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/*
* (C) 2007 Falko Strenzke
* 2007 Manuel Hartl
* 2009,2015,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include "tests.h"
#if defined(BOTAN_HAS_ECC_GROUP)
#include <botan/bigint.h>
#include <botan/numthry.h>
#include <botan/curve_nistp.h>
#include <botan/pk_keys.h>
#include <botan/point_gfp.h>
#include <botan/ec_group.h>
#include <botan/reducer.h>
#include <botan/hex.h>
#include <botan/data_src.h>
#include <botan/x509_key.h>
#endif
namespace Botan_Tests {
namespace {
#if defined(BOTAN_HAS_ECC_GROUP)
Botan::BigInt test_integer(Botan::RandomNumberGenerator& rng, size_t bits, BigInt max)
{
/*
Produces integers with long runs of ones and zeros, for testing for
carry handling problems.
*/
Botan::BigInt x = 0;
auto flip_prob = [](size_t i) -> double
{
if(i % 64 == 0)
{
return .5;
}
if(i % 32 == 0)
{
return .4;
}
if(i % 8 == 0)
{
return .05;
}
return .01;
};
bool active = rng.next_byte() % 2;
for(size_t i = 0; i != bits; ++i)
{
x <<= 1;
x += static_cast<int>(active);
const double prob = flip_prob(i);
const double sample = double(rng.next_byte() % 100) / 100.0; // biased
if(sample < prob)
{
active = !active;
}
}
if(max > 0)
{
while(x >= max)
{
const size_t b = x.bits() - 1;
BOTAN_ASSERT(x.get_bit(b) == true, "Set");
x.clear_bit(b);
}
}
return x;
}
Botan::PointGFp create_random_point(Botan::RandomNumberGenerator& rng,
const Botan::EC_Group& group)
{
const Botan::BigInt& p = group.get_p();
const Botan::Modular_Reducer mod_p(p);
for(;;)
{
const Botan::BigInt x = Botan::BigInt::random_integer(rng, 1, p);
const Botan::BigInt x3 = mod_p.multiply(x, mod_p.square(x));
const Botan::BigInt ax = mod_p.multiply(group.get_a(), x);
const Botan::BigInt y = mod_p.reduce(x3 + ax + group.get_b());
const Botan::BigInt sqrt_y = ressol(y, p);
if(sqrt_y > 1)
{
BOTAN_ASSERT_EQUAL(mod_p.square(sqrt_y), y, "Square root is correct");
return group.point(x, sqrt_y);
}
}
}
class ECC_Randomized_Tests final : public Test
{
public:
std::vector<Test::Result> run() override;
};
std::vector<Test::Result> ECC_Randomized_Tests::run()
{
std::vector<Test::Result> results;
for(const std::string& group_name : Botan::EC_Group::known_named_groups())
{
Test::Result result("ECC randomized " + group_name);
result.start_timer();
Botan::EC_Group group(group_name);
const Botan::PointGFp& pt = create_random_point(Test::rng(), group);
const Botan::BigInt& group_order = group.get_order();
std::vector<Botan::BigInt> blind_ws;
try
{
const size_t trials = (Test::run_long_tests() ? 10 : 3);
for(size_t i = 0; i < trials; ++i)
{
const Botan::BigInt a = Botan::BigInt::random_integer(Test::rng(), 2, group_order);
const Botan::BigInt b = Botan::BigInt::random_integer(Test::rng(), 2, group_order);
const Botan::BigInt c = a + b;
const Botan::PointGFp P = pt * a;
const Botan::PointGFp Q = pt * b;
const Botan::PointGFp R = pt * c;
Botan::PointGFp P1 = group.blinded_var_point_multiply(pt, a, Test::rng(), blind_ws);
Botan::PointGFp Q1 = group.blinded_var_point_multiply(pt, b, Test::rng(), blind_ws);
Botan::PointGFp R1 = group.blinded_var_point_multiply(pt, c, Test::rng(), blind_ws);
Botan::PointGFp A1 = P + Q;
Botan::PointGFp A2 = Q + P;
result.test_eq("p + q", A1, R);
result.test_eq("q + p", A2, R);
A1.force_affine();
A2.force_affine();
