Z-Botan-0.1.1.0: third_party/botan/src/tests/test_bigint.cpp
/*
* (C) 2009,2015,2016 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include "tests.h"
#if defined(BOTAN_HAS_NUMBERTHEORY)
#include <botan/bigint.h>
#include <botan/numthry.h>
#include <botan/divide.h>
#include <botan/internal/primality.h>
#include <botan/reducer.h>
#include <botan/pow_mod.h>
#include <botan/parsing.h>
#include "test_rng.h"
#endif
namespace Botan_Tests {
namespace {
#if defined(BOTAN_HAS_NUMBERTHEORY)
using Botan::BigInt;
class BigInt_Unit_Tests final : public Test
{
public:
std::vector<Test::Result> run() override
{
std::vector<Test::Result> results;
results.push_back(test_bigint_sizes());
results.push_back(test_random_prime());
results.push_back(test_encode());
results.push_back(test_bigint_io());
results.push_back(test_get_substring());
return results;
}
private:
Test::Result test_bigint_sizes()
{
Test::Result result("BigInt size functions");
for(size_t bit : { 1, 8, 16, 31, 32, 64, 97, 128, 179, 192, 512, 521 })
{
BigInt a;
a.set_bit(bit);
// Test 2^n and 2^n-1
for(size_t i = 0; i != 2; ++i)
{
const size_t exp_bits = bit + 1 - i;
result.test_eq("BigInt::bits", a.bits(), exp_bits);
result.test_eq("BigInt::bytes", a.bytes(),
(exp_bits % 8 == 0) ? (exp_bits / 8) : (exp_bits + 8 - exp_bits % 8) / 8);
if(bit == 1 && i == 1)
{
result.test_is_eq("BigInt::to_u32bit zero", a.to_u32bit(), static_cast<uint32_t>(1));
}
else if(bit <= 31 || (bit == 32 && i == 1))
{
result.test_is_eq("BigInt::to_u32bit", a.to_u32bit(), static_cast<uint32_t>((uint64_t(1) << bit) - i));
}
else
{
try
{
a.to_u32bit();
result.test_failure("BigInt::to_u32bit roundtripped out of range value");
}
catch(std::exception&)
{
result.test_success("BigInt::to_u32bit rejected out of range");
}
}
a--;
}
}
return result;
}
Test::Result test_random_prime()
{
Test::Result result("BigInt prime generation");
result.test_throws("Invalid bit size",
"random_prime: Can't make a prime of 0 bits",
[]() { Botan::random_prime(Test::rng(), 0); });
result.test_throws("Invalid bit size",
"random_prime: Can't make a prime of 1 bits",
[]() { Botan::random_prime(Test::rng(), 1); });
result.test_throws("Invalid arg",
"random_prime Invalid value for equiv/modulo",
[]() { Botan::random_prime(Test::rng(), 2, 1, 0, 2); });
BigInt p = Botan::random_prime(Test::rng(), 2);
result.confirm("Only two 2-bit primes", p == 2 || p == 3);
p = Botan::random_prime(Test::rng(), 3);
result.confirm("Only two 3-bit primes", p == 5 || p == 7);
p = Botan::random_prime(Test::rng(), 4);
result.confirm("Only two 4-bit primes", p == 11 || p == 13);
for(size_t bits = 5; bits <= 32; ++bits)
{
p = Botan::random_prime(Test::rng(), bits);
result.test_eq("Expected bit size", p.bits(), bits);
result.test_eq("P is prime", Botan::is_prime(p, Test::rng()), true);
}
const size_t safe_prime_bits = 65;
const BigInt safe_prime = Botan::random_safe_prime(Test::rng(), safe_prime_bits);
result.test_eq("Safe prime size", safe_prime.bits(), safe_prime_bits);
result.confirm("P is prime", Botan::is_prime(safe_prime, Test::rng()));
result.confirm("(P-1)/2 is prime", Botan::is_prime((safe_prime - 1) / 2, Test::rng()));
return result;
}
Test::Result test_encode()
{
Test::Result result("BigInt encoding functions");
const BigInt n1(0xffff);
const BigInt n2(1023);
Botan::secure_vector<uint8_t> encoded_n1 = BigInt::encode_1363(n1, 256);
Botan::secure_vector<uint8_t> encoded_n2 = BigInt::encode_1363(n2, 256);
Botan::secure_vector<uint8_t> expected = encoded_n1;
expected += encoded_n2;
Botan::secure_vector<uint8_t> encoded_n1_n2 = BigInt::encode_fixed_length_int_pair(n1, n2, 256);
