/* * (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 #include #include #include #include #include #include #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 run() override { std::vector 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(1)); } else if(bit <= 31 || (bit == 32 && i == 1)) { result.test_is_eq("BigInt::to_u32bit", a.to_u32bit(), static_cast((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 encoded_n1 = BigInt::encode_1363(n1, 256); Botan::secure_vector encoded_n2 = BigInt::encode_1363(n2, 256); Botan::secure_vector expected = encoded_n1; expected += encoded_n2; Botan::secure_vector 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 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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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("math", "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 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("math", "bn_rand", BigInt_Rand_Test); class Lucas_Primality_Test final : public Test { public: std::vector run() override { const uint32_t lucas_max = (Test::run_long_tests() ? 100000 : 6000); // OEIS A217120 std::set 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("math", "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 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 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("math", "dsa_param", DSA_ParamGen_Test); #endif } }