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test.cpp
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test.cpp
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// Copyright 2020 Chia Network Inc
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#define CATCH_CONFIG_RUNNER
#include <thread>
#include "bls.hpp"
#include <catch2/catch.hpp>
extern "C" {
#include "relic.h"
}
#include "test-utils.hpp"
using std::cout;
using std::endl;
using std::string;
using std::vector;
using namespace bls;
void TestHKDF(string ikm_hex, string salt_hex, string info_hex, string prk_expected_hex, string okm_expected_hex, int L) {
vector<uint8_t> ikm = Util::HexToBytes(ikm_hex);
vector<uint8_t> salt = Util::HexToBytes(salt_hex);
vector<uint8_t> info = Util::HexToBytes(info_hex);
vector<uint8_t> prk_expected = Util::HexToBytes(prk_expected_hex);
vector<uint8_t> okm_expected = Util::HexToBytes(okm_expected_hex);
uint8_t prk[32];
HKDF256::Extract(prk, salt.data(), salt.size(), ikm.data(), ikm.size());
uint8_t* okm = new uint8_t[L];
HKDF256::Expand(okm, L, prk, info.data(), info.size());
REQUIRE(32 == prk_expected.size());
REQUIRE(L == okm_expected.size());
for (size_t i=0; i < 32; i++) {
REQUIRE(prk[i] == prk_expected[i]);
}
for (size_t i=0; i < L; i++) {
REQUIRE(okm[i] == okm_expected[i]);
}
delete[] okm;
}
TEST_CASE("class PrivateKey") {
uint8_t buffer[PrivateKey::PRIVATE_KEY_SIZE];
memcmp(buffer, getRandomSeed().data(), PrivateKey::PRIVATE_KEY_SIZE);
SECTION("Copy {constructor|assignment operator}") {
PrivateKey pk1 = PrivateKey::RandomPrivateKey();
PrivateKey pk2 = PrivateKey::RandomPrivateKey();
PrivateKey pk3 = PrivateKey(pk2);
REQUIRE(!pk1.IsZero());
REQUIRE(!pk2.IsZero());
REQUIRE(!pk3.IsZero());
REQUIRE(pk1 != pk2);
REQUIRE(pk3 == pk2);
REQUIRE(pk2.GetG1Element().IsValid()); // cache previous g1
REQUIRE(pk2.GetG2Element().IsValid()); // cache previous g2
pk2 = pk1;
REQUIRE(pk1 == pk2);
REQUIRE(pk1.GetG1Element() == pk2.GetG1Element());
REQUIRE(pk1.GetG2Element() == pk2.GetG2Element());
REQUIRE(pk3 != pk2);
}
SECTION("Move {constructor|assignment operator}") {
PrivateKey pk1 = PrivateKey::RandomPrivateKey();
std::vector<uint8_t> vec1 = pk1.Serialize();
PrivateKey pk2 = PrivateKey::RandomPrivateKey();
std::vector<uint8_t> vec2 = pk2.Serialize();
PrivateKey pk3 = PrivateKey(std::move(pk2));
REQUIRE(!pk1.IsZero());
REQUIRE_THROWS(pk2.IsZero());
REQUIRE(!pk3.IsZero());
REQUIRE(vec2 == pk3.Serialize());
pk3 = std::move(pk1);
REQUIRE_THROWS(pk1.IsZero());
REQUIRE_THROWS(pk2.IsZero());
REQUIRE(!pk3.IsZero());
REQUIRE(vec1 == pk3.Serialize());
pk3 = std::move(pk1);
REQUIRE_THROWS(pk1.IsZero());
REQUIRE_THROWS(pk2.IsZero());
REQUIRE_THROWS(pk3.IsZero());
}
SECTION("Equality operators") {
PrivateKey pk1 = PrivateKey::RandomPrivateKey();
PrivateKey pk2 = PrivateKey::RandomPrivateKey();
PrivateKey pk3 = pk2;
REQUIRE(pk1 != pk2);
REQUIRE(pk1 != pk3);
REQUIRE(pk2 == pk3);
}
SECTION("(De)Serialization") {
PrivateKey pk1 = PrivateKey::RandomPrivateKey();
pk1.Serialize(buffer);
REQUIRE(memcmp(buffer, pk1.Serialize().data(), PrivateKey::PRIVATE_KEY_SIZE) == 0);
PrivateKey pk2 = PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE), true);
REQUIRE(pk1 == pk2);
REQUIRE_THROWS(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE - 1), true));
REQUIRE_THROWS(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE + 1), true));
REQUIRE_NOTHROW(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE), true));
bn_t order;
bn_new(order);
g1_get_ord(order);
bn_write_bin(buffer, PrivateKey::PRIVATE_KEY_SIZE, order);