result.test_eq("p + q", A1, R);
result.test_eq("q + p", A2, R);
result.test_eq("p on the curve", P.on_the_curve(), true);
result.test_eq("q on the curve", Q.on_the_curve(), true);
result.test_eq("r on the curve", R.on_the_curve(), true);
result.test_eq("P1", P1, P);
result.test_eq("Q1", Q1, Q);
result.test_eq("R1", R1, R);
P1.force_affine();
Q1.force_affine();
R1.force_affine();
result.test_eq("P1", P1, P);
result.test_eq("Q1", Q1, Q);
result.test_eq("R1", R1, R);
}
}
catch(std::exception& e)
{
result.test_failure(group_name, e.what());
}
result.end_timer();
results.push_back(result);
}
return results;
}
BOTAN_REGISTER_TEST("ecc_randomized", ECC_Randomized_Tests);
class NIST_Curve_Reduction_Tests final : public Test
{
public:
typedef std::function<void (Botan::BigInt&, Botan::secure_vector<Botan::word>&)> reducer_fn;
std::vector<Test::Result> run() override
{
std::vector<Test::Result> results;
// Using lambdas here to avoid strange UbSan warning (#1370)
#if defined(BOTAN_HAS_NIST_PRIME_REDUCERS_W32)
results.push_back(random_redc_test(
"P-384",
Botan::prime_p384(),
[](Botan::BigInt& p, Botan::secure_vector<Botan::word>& ws) -> void
{
Botan::redc_p384(p, ws);
}));
results.push_back(random_redc_test(
"P-256",
Botan::prime_p256(),
[](Botan::BigInt& p, Botan::secure_vector<Botan::word>& ws) -> void
{
Botan::redc_p256(p, ws);
}));
results.push_back(random_redc_test(
"P-224",
Botan::prime_p224(),
[](Botan::BigInt& p, Botan::secure_vector<Botan::word>& ws) -> void
{
Botan::redc_p224(p, ws);
}));
results.push_back(random_redc_test(
"P-192",
Botan::prime_p192(),
[](Botan::BigInt& p, Botan::secure_vector<Botan::word>& ws) -> void
{
Botan::redc_p192(p, ws);
}));
#endif
results.push_back(random_redc_test(
"P-521",
Botan::prime_p521(),
[](Botan::BigInt& p, Botan::secure_vector<Botan::word>& ws) -> void
{
Botan::redc_p521(p, ws);
}));
return results;
}
Test::Result random_redc_test(const std::string& prime_name,
const Botan::BigInt& p,
reducer_fn redc_fn)
{
const Botan::BigInt p2 = p * p;
const size_t p_bits = p.bits();
Botan::Modular_Reducer p_redc(p);
Botan::secure_vector<Botan::word> ws;
Test::Result result("NIST " + prime_name + " reduction");
result.start_timer();
const size_t trials = (Test::run_long_tests() ? 128 : 16);
for(size_t i = 0; i <= trials; ++i)
{
const Botan::BigInt x = test_integer(Test::rng(), 2 * p_bits, p2);
// TODO: time and report all three approaches
const Botan::BigInt v1 = x % p;
const Botan::BigInt v2 = p_redc.reduce(x);
Botan::BigInt v3 = x;
redc_fn(v3, ws);
if(!result.test_eq("reference redc", v1, v2) ||
!result.test_eq("specialized redc", v2, v3))
{
result.test_note("failing input" + Botan::hex_encode(Botan::BigInt::encode(x)));
}
}
result.end_timer();
return result;
}
};
BOTAN_REGISTER_TEST("nist_redc", NIST_Curve_Reduction_Tests);
class EC_Group_Tests : public Test
{
public:
std::vector<Test::Result> run() override
{
std::vector<Test::Result> results;
for(const std::string& group_name : Botan::EC_Group::known_named_groups())
{
Test::Result result("EC_Group " + group_name);
const Botan::EC_Group group(group_name);
result.confirm("EC_Group is known", !group.get_curve_oid().empty());
result.test_eq("EC_Group has correct bit size", group.get_p().bits(), group.get_p_bits());
