum a(1), b(2);
    ASSERT_EQ(a|3, 3);
    ASSERT_EQ(b|3, 3);
    Bignum x = a|3;
    ASSERT_EQ(x, 3);
    x = b|3;
    ASSERT_EQ(x, 3);
}
 
TEST(bignum_test, bit_ops_xor)
{
    auto doit = [](int wa, int wb){
        Bignum a(1);
        a <<= wa-1;
        Bignum b(1);
        b <<= wb-1;
        Bignum c;
        c = a + b;
        Bignum x;
        x = a ^ b;
        ASSERT_EQ(x, c);
        x = a ^ c;
        ASSERT_EQ(x, b);
        x = b ^ c;
        ASSERT_EQ(x, a);
        x = c;
        x ^= a;
        ASSERT_EQ(x, b);
        x = c;
        x ^= b;
        ASSERT_EQ(x, a);
    };
    doit(1, 2);
    doit(30, 31);
    doit(31, 32);
    doit(32, 33);
 
    Bignum a(1), b(2), c(3);
    ASSERT_EQ(c^1, 2);
    ASSERT_EQ(c^2, 1);
    Bignum x = c^1;
    ASSERT_EQ(x, 2);
    x = c^2;
    ASSERT_EQ(x, 1);
}
 
TEST(bignum_test, bit_ops_not)
{
    Bignum a=1, b=0;
    ASSERT_EQ(~a, b);
    ASSERT_EQ(~b, a);
    a=0xffff0000;
    b=0xffff;
    ASSERT_EQ(~a, b);
    a <<= 16;
    b=0xffffffff;
    ASSERT_EQ(~a, b);
}
 
TEST(bignum_test, width)
{
    Bignum a(0xf);
    ASSERT_EQ(a.width(), 4);
    auto p = [](int shift)
    {
        Bignum b = 1;
        b <<= shift;
        cout << "width of " << b.str(true) << ": " << b.width() << endl;
        ASSERT_EQ(b.width(), shift+1);
    };
    Bignum b = 0;
    cout << "width of " << b.str(true) << ": " << b.width() << endl;
    ASSERT_EQ(b.width(), 1);
    p(0);
    p(1);
    p(30);
    p(31);
    p(32);
    p(33);
    p(147);
}
 
TEST(bignum_test, negative)
{
    Bignum a;
    
    ASSERT_FALSE(a.is_negative());
    a = 128;
    ASSERT_FALSE(a.is_negative());
    a = -a;
    ASSERT_TRUE(a.is_negative());
}
 
TEST(bignum_test, get)
{
    Bignum a;
    vector<char> v;
 
    auto get_test = [&]
    {
        v.resize(a.len());
        a.get((void*)v.data(), v.size());
        cout << "a = " << a << " get hex " << Hex::bin_to_hexstr(v, " ") << endl;
    };
 
    get_test();
    a = 127;
    get_test();
    ASSERT_EQ(v, vector<char>{'\x7f'});
    a = -a;
    ASSERT_THROW(get_test(), runtime_error);
    a = 128;
    get_test();
    ASSERT_EQ(v, vector<char>{'\x80'});
}
 
TEST(bignum_test, get_2sc)
{
    Bignum a;
    vector<char> v;
 
    auto get_test = [&](vector<char> chk)
    {
        cout << "a = " << a << " len_2sc() = " << a.len_2sc() << endl;
        v.resize(a.len_2sc());
        a.get_2sc((void*)v.data(), v.size());
        cout << "a = " << a << " get hex " << Hex::bin_to_hexstr(v, " ") << endl;
        ASSERT_EQ(v, chk);
    };
/*
        128 0000 0000 1000 0000 - 00 80
        127 0111 1111 - 7f
        -1 1111 1111 - ff
        -127 1000 0001 - 81
        -128 1000 0000 - 80
        -129 1111 1111 0111 1111 - ff 7f
*/
 
    get_test({'\x00'});
    a = 128;
    get_test({'\x00','\x80'});
    a = 127;
    get_test({'\x7f'});
    a = 1;
    a = -a;
    get_test({'\xff'});
    a = 127;
    a = -a;
    get_test({'\x81'});
    a = 128;
    a = -a;
    get_test({'\x80'});
    a = 129;
    a = -a;
    get_test({'\xff','\x7f'});
}