REQUIRE_NOTHROW(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE), false));
REQUIRE_NOTHROW(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE), true));
bn_add(order, order, order);
bn_write_bin(buffer, PrivateKey::PRIVATE_KEY_SIZE, order);
REQUIRE_THROWS(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE), false));
REQUIRE_NOTHROW(PrivateKey::FromBytes(Bytes(buffer, PrivateKey::PRIVATE_KEY_SIZE), true));
}
SECTION("BIP32 Seed") {
uint8_t aliceSeed[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
PrivateKey pk1 = PrivateKey::FromSeedBIP32(Bytes(aliceSeed, 10));
REQUIRE(pk1.HasKeyData());
vector<uint8_t> privateKey = pk1.Serialize(true);
vector<uint8_t> knownPrivateKey = Util::HexToBytes("46891c2cec49593c81921e473db7480029e0fc1eb933c6b93d81f5370eb19fbd");
REQUIRE(privateKey == knownPrivateKey);
G1Element pubKey1 = pk1.GetG1Element();
vector<uint8_t> pubKey1Bytes = pubKey1.Serialize(true);
vector<uint8_t> knownPublicKey = Util::HexToBytes("1790635de8740e9a6a6b15fb6b72f3a16afa0973d971979b6ba54761d6e2502c50db76f4d26143f05459a42cfd520d44");
REQUIRE(pubKey1Bytes == knownPublicKey);
}
SECTION("keydata checks") {
PrivateKey pk1 = PrivateKey::RandomPrivateKey();
G1Element g1 = pk1.GetG1Element();
G2Element g2 = pk1.GetG2Element();
PrivateKey pk2 = std::move(pk1);
REQUIRE_THROWS(PrivateKey(pk1));
REQUIRE_THROWS(pk1 = pk2);
REQUIRE_THROWS(pk1.GetG1Element());
REQUIRE_THROWS(pk1.GetG2Element());
REQUIRE_THROWS(g1 * pk1);
REQUIRE_THROWS(pk1 * g1);
REQUIRE_THROWS(g2 * pk1);
REQUIRE_THROWS(pk1 * g2);
REQUIRE_THROWS(pk1.GetG2Power(g2));
REQUIRE_THROWS(PrivateKey::Aggregate({pk1, pk2}));
REQUIRE_THROWS(pk1.IsZero());
REQUIRE_THROWS(pk1 == pk2);
REQUIRE_THROWS(pk1 != pk2);
REQUIRE_THROWS(pk1.Serialize(buffer));
REQUIRE_THROWS(pk1.Serialize());
REQUIRE_THROWS(pk1.SignG2(buffer, sizeof(buffer), buffer, sizeof(buffer)));
}
}
TEST_CASE("HKDF") {
// https://tools.ietf.org/html/rfc5869 test vectors
SECTION("Test case 2") {
TestHKDF("0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b",
"000102030405060708090a0b0c",
"f0f1f2f3f4f5f6f7f8f9",
"077709362c2e32df0ddc3f0dc47bba6390b6c73bb50f9c3122ec844ad7c2b3e5",
"3cb25f25faacd57a90434f64d0362f2a2d2d0a90cf1a5a4c5db02d56ecc4c5bf34007208d5b887185865",
42
);
}
SECTION("Test case 2") {
TestHKDF("000102030405060708090a0b0c0d0e0f"
"101112131415161718191a1b1c1d1e1f"
"202122232425262728292a2b2c2d2e2f"
"303132333435363738393a3b3c3d3e3f"
"404142434445464748494a4b4c4d4e4f", // 80 octets
"0x606162636465666768696a6b6c6d6e6f"
"707172737475767778797a7b7c7d7e7f"
"808182838485868788898a8b8c8d8e8f"
"909192939495969798999a9b9c9d9e9f"
"a0a1a2a3a4a5a6a7a8a9aaabacadaeaf", // 80 octets
"0xb0b1b2b3b4b5b6b7b8b9babbbcbdbebf"
"c0c1c2c3c4c5c6c7c8c9cacbcccdcecf"
"d0d1d2d3d4d5d6d7d8d9dadbdcdddedf"
"e0e1e2e3e4e5e6e7e8e9eaebecedeeef"
"f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff", // 80 octets
"0x06a6b88c5853361a06104c9ceb35b45cef760014904671014a193f40c15fc244", // 32 octets
"0xb11e398dc80327a1c8e7f78c596a4934"
"4f012eda2d4efad8a050cc4c19afa97c"
"59045a99cac7827271cb41c65e590e09"
"da3275600c2f09b8367793a9aca3db71"
"cc30c58179ec3e87c14c01d5c1f3434f"
"1d87", // 82 octets
82
);
}
SECTION("Test case 3") {
TestHKDF("0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b0b",
"",
"",
"19ef24a32c717b167f33a91d6f648bdf96596776afdb6377ac434c1c293ccb04",
"8da4e775a563c18f715f802a063c5a31b8a11f5c5ee1879ec3454e5f3c738d2d9d201395faa4b61a96c8",
42
);
}
SECTION("Works with multiple of 32") {
// This generates exactly 64 bytes. Uses a 32 byte key and 4 byte salt as in EIP2333.