result.test_eq("encode_fixed_length_int_pair", encoded_n1_n2, expected);
for(size_t i = 0; i < 256 - n1.bytes(); ++i)
{
if(encoded_n1[i] != 0)
{
result.test_failure("encode_1363", "no zero byte");
}
}
return result;
}
Test::Result test_get_substring()
{
Test::Result result("BigInt get_substring");
const size_t rbits = 1024;
const Botan::BigInt r(Test::rng(), rbits);
for(size_t wlen = 1; wlen <= 32; ++wlen)
{
for(size_t offset = 0; offset != rbits + 64; ++offset)
{
const uint32_t val = r.get_substring(offset, wlen);
Botan::BigInt t = r >> offset;
t.mask_bits(wlen);
const uint32_t cmp = t.to_u32bit();
result.test_eq("Same value", size_t(val), size_t(cmp));
}
}
return result;
}
Test::Result test_bigint_io()
{
Test::Result result("BigInt IO operators");
const std::map<std::string, Botan::BigInt> str_to_val =
{
{ "-13", -Botan::BigInt(13) },
{ "0", Botan::BigInt(0) },
{ "0x13", Botan::BigInt(0x13) },
{ "1", Botan::BigInt(1) },
{ "4294967297", Botan::BigInt(2147483648) * 2 + 1 }
};
for(auto vec : str_to_val)
{
Botan::BigInt n;
std::istringstream iss;
iss.str(vec.first);
iss >> n;
result.test_eq("input '" + vec.first + "'", n, vec.second);
}
BigInt n = 33;
std::ostringstream oss;
oss << n;
result.test_eq("output 33 dec", oss.str(), "33");
oss.str("");
oss << std::hex << n;
result.test_eq("output 33 hex", oss.str(), "21");
result.test_throws("octal output not supported", [&]() { oss << std::oct << n; });
return result;
}
};
BOTAN_REGISTER_TEST("bigint_unit", BigInt_Unit_Tests);
class BigInt_Add_Test final : public Text_Based_Test
{
public:
BigInt_Add_Test() : Text_Based_Test("bn/add.vec", "In1,In2,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Addition");
using Botan::BigInt;
const BigInt a = vars.get_req_bn("In1");
const BigInt b = vars.get_req_bn("In2");
const BigInt c = vars.get_req_bn("Output");
result.test_eq("a + b", a + b, c);
result.test_eq("b + a", b + a, c);
BigInt e = a;
e += b;
result.test_eq("a += b", e, c);
e = b;
e += a;
result.test_eq("b += a", e, c);
return result;
}
};
BOTAN_REGISTER_TEST("bn_add", BigInt_Add_Test);
class BigInt_Sub_Test final : public Text_Based_Test
{
public:
BigInt_Sub_Test() : Text_Based_Test("bn/sub.vec", "In1,In2,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Subtraction");
const BigInt a = vars.get_req_bn("In1");
const BigInt b = vars.get_req_bn("In2");
const BigInt c = vars.get_req_bn("Output");
result.test_eq("a - b", a - b, c);
BigInt e = a;
e -= b;
result.test_eq("a -= b", e, c);
return result;
}
};
BOTAN_REGISTER_TEST("bn_sub", BigInt_Sub_Test);
class BigInt_Mul_Test final : public Text_Based_Test
{
public:
BigInt_Mul_Test() : Text_Based_Test("bn/mul.vec", "In1,In2,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Multiply");
const BigInt a = vars.get_req_bn("In1");
const BigInt b = vars.get_req_bn("In2");
const BigInt c = vars.get_req_bn("Output");
result.test_eq("a * b", a * b, c);
result.test_eq("b * a", b * a, c);
BigInt e = a;
e *= b;
result.test_eq("a *= b", e, c);
e = b;
e *= a;
result.test_eq("b *= a", e, c);
return result;
}
};
BOTAN_REGISTER_TEST("bn_mul", BigInt_Mul_Test);
class BigInt_Sqr_Test final : public Text_Based_Test
{
public:
BigInt_Sqr_Test() : Text_Based_Test("bn/sqr.vec", "Input,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Square");
const BigInt input = vars.get_req_bn("Input");
const BigInt output = vars.get_req_bn("Output");
result.test_eq("a * a", input * input, output);
result.test_eq("sqr(a)", square(input), output);
return result;
}
};
BOTAN_REGISTER_TEST("bn_sqr", BigInt_Sqr_Test);
class BigInt_Div_Test final : public Text_Based_Test
{
public:
BigInt_Div_Test() : Text_Based_Test("bn/divide.vec", "In1,In2,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Divide");
const BigInt a = vars.get_req_bn("In1");
const BigInt b = vars.get_req_bn("In2");
const BigInt c = vars.get_req_bn("Output");
result.test_eq("a / b", a / b, c);
BigInt e = a;
e /= b;
result.test_eq("a /= b", e, c);
if(b.bytes() == 1)
{
const uint8_t b8 = b.byte_at(0);
Botan::BigInt ct_q;
uint8_t ct_r;
Botan::ct_divide_u8(a, b8, ct_q, ct_r);
result.test_eq("ct_divide_u8 q", ct_q, c);
}
Botan::BigInt ct_q, ct_r;
Botan::ct_divide(a, b, ct_q, ct_r);
result.test_eq("ct_divide q", ct_q, c);
return result;
}
};
BOTAN_REGISTER_TEST("bn_div", BigInt_Div_Test);
class BigInt_Mod_Test final : public Text_Based_Test
{
public:
BigInt_Mod_Test() : Text_Based_Test("bn/mod.vec", "In1,In2,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Mod");
const BigInt a = vars.get_req_bn("In1");
const BigInt b = vars.get_req_bn("In2");
const BigInt expected = vars.get_req_bn("Output");
result.test_eq("a % b", a % b, expected);
BigInt e = a;
e %= b;
result.test_eq("a %= b", e, expected);
const Botan::Modular_Reducer mod_b(b);
result.test_eq("Barrett", mod_b.reduce(a), expected);
// if b fits into a Botan::word test %= operator for words
if(b.sig_words() == 1)
{
const Botan::word b_word = b.word_at(0);
e = a;
e %= b_word;
result.test_eq("a %= b (as word)", e, expected);
result.test_eq("a % b (as word)", a % b_word, expected);
}
if(b.bytes() == 1)
{
Botan::BigInt ct_q;
Botan::uint8_t ct_r;
Botan::ct_divide_u8(a, b.byte_at(0), ct_q, ct_r);
result.test_eq("ct_divide_u8 r", ct_r, expected);
}
Botan::BigInt ct_q, ct_r;
Botan::ct_divide(a, b, ct_q, ct_r);
result.test_eq("ct_divide r", ct_r, expected);
return result;
}
};
BOTAN_REGISTER_TEST("bn_mod", BigInt_Mod_Test);
class BigInt_GCD_Test final : public Text_Based_Test
{
public:
BigInt_GCD_Test() : Text_Based_Test("bn/gcd.vec", "X,Y,GCD") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt GCD");
const BigInt x = vars.get_req_bn("X");
const BigInt y = vars.get_req_bn("Y");
const BigInt expected = vars.get_req_bn("GCD");
const BigInt g = Botan::gcd(x, y);
result.test_eq("gcd", g, expected);
return result;
}
};
BOTAN_REGISTER_TEST("bn_gcd", BigInt_GCD_Test);
class BigInt_Jacobi_Test final : public Text_Based_Test
{
public:
BigInt_Jacobi_Test() : Text_Based_Test("bn/jacobi.vec", "A,N,J") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Jacobi");
const BigInt a = vars.get_req_bn("A");
const BigInt n = vars.get_req_bn("N");
const std::string expected = vars.get_req_str("J");
const int32_t j = Botan::jacobi(a, n);
if(j == 0)
result.test_eq("jacobi", expected, "0");
else if(j == -1)
result.test_eq("jacobi", expected, "-1");
else
result.test_eq("jacobi", expected, "1");
return result;
}
};
BOTAN_REGISTER_TEST("bn_jacobi", BigInt_Jacobi_Test);
class BigInt_Lshift_Test final : public Text_Based_Test
{
public:
BigInt_Lshift_Test() : Text_Based_Test("bn/lshift.vec", "Value,Shift,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Lshift");
const BigInt value = vars.get_req_bn("Value");
const size_t shift = vars.get_req_bn("Shift").to_u32bit();
const BigInt output = vars.get_req_bn("Output");
result.test_eq("a << s", value << shift, output);
BigInt e = value;
e <<= shift;
result.test_eq("a <<= s", e, output);
return result;
}
};
BOTAN_REGISTER_TEST("bn_lshift", BigInt_Lshift_Test);
class BigInt_Rshift_Test final : public Text_Based_Test
{
public:
BigInt_Rshift_Test() : Text_Based_Test("bn/rshift.vec", "Value,Shift,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Rshift");
const BigInt value = vars.get_req_bn("Value");
const size_t shift = vars.get_req_bn("Shift").to_u32bit();