result.test_eq("EC_Group has byte size", group.get_p().bytes(), group.get_p_bytes());
const auto pt_mult_by_order = group.get_base_point() * group.get_order();
result.confirm("Multiplying point by the order results in zero point", pt_mult_by_order.is_zero());
if(group.a_is_minus_3())
result.test_eq("Group A equals -3", group.get_a(), group.get_p() - 3);
else
result.test_ne("Group " + group_name + " A does not equal -3", group.get_a(), group.get_p() - 3);
if(group.a_is_zero())
result.test_eq("Group A is zero", group.get_a(), BigInt(0));
else
result.test_ne("Group " + group_name + " A does not equal zero", group.get_a(), BigInt(0));
// get a valid point
Botan::PointGFp p = group.get_base_point() * Test::rng().next_nonzero_byte();
// get a copy
Botan::PointGFp q = p;
p.randomize_repr(Test::rng());
q.randomize_repr(Test::rng());
result.test_eq("affine x after copy", p.get_affine_x(), q.get_affine_x());
result.test_eq("affine y after copy", p.get_affine_y(), q.get_affine_y());
q.force_affine();
result.test_eq("affine x after copy", p.get_affine_x(), q.get_affine_x());
result.test_eq("affine y after copy", p.get_affine_y(), q.get_affine_y());
test_ser_der(result, group);
test_basic_math(result, group);
test_point_swap(result, group);
test_zeropoint(result, group);
results.push_back(result);
}
return results;
}
private:
void test_ser_der(Test::Result& result, const Botan::EC_Group& group)
{
// generate point
const Botan::PointGFp pt = create_random_point(Test::rng(), group);
const Botan::PointGFp zero = group.zero_point();
for(auto scheme : { Botan::PointGFp::UNCOMPRESSED,
Botan::PointGFp::COMPRESSED,
Botan::PointGFp::HYBRID })
{
result.test_eq("encoded/decode rt works", group.OS2ECP(pt.encode(scheme)), pt);
result.test_eq("encoded/decode rt works", group.OS2ECP(zero.encode(scheme)), zero);
}
}
void test_basic_math(Test::Result& result, const Botan::EC_Group& group)
{
const Botan::PointGFp& G = group.get_base_point();
Botan::PointGFp p1 = G * 2;
p1 += G;
result.test_eq("point addition", p1, G * 3);
p1 -= G * 2;
result.test_eq("point subtraction", p1, G);
}
void test_point_swap(Test::Result& result, const Botan::EC_Group& group)
{
Botan::PointGFp a(create_random_point(Test::rng(), group));
Botan::PointGFp b(create_random_point(Test::rng(), group));
b *= Botan::BigInt(Test::rng(), 20);
Botan::PointGFp c(a);
Botan::PointGFp d(b);
d.swap(c);
result.test_eq("swap correct", a, d);
result.test_eq("swap correct", b, c);
}
void test_zeropoint(Test::Result& result, const Botan::EC_Group& group)
{
const Botan::PointGFp zero = group.zero_point();
const Botan::PointGFp p1 = group.get_base_point() * 2;
result.confirm("point is on the curve", p1.on_the_curve());
result.confirm("point is not zero", !p1.is_zero());
Botan::PointGFp p2 = p1;
p2 -= p1;
result.confirm("p - q with q = p results in zero", p2.is_zero());
const Botan::PointGFp minus_p1 = -p1;
result.confirm("point is on the curve", minus_p1.on_the_curve());
const Botan::PointGFp shouldBeZero = p1 + minus_p1;
result.confirm("point is on the curve", shouldBeZero.on_the_curve());
result.confirm("point is zero", shouldBeZero.is_zero());
result.test_eq("minus point x", minus_p1.get_affine_x(), p1.get_affine_x());
result.test_eq("minus point y", minus_p1.get_affine_y(), group.get_p() - p1.get_affine_y());