TestHKDF("8704f9ac024139fe62511375cf9bc534c0507dcf00c41603ac935cd5943ce0b4b88599390de14e743ca2f56a73a04eae13aa3f3b969b39d8701e0d69a6f8d42f",
"53d8e19b",
"",
"eb01c9cd916653df76ffa61b6ab8a74e254ebfd9bfc43e624cc12a72b0373dee",
"8faabea85fc0c64e7ca86217cdc6dcdc88551c3244d56719e630a3521063082c46455c2fd5483811f9520a748f0099c1dfcfa52c54e1c22b5cdf70efb0f3c676",
64
);
}
}
void TestEIP2333(string seedHex, string masterSkHex, string childSkHex, uint32_t childIndex) {
auto masterSk = Util::HexToBytes(masterSkHex);
auto childSk = Util::HexToBytes(childSkHex);
PrivateKey master = BasicSchemeMPL().KeyGen(Util::HexToBytes(seedHex));
PrivateKey child = HDKeys::DeriveChildSk(master, childIndex);
uint8_t master_arr[32];
master.Serialize(master_arr);
auto calculatedMaster = master.Serialize();
auto calculatedChild = child.Serialize();
REQUIRE(calculatedMaster.size() == 32);
REQUIRE(calculatedChild.size() == 32);
for (int i=0; i<32; i++) {
REQUIRE(calculatedMaster[i] == masterSk[i]);
}
for (int i=0; i<32; i++) {
REQUIRE(calculatedChild[i] == childSk[i]);
}
}
TEST_CASE("EIP-2333 hardened HD keys") {
// The comments in the test cases correspond to integers that are converted to
// bytes using python int.to_bytes(32, "big").hex(), since the EIP spec provides ints, but c++
// does not support bigint by default
SECTION("EIP-2333 Test case 1"){
TestEIP2333("3141592653589793238462643383279502884197169399375105820974944592",
// 36167147331491996618072159372207345412841461318189449162487002442599770291484
"4ff5e145590ed7b71e577bb04032396d1619ff41cb4e350053ed2dce8d1efd1c",
// 41787458189896526028601807066547832426569899195138584349427756863968330588237
"5c62dcf9654481292aafa3348f1d1b0017bbfb44d6881d26d2b17836b38f204d",
3141592653
);
}
SECTION("EIP-2333 Test case 2"){
TestEIP2333("0x0099FF991111002299DD7744EE3355BBDD8844115566CC55663355668888CC00",
// 13904094584487173309420026178174172335998687531503061311232927109397516192843
"1ebd704b86732c3f05f30563dee6189838e73998ebc9c209ccff422adee10c4b",
// 12482522899285304316694838079579801944734479969002030150864436005368716366140
"1b98db8b24296038eae3f64c25d693a269ef1e4d7ae0f691c572a46cf3c0913c",
4294967295
);
}
SECTION("EIP-2333 Test case 3"){
TestEIP2333("0xd4e56740f876aef8c010b86a40d5f56745a118d0906a34e69aec8c0db1cb8fa3",
// 44010626067374404458092393860968061149521094673473131545188652121635313364506
"614d21b10c0e4996ac0608e0e7452d5720d95d20fe03c59a3321000a42432e1a",
// 4011524214304750350566588165922015929937602165683407445189263506512578573606
"08de7136e4afc56ae3ec03b20517d9c1232705a747f588fd17832f36ae337526",
42
);
}
SECTION("EIP-2333 Test vector with intermediate values"){
TestEIP2333("c55257c360c07c72029aebc1b53c05ed0362ada38ead3e3e9efa3708e53495531f09a6987599d18264c1e1c92f2cf141630c7a3c4ab7c81b2f001698e7463b04",
// 5399117110774477986698372024995405256382522670366369834617409486544348441851
"0x0befcabff4a664461cc8f190cdd51c05621eb2837c71a1362df5b465a674ecfb",
// 11812940737387919040225825939013910852517748782307378293770044673328955938106
"1a1de3346883401f1e3b2281be5774080edb8e5ebe6f776b0f7af9fea942553a",
0
);
}
}
TEST_CASE("Unhardened HD keys") {
SECTION("Should match derivation through private and public keys"){
const vector<uint8_t> seed = {1, 50, 6, 244, 24, 199, 1, 25, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29};
PrivateKey sk = BasicSchemeMPL().KeyGen(seed);
G1Element pk = sk.GetG1Element();
PrivateKey childSk = BasicSchemeMPL().DeriveChildSkUnhardened(sk, 42);