const BigInt output = vars.get_req_bn("Output");
result.test_eq("a >> s", value >> shift, output);
BigInt e = value;
e >>= shift;
result.test_eq("a >>= s", e, output);
return result;
}
};
BOTAN_REGISTER_TEST("bn_rshift", BigInt_Rshift_Test);
class BigInt_Powmod_Test final : public Text_Based_Test
{
public:
BigInt_Powmod_Test() : Text_Based_Test("bn/powmod.vec", "Base,Exponent,Modulus,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Powmod");
const BigInt base = vars.get_req_bn("Base");
const BigInt exponent = vars.get_req_bn("Exponent");
const BigInt modulus = vars.get_req_bn("Modulus");
const BigInt expected = vars.get_req_bn("Output");
result.test_eq("power_mod", Botan::power_mod(base, exponent, modulus), expected);
/*
* Only the basic power_mod interface supports negative base
*/
if(base.is_negative())
return result;
Botan::Power_Mod pow_mod1(modulus);
pow_mod1.set_base(base);
pow_mod1.set_exponent(exponent);
result.test_eq("pow_mod1", pow_mod1.execute(), expected);
Botan::Power_Mod pow_mod2(modulus);
// Reverses ordering which affects window size
pow_mod2.set_exponent(exponent);
pow_mod2.set_base(base);
result.test_eq("pow_mod2", pow_mod2.execute(), expected);
result.test_eq("pow_mod2 #2", pow_mod2.execute(), expected);
if(modulus.is_odd())
{
// TODO: test different hints
// also TODO: remove bogus hinting arguments :)
Botan::Power_Mod pow_mod3(modulus, Botan::Power_Mod::NO_HINTS, /*disable_montgomery=*/true);
pow_mod3.set_exponent(exponent);
pow_mod3.set_base(base);
result.test_eq("pow_mod_fixed_window", pow_mod3.execute(), expected);
}
return result;
}
};
BOTAN_REGISTER_TEST("bn_powmod", BigInt_Powmod_Test);
class BigInt_IsPrime_Test final : public Text_Based_Test
{
public:
BigInt_IsPrime_Test() : Text_Based_Test("bn/isprime.vec", "X") {}
Test::Result run_one_test(const std::string& header, const VarMap& vars) override
{
if(header != "Prime" && header != "NonPrime")
{
throw Test_Error("Bad header for prime test " + header);
}
const BigInt value = vars.get_req_bn("X");
const bool is_prime = (header == "Prime");
Test::Result result("BigInt Test " + header);
result.test_eq("is_prime", Botan::is_prime(value, Test::rng()), is_prime);
return result;
}
};
BOTAN_REGISTER_TEST("bn_isprime", BigInt_IsPrime_Test);
class BigInt_IsSquare_Test final : public Text_Based_Test
{
public:
BigInt_IsSquare_Test() : Text_Based_Test("bn/perfect_square.vec", "X,R") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
const BigInt value = vars.get_req_bn("X");
const BigInt expected = vars.get_req_bn("R");
const BigInt computed = Botan::is_perfect_square(value);
Test::Result result("BigInt IsSquare");
result.test_eq("is_perfect_square", computed, expected);
return result;
}
};
BOTAN_REGISTER_TEST("bn_issquare", BigInt_IsSquare_Test);
class BigInt_Ressol_Test final : public Text_Based_Test
{
public:
BigInt_Ressol_Test() : Text_Based_Test("bn/ressol.vec", "Input,Modulus,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Ressol");
const Botan::BigInt a = vars.get_req_bn("Input");
const Botan::BigInt p = vars.get_req_bn("Modulus");
const Botan::BigInt exp = vars.get_req_bn("Output");
const Botan::BigInt a_sqrt = Botan::ressol(a, p);
result.test_eq("ressol", a_sqrt, exp);
if(a_sqrt > 1)
{
const Botan::BigInt a_sqrt2 = (a_sqrt * a_sqrt) % p;
result.test_eq("square correct", a_sqrt2, a);
}
return result;
}
};
BOTAN_REGISTER_TEST("bn_ressol", BigInt_Ressol_Test);
class BigInt_InvMod_Test final : public Text_Based_Test
{
public:
BigInt_InvMod_Test() : Text_Based_Test("bn/invmod.vec", "Input,Modulus,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt InvMod");