result.confirm("zero point is zero", zero.is_zero());
result.confirm("zero point is on the curve", zero.on_the_curve());
result.test_eq("addition of zero does nothing", p1, p1 + zero);
result.test_eq("addition of zero does nothing", p1, zero + p1);
result.test_eq("addition of zero does nothing", p1, p1 - zero);
result.confirm("zero times anything is the zero point", (zero * 39193).is_zero());
for(auto scheme : { Botan::PointGFp::UNCOMPRESSED,
Botan::PointGFp::COMPRESSED,
Botan::PointGFp::HYBRID })
{
const std::vector<uint8_t> v = zero.encode(scheme);
result.test_eq("encoded/decode rt works", group.OS2ECP(v), zero);
}
}
};
BOTAN_REGISTER_TEST("ec_group", EC_Group_Tests);
Test::Result test_decoding_with_seed()
{
Test::Result result("ECC Unit");
Botan::EC_Group secp384r1_with_seed(
Test::read_data_file("x509/ecc/secp384r1_seed.pem"));
result.confirm("decoding worked", secp384r1_with_seed.initialized());
Botan::EC_Group secp384r1("secp384r1");
result.test_eq("P-384 prime", secp384r1_with_seed.get_p(), secp384r1.get_p());
return result;
}
Test::Result test_coordinates()
{
Test::Result result("ECC Unit");
const Botan::BigInt exp_affine_x("16984103820118642236896513183038186009872590470");
const Botan::BigInt exp_affine_y("1373093393927139016463695321221277758035357890939");
// precalculation
const Botan::EC_Group secp160r1("secp160r1");
const Botan::PointGFp& p_G = secp160r1.get_base_point();
const Botan::PointGFp point_exp = secp160r1.point(exp_affine_x, exp_affine_y);
result.confirm("Point is on the curve", point_exp.on_the_curve());
const Botan::PointGFp p1 = p_G * 2;
result.test_eq("Point affine x", p1.get_affine_x(), exp_affine_x);
result.test_eq("Point affine y", p1.get_affine_y(), exp_affine_y);
return result;
}
/**
Test point multiplication according to
--------
SEC 2: Test Vectors for SEC 1
Certicom Research
Working Draft
September, 1999
Version 0.3;
Section 2.1.2
--------
*/
Test::Result test_point_mult()
{
Test::Result result("ECC Unit");
Botan::EC_Group secp160r1("secp160r1");
const Botan::PointGFp& p_G = secp160r1.get_base_point();
Botan::BigInt d_U("0xaa374ffc3ce144e6b073307972cb6d57b2a4e982");
Botan::PointGFp Q_U = d_U * p_G;
result.test_eq("affine x", Q_U.get_affine_x(), Botan::BigInt("466448783855397898016055842232266600516272889280"));
result.test_eq("affine y", Q_U.get_affine_y(), Botan::BigInt("1110706324081757720403272427311003102474457754220"));
return result;
}
Test::Result test_point_negative()
{
Test::Result result("ECC Unit");
Botan::EC_Group secp160r1("secp160r1");
const Botan::PointGFp& p_G = secp160r1.get_base_point();
const Botan::PointGFp p1 = p_G * 2;
result.test_eq("affine x", p1.get_affine_x(), Botan::BigInt("16984103820118642236896513183038186009872590470"));
result.test_eq("affine y", p1.get_affine_y(), Botan::BigInt("1373093393927139016463695321221277758035357890939"));
const Botan::PointGFp p1_neg = -p1;
result.test_eq("affine x", p1_neg.get_affine_x(), p1.get_affine_x());
result.test_eq("affine y", p1_neg.get_affine_y(), Botan::BigInt("88408243403763901739989511495005261618427168388"));
return result;
}
Test::Result test_mult_point()
{
Test::Result result("ECC Unit");
Botan::EC_Group secp160r1("secp160r1");
const Botan::PointGFp& p_G = secp160r1.get_base_point();
Botan::PointGFp p0 = p_G;