G1Element childPk = BasicSchemeMPL().DeriveChildPkUnhardened(pk, 42);
REQUIRE(childSk.GetG1Element() == childPk);
PrivateKey grandchildSk = BasicSchemeMPL().DeriveChildSkUnhardened(childSk, 12142);
G1Element grandcihldPk = BasicSchemeMPL().DeriveChildPkUnhardened(childPk, 12142);
REQUIRE(grandchildSk.GetG1Element() == grandcihldPk);
}
SECTION("Should derive public child from parent") {
const vector<uint8_t> seed = {2, 50, 6, 244, 24, 199, 1, 25, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29};
PrivateKey sk = BasicSchemeMPL().KeyGen(seed);
G1Element pk = sk.GetG1Element();
PrivateKey childSk = BasicSchemeMPL().DeriveChildSkUnhardened(sk, 42);
G1Element childPk = BasicSchemeMPL().DeriveChildPkUnhardened(pk, 42);
PrivateKey childSkHardened = BasicSchemeMPL().DeriveChildSk(sk, 42);
REQUIRE(childSk.GetG1Element() == childPk);
REQUIRE(childSkHardened != childSk);
REQUIRE(childSkHardened.GetG1Element() != childPk);
}
}
TEST_CASE("IETF test vectors") {
SECTION ("Pyecc vector") {
string sig1BasicHex = "96ba34fac33c7f129d602a0bc8a3d43f9abc014eceaab7359146b4b150e57b808645738f35671e9e10e0d862a30cab70074eb5831d13e6a5b162d01eebe687d0164adbd0a864370a7c222a2768d7704da254f1bf1823665bc2361f9dd8c00e99";
string sk = "0x0101010101010101010101010101010101010101010101010101010101010101";
vector<uint8_t> msg = {3, 1, 4, 1, 5, 9};
auto skobj = PrivateKey::FromBytes(Bytes(Util::HexToBytes(sk)));
G2Element sig = BasicSchemeMPL().Sign(skobj, msg);
vector<uint8_t> sig1;
for (const uint8_t byte : Util::HexToBytes(sig1BasicHex)) {
sig1.push_back(byte);
}
REQUIRE(sig == G2Element::FromByteVector(sig1));
}
}
TEST_CASE("Chia test vectors") {
SECTION("Chia test vectors 1 (Basic)") {
vector<uint8_t> seed1(32, 0x00); // All 0s
vector<uint8_t> seed2(32, 0x01); // All 1s
vector<uint8_t> message1 = {7, 8, 9};
vector<uint8_t> message2 = {10, 11, 12};
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed1);
G1Element pk1 = sk1.GetG1Element();
G2Element sig1 = BasicSchemeMPL().Sign(sk1, message1);
PrivateKey sk2 = BasicSchemeMPL().KeyGen(seed2);
G1Element pk2 = sk2.GetG1Element();
G2Element sig2 = BasicSchemeMPL().Sign(sk2, message2);
REQUIRE(pk1.GetFingerprint() == 0xb40dd58a);
REQUIRE(pk2.GetFingerprint() == 0xb839add1);
REQUIRE(
Util::HexStr(sig1.Serialize()) ==
"b8faa6d6a3881c9fdbad803b170d70ca5cbf1e6ba5a586262df368c75acd1d1f"
"fa3ab6ee21c71f844494659878f5eb230c958dd576b08b8564aad2ee0992e85a"
"1e565f299cd53a285de729937f70dc176a1f01432129bb2b94d3d5031f8065a1");
REQUIRE(
Util::HexStr(sk1.Serialize()) ==
"4a353be3dac091a0a7e640620372f5e1e2e4401717c1e79cac6ffba8f6905604");
REQUIRE(
Util::HexStr(pk1.Serialize()) ==
"85695fcbc06cc4c4c9451f4dce21cbf8de3e5a13bf48f44cdbb18e2038ba7b8bb1632d7911e"
"f1e2e08749bddbf165352");
REQUIRE(
Util::HexStr(sig2.Serialize()) ==
"a9c4d3e689b82c7ec7e838dac2380cb014f9a08f6cd6ba044c263746e39a8f7a60ffee4afb7"
"8f146c2e421360784d58f0029491e3bd8ab84f0011d258471ba4e87059de295d9aba845c044e"
"e83f6cf2411efd379ef38bf4cf41d5f3c0ae1205d");
G2Element aggSig1 = BasicSchemeMPL().Aggregate({sig1, sig2});
REQUIRE(
Util::HexStr(aggSig1.Serialize()) ==
"aee003c8cdaf3531b6b0ca354031b0819f7586b5846796615aee8108fec75ef838d181f9d24"
"4a94d195d7b0231d4afcf06f27f0cc4d3c72162545c240de7d5034a7ef3a2a03c0159de982fb"
"c2e7790aeb455e27beae91d64e077c70b5506dea3");
REQUIRE(BasicSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message1, message2}, aggSig1));