const Botan::BigInt a = vars.get_req_bn("Input");
const Botan::BigInt mod = vars.get_req_bn("Modulus");
const Botan::BigInt expected = vars.get_req_bn("Output");
const Botan::BigInt a_inv = Botan::inverse_mod(a, mod);
result.test_eq("inverse_mod", a_inv, expected);
if(a_inv > 1)
{
result.test_eq("inverse ok", (a * a_inv) % mod, 1);
}
/*
else if((a % mod) > 0)
{
result.confirm("no inverse with gcd > 1", gcd(a, mod) > 1);
}
*/
if(mod.is_odd() && a_inv != 0)
{
result.test_eq("normalized_montgomery_inverse",
normalized_montgomery_inverse(a, mod),
expected);
}
return result;
}
};
BOTAN_REGISTER_TEST("bn_invmod", BigInt_InvMod_Test);
class BigInt_Rand_Test final : public Text_Based_Test
{
public:
BigInt_Rand_Test() : Text_Based_Test("bn/random.vec", "Seed,Min,Max,Output") {}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("BigInt Random");
const std::vector<uint8_t> seed = vars.get_req_bin("Seed");
const Botan::BigInt min = vars.get_req_bn("Min");
const Botan::BigInt max = vars.get_req_bn("Max");
const Botan::BigInt expected = vars.get_req_bn("Output");
Fixed_Output_RNG rng(seed);
Botan::BigInt generated = BigInt::random_integer(rng, min, max);
result.test_eq("random_integer KAT", generated, expected);
return result;
}
};
BOTAN_REGISTER_TEST("bn_rand", BigInt_Rand_Test);
class Lucas_Primality_Test final : public Test
{
public:
std::vector<Test::Result> run() override
{
const uint32_t lucas_max = (Test::run_long_tests() ? 100000 : 6000);
// OEIS A217120
std::set<uint32_t> lucas_pp{
323, 377, 1159, 1829, 3827, 5459, 5777, 9071, 9179,
10877, 11419, 11663, 13919, 14839, 16109, 16211, 18407, 18971,
19043, 22499, 23407, 24569, 25199, 25877, 26069, 27323, 32759,
34943, 35207, 39059, 39203, 39689, 40309, 44099, 46979, 47879,
50183, 51983, 53663, 56279, 58519, 60377, 63881, 69509, 72389,
73919, 75077, 77219, 79547, 79799, 82983, 84419, 86063, 90287,
94667, 97019, 97439,
};
Test::Result result("Lucas primality test");
for(uint32_t i = 3; i <= lucas_max; i += 2)
{
Botan::Modular_Reducer mod_i(i);
const bool passes_lucas = Botan::is_lucas_probable_prime(i, mod_i);
const bool is_prime = Botan::is_prime(i, Test::rng());
const bool is_lucas_pp = (is_prime == false && passes_lucas == true);
if(is_lucas_pp)
result.confirm("Lucas pseudoprime is in list", lucas_pp.count(i) == 1);
else
result.confirm("Lucas non-pseudoprime is not in list", lucas_pp.count(i) == 0);
}
return {result};
}
};
BOTAN_REGISTER_TEST("bn_lucas", Lucas_Primality_Test);
class DSA_ParamGen_Test final : public Text_Based_Test
{
public:
DSA_ParamGen_Test() : Text_Based_Test("bn/dsa_gen.vec", "P,Q,Counter,Seed") {}
Test::Result run_one_test(const std::string& header, const VarMap& vars) override
{
const std::vector<uint8_t> seed = vars.get_req_bin("Seed");
const size_t offset = vars.get_req_sz("Counter");
const Botan::BigInt exp_P = vars.get_req_bn("P");
const Botan::BigInt exp_Q = vars.get_req_bn("Q");
const std::vector<std::string> header_parts = Botan::split_on(header, ',');
if(header_parts.size() != 2)
{
throw Test_Error("Unexpected header '" + header + "' in DSA param gen test");
}
const size_t p_bits = Botan::to_u32bit(header_parts[1]);
const size_t q_bits = Botan::to_u32bit(header_parts[0]);
Test::Result result("DSA Parameter Generation");
try
{
Botan::BigInt gen_P, gen_Q;
if(Botan::generate_dsa_primes(Test::rng(), gen_P, gen_Q, p_bits, q_bits, seed, offset))
{
result.test_eq("P", gen_P, exp_P);
result.test_eq("Q", gen_Q, exp_Q);
}
else
{
result.test_failure("Seed did not generate a DSA parameter");
}
}
catch(Botan::Lookup_Error&)
{
}
return result;
}
};
BOTAN_REGISTER_TEST("dsa_param", DSA_ParamGen_Test);
#endif
}
}