Botan::PointGFp p1 = p_G * 2;
p1 *= p0.get_affine_x();
const Botan::BigInt exp_mult_x(std::string("967697346845926834906555988570157345422864716250"));
const Botan::BigInt exp_mult_y(std::string("512319768365374654866290830075237814703869061656"));
Botan::PointGFp expected = secp160r1.point(exp_mult_x, exp_mult_y);
result.test_eq("point mult", p1, expected);
return result;
}
Test::Result test_basic_operations()
{
Test::Result result("ECC Unit");
// precalculation
Botan::EC_Group secp160r1("secp160r1");
const Botan::PointGFp& p_G = secp160r1.get_base_point();
const Botan::PointGFp p0 = p_G;
const Botan::PointGFp p1 = p_G * 2;
result.test_eq("p1 affine x", p1.get_affine_x(), Botan::BigInt("16984103820118642236896513183038186009872590470"));
result.test_eq("p1 affine y", p1.get_affine_y(), Botan::BigInt("1373093393927139016463695321221277758035357890939"));
const Botan::PointGFp simplePlus = p1 + p0;
const Botan::PointGFp exp_simplePlus = secp160r1.point(Botan::BigInt("704859595002530890444080436569091156047721708633"),
Botan::BigInt("1147993098458695153857594941635310323215433166682"));
result.test_eq("point addition", simplePlus, exp_simplePlus);
const Botan::PointGFp simpleMinus = p1 - p0;
const Botan::PointGFp exp_simpleMinus= secp160r1.point(Botan::BigInt("425826231723888350446541592701409065913635568770"),
Botan::BigInt("203520114162904107873991457957346892027982641970"));
result.test_eq("point subtraction", simpleMinus, exp_simpleMinus);
const Botan::PointGFp simpleMult = p1 * 123456789;
result.test_eq("point mult affine x", simpleMult.get_affine_x(),
Botan::BigInt("43638877777452195295055270548491599621118743290"));
result.test_eq("point mult affine y", simpleMult.get_affine_y(),
Botan::BigInt("56841378500012376527163928510402662349220202981"));
return result;
}
Test::Result test_enc_dec_compressed_160()
{
Test::Result result("ECC Unit");
// Test for compressed conversion (02/03) 160bit
Botan::EC_Group secp160r1("secp160r1");
const std::vector<uint8_t> G_comp = Botan::hex_decode("024A96B5688EF573284664698968C38BB913CBFC82");
const Botan::PointGFp p = secp160r1.OS2ECP(G_comp);
std::vector<uint8_t> sv_result = p.encode(Botan::PointGFp::COMPRESSED);
result.test_eq("result", sv_result, G_comp);
return result;
}
Test::Result test_enc_dec_compressed_256()
{
Test::Result result("ECC Unit");
Botan::EC_Group group("secp256r1");
const std::string G_secp_comp = "036B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296";
const std::vector<uint8_t> sv_G_secp_comp = Botan::hex_decode(G_secp_comp);
Botan::PointGFp p_G = group.OS2ECP(sv_G_secp_comp);
std::vector<uint8_t> sv_result = p_G.encode(Botan::PointGFp::COMPRESSED);
result.test_eq("compressed_256", sv_result, sv_G_secp_comp);
return result;
}
Test::Result test_enc_dec_uncompressed_112()
{
Test::Result result("ECC Unit");
// Test for uncompressed conversion (04) 112bit
// Curve is secp112r2
const Botan::BigInt p("0xdb7c2abf62e35e668076bead208b");
const Botan::BigInt a("0x6127C24C05F38A0AAAF65C0EF02C");
const Botan::BigInt b("0x51DEF1815DB5ED74FCC34C85D709");
const Botan::BigInt g_x("0x4BA30AB5E892B4E1649DD0928643");
const Botan::BigInt g_y("0xADCD46F5882E3747DEF36E956E97");
const Botan::BigInt order("0x36DF0AAFD8B8D7597CA10520D04B");
const Botan::BigInt cofactor("4"); // !