REQUIRE(!BasicSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message1, message2}, sig1));
REQUIRE(!BasicSchemeMPL().Verify(pk1, message1, sig2));
REQUIRE(!BasicSchemeMPL().Verify(pk1, message2, sig1));
vector<uint8_t> message3 = {1, 2, 3};
vector<uint8_t> message4 = {1, 2, 3, 4};
vector<uint8_t> message5 = {1, 2};
G2Element sig3 = BasicSchemeMPL().Sign(sk1, message3);
G2Element sig4 = BasicSchemeMPL().Sign(sk1, message4);
G2Element sig5 = BasicSchemeMPL().Sign(sk2, message5);
G2Element aggSig2 = BasicSchemeMPL().Aggregate({sig3, sig4, sig5});
REQUIRE(BasicSchemeMPL().AggregateVerify({pk1, pk1, pk2}, vector<vector<uint8_t>>{message3, message4, message5}, aggSig2));
REQUIRE(
Util::HexStr(aggSig2.Serialize()) ==
"a0b1378d518bea4d1100adbc7bdbc4ff64f2c219ed6395cd36fe5d2aa44a4b8e710b607afd9"
"65e505a5ac3283291b75413d09478ab4b5cfbafbeea366de2d0c0bcf61deddaa521f6020460f"
"d547ab37659ae207968b545727beba0a3c5572b9c");
}
SECTION("Chia test vector 2 (Augmented, aggregate of aggregates)") {
vector<uint8_t> message1 = {1, 2, 3, 40};
vector<uint8_t> message2 = {5, 6, 70, 201};
vector<uint8_t> message3 = {9, 10, 11, 12, 13};
vector<uint8_t> message4 = {15, 63, 244, 92, 0, 1};
vector<uint8_t> seed1(32, 0x02); // All 2s
vector<uint8_t> seed2(32, 0x03); // All 3s
PrivateKey sk1 = AugSchemeMPL().KeyGen(seed1);
PrivateKey sk2 = AugSchemeMPL().KeyGen(seed2);
G1Element pk1 = sk1.GetG1Element();
G1Element pk2 = sk2.GetG1Element();
G2Element sig1 = AugSchemeMPL().Sign(sk1, message1);
G2Element sig2 = AugSchemeMPL().Sign(sk2, message2);
G2Element sig3 = AugSchemeMPL().Sign(sk2, message1);
G2Element sig4 = AugSchemeMPL().Sign(sk1, message3);
G2Element sig5 = AugSchemeMPL().Sign(sk1, message1);
G2Element sig6 = AugSchemeMPL().Sign(sk1, message4);
G2Element aggSigL = AugSchemeMPL().Aggregate({sig1, sig2});
G2Element aggSigR = AugSchemeMPL().Aggregate({sig3, sig4, sig5});
G2Element aggSig = AugSchemeMPL().Aggregate({aggSigL, aggSigR, sig6});
REQUIRE(AugSchemeMPL().AggregateVerify({pk1, pk2, pk2, pk1, pk1, pk1}, vector<vector<uint8_t>>{message1, message2, message1, message3, message1, message4}, aggSig));
REQUIRE(
Util::HexStr(aggSig.Serialize()) ==
"a1d5360dcb418d33b29b90b912b4accde535cf0e52caf467a005dc632d9f7af44b6c4e9acd4"
"6eac218b28cdb07a3e3bc087df1cd1e3213aa4e11322a3ff3847bbba0b2fd19ddc25ca964871"
"997b9bceeab37a4c2565876da19382ea32a962200");
}
SECTION("Chia test vector 3 (PoP)") {
vector<uint8_t> message1 = {1, 2, 3, 40, 50};
vector<uint8_t> seed1(32, 0x04); // All 4s
PrivateKey sk1 = PopSchemeMPL().KeyGen(seed1);
G2Element pop = PopSchemeMPL().PopProve(sk1);
REQUIRE(PopSchemeMPL().PopVerify(sk1.GetG1Element(), pop));
REQUIRE(Util::HexStr(pop.Serialize()) == "84f709159435f0dc73b3e8bf6c78d85282d19231555a8ee3b6e2573aaf66872d9203fefa1ef"
"700e34e7c3f3fb28210100558c6871c53f1ef6055b9f06b0d1abe22ad584ad3b957f3018a8f5"
"8227c6c716b1e15791459850f2289168fa0cf9115");
}
}
TEST_CASE("Key generation")
{
SECTION("Should generate a keypair from a seed")
{
vector<uint8_t> seed1(31, 0x08);
vector<uint8_t> seed2(32, 0x08);
REQUIRE_THROWS(BasicSchemeMPL().KeyGen(seed1));
PrivateKey sk = BasicSchemeMPL().KeyGen(seed2);
G1Element pk = sk.GetG1Element();
REQUIRE(core_get()->code == RLC_OK);
REQUIRE(pk.GetFingerprint() == 0x8ee7ba56);
}
}
TEST_CASE("Error handling")
{
SECTION("Should throw on a bad private key")
{
vector<uint8_t> seed(32, 0x10);
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
uint8_t* skData = Util::SecAlloc<uint8_t>(G2Element::SIZE);
sk1.Serialize(skData);
skData[0] = 255;
REQUIRE_THROWS(PrivateKey::FromBytes(Bytes(skData, PrivateKey::PRIVATE_KEY_SIZE)));
Util::SecFree(skData);
}
SECTION("Should throw on a bad public key")
{
vector<uint8_t> buf(G1Element::SIZE, 0);
for (int i = 0; i < 0xFF; i++) {
buf[0] = (uint8_t)i;
if (i == 0xc0) { // Infinity prefix shouldn't throw here as we have only zero values
REQUIRE_NOTHROW(G1Element::FromByteVector(buf));
} else {
REQUIRE_THROWS(G1Element::FromByteVector(buf));
}
}
}
SECTION("Should throw on a bad G2Element")
{
vector<uint8_t> buf(G2Element::SIZE, 0);
for (int i = 0; i < 0xFF; i++) {
buf[0] = (uint8_t)i;
if (i == 0xc0) { // Infinity prefix shouldn't throw here as we have only zero values
REQUIRE_NOTHROW(G2Element::FromByteVector(buf));
} else {
REQUIRE_THROWS(G2Element::FromByteVector(buf));
}
}
// Trigger "G2 element must always have 48th byte start with 0b000" error case
buf[48] = 0xFF;
REQUIRE_THROWS(G2Element::FromByteVector(buf));
}
SECTION("Error handling should be thread safe")
{
core_get()->code = 10;
REQUIRE(core_get()->code == 10);
ctx_t* ctx1 = core_get();
// spawn a thread and make sure it uses a different/same context depending on relic's multithreading setup
std::thread([&]() {
#if MULTI != RELIC_NONE
REQUIRE(ctx1 != core_get());
REQUIRE(core_get()->code == RLC_OK);
#else
REQUIRE(ctx1 == core_get());
REQUIRE(core_get()->code != RLC_OK);
#endif
core_get()->code = 1;
}).join();
#if MULTI != RELIC_NONE
REQUIRE(core_get()->code == 10);
#else
REQUIRE(core_get()->code == 1);
#endif
// reset so that future test cases don't fail
core_get()->code = RLC_OK;
}
}
TEST_CASE("Util tests")
{
SECTION("Should convert an int to four bytes")
{
uint32_t x = 1024;
uint8_t expected[4] = {0x00, 0x00, 0x04, 0x00};
uint8_t result[4];
Util::IntToFourBytes(result, x);
REQUIRE(result[0] == expected[0]);
REQUIRE(result[1] == expected[1]);
REQUIRE(result[2] == expected[2]);
REQUIRE(result[3] == expected[3]);
uint32_t again = Util::FourBytesToInt(result);
REQUIRE(again == x);
}
}
TEST_CASE("Signature tests")
{
SECTION("Should use copy constructor")
{
vector<uint8_t> message1 = {1, 65, 254, 88, 90, 45, 22};
vector<uint8_t> seed(32, 0x30);
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
G1Element pk1 = sk1.GetG1Element();
PrivateKey sk2 = PrivateKey(sk1);
uint8_t skBytes[PrivateKey::PRIVATE_KEY_SIZE];
sk2.Serialize(skBytes);
PrivateKey sk4 = PrivateKey::FromBytes(Bytes(skBytes, PrivateKey::PRIVATE_KEY_SIZE));
G1Element pk2 = G1Element(pk1);
G2Element sig1 = BasicSchemeMPL().Sign(sk4, message1);
G2Element sig2 = G2Element(sig1);
REQUIRE(BasicSchemeMPL().Verify(pk2, message1, sig2));
}
SECTION("Should sign with the zero key") {
vector<uint8_t> sk0(32, 0);
PrivateKey sk = PrivateKey::FromByteVector(sk0);
REQUIRE(sk.GetG1Element() == G1Element()); // Infinity
REQUIRE(sk.GetG2Element() == G2Element()); // Infinity
REQUIRE(BasicSchemeMPL().Sign(sk, {1, 2, 3}) == G2Element());
REQUIRE(AugSchemeMPL().Sign(sk, {1, 2, 3}) == G2Element());
REQUIRE(PopSchemeMPL().Sign(sk, {1, 2, 3}) == G2Element());
}
SECTION("Should use equality operators")
{
vector<uint8_t> message1 = {1, 65, 254, 88, 90, 45, 22};
vector<uint8_t> seed(32, 0x40);
vector<uint8_t> seed3(32, 0x50);
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
PrivateKey sk2 = PrivateKey(sk1);
PrivateKey sk3 = BasicSchemeMPL().KeyGen(seed3);
G1Element pk1 = sk1.GetG1Element();
G1Element pk2 = sk2.GetG1Element();