const Botan::EC_Group group(p, a, b, g_x, g_y, order, cofactor);
const std::string G_secp_uncomp = "044BA30AB5E892B4E1649DD0928643ADCD46F5882E3747DEF36E956E97";
const std::vector<uint8_t> sv_G_secp_uncomp = Botan::hex_decode(G_secp_uncomp);
Botan::PointGFp p_G = group.OS2ECP(sv_G_secp_uncomp);
std::vector<uint8_t> sv_result = p_G.encode(Botan::PointGFp::UNCOMPRESSED);
result.test_eq("uncompressed_112", sv_result, sv_G_secp_uncomp);
return result;
}
Test::Result test_enc_dec_uncompressed_521()
{
Test::Result result("ECC Unit");
// Test for uncompressed conversion(04) with big values(521 bit)
const std::string G_secp_uncomp =
"0400C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2ffA8DE3348B3C1856A429BF97E7E31C2E5BD66011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650";
const std::vector<uint8_t> sv_G_secp_uncomp = Botan::hex_decode(G_secp_uncomp);
Botan::EC_Group group("secp521r1");
Botan::PointGFp p_G = group.OS2ECP(sv_G_secp_uncomp);
std::vector<uint8_t> sv_result = p_G.encode(Botan::PointGFp::UNCOMPRESSED);
result.test_eq("expected", sv_result, sv_G_secp_uncomp);
return result;
}
Test::Result test_ecc_registration()
{
Test::Result result("ECC registration");
// secp112r1
const Botan::BigInt p("0xDB7C2ABF62E35E668076BEAD208B");
const Botan::BigInt a("0xDB7C2ABF62E35E668076BEAD2088");
const Botan::BigInt b("0x659EF8BA043916EEDE8911702B22");
const Botan::BigInt g_x("0x09487239995A5EE76B55F9C2F098");
const Botan::BigInt g_y("0xA89CE5AF8724C0A23E0E0FF77500");
const Botan::BigInt order("0xDB7C2ABF62E35E7628DFAC6561C5");
const Botan::OID oid("1.3.132.0.6");
// Creating this object implicitly registers the curve for future use ...
Botan::EC_Group reg_group(p, a, b, g_x, g_y, order, 1, oid);
Botan::EC_Group group(oid);
result.test_eq("Group registration worked", group.get_p(), p);
return result;
}
class ECC_Unit_Tests final : public Test
{
public:
std::vector<Test::Result> run() override
{
std::vector<Test::Result> results;
results.push_back(test_coordinates());
results.push_back(test_decoding_with_seed());
results.push_back(test_point_mult());
results.push_back(test_point_negative());
results.push_back(test_mult_point());
results.push_back(test_basic_operations());
results.push_back(test_enc_dec_compressed_160());
results.push_back(test_enc_dec_compressed_256());
results.push_back(test_enc_dec_uncompressed_112());
results.push_back(test_enc_dec_uncompressed_521());
results.push_back(test_ecc_registration());
return results;
}
};
BOTAN_REGISTER_TEST("ecc_unit", ECC_Unit_Tests);
#if defined(BOTAN_HAS_ECDSA)
class ECC_Invalid_Key_Tests final : public Text_Based_Test
{
public:
ECC_Invalid_Key_Tests() :
Text_Based_Test("pubkey/ecc_invalid.vec", "SubjectPublicKey") {}
bool clear_between_callbacks() const override
{
return false;
}
Test::Result run_one_test(const std::string&, const VarMap& vars) override
{
Test::Result result("ECC invalid keys");
const std::string encoded = vars.get_req_str("SubjectPublicKey");
Botan::DataSource_Memory key_data(Botan::hex_decode(encoded));
try
{
std::unique_ptr<Botan::Public_Key> key(Botan::X509::load_key(key_data));
result.test_eq("public key fails check", key->check_key(Test::rng(), false), false);
}
catch(Botan::Decoding_Error&)
{
result.test_success("Decoding invalid ECC key results in decoding error exception");
}
return result;
}
};
BOTAN_REGISTER_TEST("ecc_invalid", ECC_Invalid_Key_Tests);
#endif
#endif
}
}
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