G1Element pk3 = G1Element(pk2);
G1Element pk4 = sk3.GetG1Element();
G2Element sig1 = BasicSchemeMPL().Sign(sk1, message1);
G2Element sig2 = BasicSchemeMPL().Sign(sk1, message1);
G2Element sig3 = BasicSchemeMPL().Sign(sk2, message1);
G2Element sig4 = BasicSchemeMPL().Sign(sk3, message1);
REQUIRE(sk1 == sk2);
REQUIRE(sk1 != sk3);
REQUIRE(pk1 == pk2);
REQUIRE(pk2 == pk3);
REQUIRE(pk1 != pk4);
REQUIRE(sig1 == sig2);
REQUIRE(sig2 == sig3);
REQUIRE(sig3 != sig4);
REQUIRE(pk1.Serialize() == pk2.Serialize());
REQUIRE(sig1.Serialize() == sig2.Serialize());
}
SECTION("Should serialize and deserialize")
{
vector<uint8_t> message1 = {1, 65, 254, 88, 90, 45, 22};
vector<uint8_t> seed(32, 0x40);
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
G1Element pk1 = sk1.GetG1Element();
uint8_t* skData = Util::SecAlloc<uint8_t>(G2Element::SIZE);
sk1.Serialize(skData);
PrivateKey sk2 = PrivateKey::FromBytes(Bytes(skData, PrivateKey::PRIVATE_KEY_SIZE));
REQUIRE(sk1 == sk2);
auto pkData = pk1.Serialize();
G1Element pk2 = G1Element::FromBytes(Bytes(pkData));
REQUIRE(pk1 == pk2);
G2Element sig1 = BasicSchemeMPL().Sign(sk1, message1);
auto sigData = sig1.Serialize();
G2Element sig2 = G2Element::FromBytes(Bytes(sigData));
REQUIRE(sig1 == sig2);
REQUIRE(BasicSchemeMPL().Verify(pk2, message1, sig2));
Util::SecFree(skData);
}
SECTION("Should not verify aggregate with same message under BasicScheme")
{
vector<uint8_t> message = {100, 2, 254, 88, 90, 45, 23};
uint8_t hash[BLS::MESSAGE_HASH_LEN];
vector<uint8_t> seed(32, 0x50);
vector<uint8_t> seed2(32, 0x70);
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
PrivateKey sk2 = BasicSchemeMPL().KeyGen(seed2);
G1Element pk1 = sk1.GetG1Element();
G1Element pk2 = sk2.GetG1Element();
G2Element sig1 = BasicSchemeMPL().Sign(sk1, message);
G2Element sig2 = BasicSchemeMPL().Sign(sk2, message);
G2Element aggSig = BasicSchemeMPL().Aggregate({sig1, sig2});
REQUIRE(BasicSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message, message}, aggSig) == false);
}
SECTION("Should verify aggregate with same message under AugScheme/PopScheme")
{
vector<uint8_t> message = {100, 2, 254, 88, 90, 45, 23};
uint8_t hash[BLS::MESSAGE_HASH_LEN];
vector<uint8_t> seed(32, 0x50);
vector<uint8_t> seed2(32, 0x70);
PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
PrivateKey sk2 = BasicSchemeMPL().KeyGen(seed2);
G1Element pk1 = sk1.GetG1Element();
G1Element pk2 = sk2.GetG1Element();
G2Element sig1Aug = AugSchemeMPL().Sign(sk1, message);
G2Element sig2Aug = AugSchemeMPL().Sign(sk2, message);
G2Element aggSigAug = AugSchemeMPL().Aggregate({sig1Aug, sig2Aug});
REQUIRE(AugSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message, message}, aggSigAug));
G2Element sig1Pop = PopSchemeMPL().Sign(sk1, message);
G2Element sig2Pop = PopSchemeMPL().Sign(sk2, message);
G2Element aggSigPop = PopSchemeMPL().Aggregate({sig1Pop, sig2Pop});
REQUIRE(PopSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message, message}, aggSigPop));
}
SECTION("Should Aug aggregate many G2Elements, diff message")
{
vector<G1Element> pks;
vector<G2Element> sigs;
vector<vector<uint8_t> > ms;
for (uint8_t i = 0; i < 80; i++) {
vector<uint8_t> message = {0, 100, 2, 45, 64, 12, 12, 63, i};
PrivateKey sk = BasicSchemeMPL().KeyGen(getRandomSeed());
pks.push_back(sk.GetG1Element());
auto sig = AugSchemeMPL().Sign(sk, message);
sigs.push_back(sig);
ms.push_back(message);
}
G2Element aggSig = AugSchemeMPL().Aggregate(sigs);
REQUIRE(AugSchemeMPL().AggregateVerify(pks, ms, aggSig));
}
SECTION("Aggregate Verification of zero items with infinity should pass")
{
vector<G1Element> pks_as_g1;
vector<vector<uint8_t> > pks_as_bytes;
vector<vector<uint8_t> > msgs;
vector<G2Element> sigs;
sigs.push_back(G2Element());
G2Element aggSig = AugSchemeMPL().Aggregate(sigs);
REQUIRE(aggSig.Serialize().size() != 0);
REQUIRE(aggSig == G2Element());
REQUIRE(AugSchemeMPL().AggregateVerify(pks_as_g1, msgs, aggSig));
REQUIRE(AugSchemeMPL().AggregateVerify(pks_as_bytes, msgs, aggSig.Serialize()));
REQUIRE(BasicSchemeMPL().AggregateVerify(pks_as_g1, msgs, aggSig));
REQUIRE(BasicSchemeMPL().AggregateVerify(pks_as_bytes, msgs, aggSig.Serialize()));
// FastAggregateVerify takes one message, and requires at least one key
vector<uint8_t> msg;
REQUIRE(pks_as_g1.size() == 0);
REQUIRE(PopSchemeMPL().FastAggregateVerify(pks_as_g1, msg, aggSig) == false);
REQUIRE(pks_as_bytes.size() == 0);
REQUIRE(PopSchemeMPL().FastAggregateVerify(pks_as_bytes, msg, aggSig.Serialize()) == false);
}
}
TEST_CASE("Agg sks") {
SECTION("Should create aggregates with agg sk (basic scheme)")
{
const vector<uint8_t> message = {100, 2, 254, 88, 90, 45, 23};
const vector<uint8_t> seed(32, 0x07);
const vector<uint8_t> seed2(32, 0x08);
const PrivateKey sk1 = BasicSchemeMPL().KeyGen(seed);
const G1Element pk1 = sk1.GetG1Element();
const PrivateKey sk2 = BasicSchemeMPL().KeyGen(seed2);
const G1Element pk2 = sk2.GetG1Element();
const PrivateKey aggSk = PrivateKey::Aggregate({sk1, sk2});
const PrivateKey aggSkAlt = PrivateKey::Aggregate({sk2, sk1});
REQUIRE(aggSk == aggSkAlt);
const G1Element aggPubKey = pk1 + pk2;
REQUIRE(aggPubKey == aggSk.GetG1Element());
const G2Element sig1 = BasicSchemeMPL().Sign(sk1, message);
const G2Element sig2 = BasicSchemeMPL().Sign(sk2, message);
const G2Element aggSig2 = BasicSchemeMPL().Sign(aggSk, message);
const G2Element aggSig = BasicSchemeMPL().Aggregate({sig1, sig2});
REQUIRE(aggSig == aggSig2);
// Verify as a single G2Element
REQUIRE(BasicSchemeMPL().Verify(aggPubKey, message, aggSig));
REQUIRE(BasicSchemeMPL().Verify(aggPubKey, message, aggSig2));
// Verify aggregate with both keys (Fails since not distinct)
REQUIRE(BasicSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message, message}, aggSig) == false);
REQUIRE(BasicSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message, message}, aggSig2) == false);
// Try the same with distinct message, and same sk
vector<uint8_t> message2 = {200, 29, 54, 8, 9, 29, 155, 55};
G2Element sig3 = BasicSchemeMPL().Sign(sk2, message2);
G2Element aggSigFinal = BasicSchemeMPL().Aggregate({aggSig, sig3});
G2Element aggSigAlt = BasicSchemeMPL().Aggregate({sig1, sig2, sig3});
G2Element aggSigAlt2 = BasicSchemeMPL().Aggregate({sig1, sig3, sig2});
REQUIRE(aggSigFinal == aggSigAlt);
REQUIRE(aggSigFinal == aggSigAlt2);
PrivateKey skFinal = PrivateKey::Aggregate({aggSk, sk2});
PrivateKey skFinalAlt = PrivateKey::Aggregate({sk2, sk1, sk2});
REQUIRE(skFinal == skFinalAlt);
REQUIRE(skFinal != aggSk);
G1Element pkFinal = aggPubKey + pk2;
G1Element pkFinalAlt = pk2 + pk1 + pk2;
REQUIRE(pkFinal == pkFinalAlt);
REQUIRE(pkFinal != aggPubKey);
// Cannot verify with aggPubKey (since we have multiple messages)
REQUIRE(BasicSchemeMPL().AggregateVerify({aggPubKey, pk2}, vector<vector<uint8_t>>{message, message2}, aggSigFinal));
}
}
TEST_CASE("Advanced") {
SECTION("Should aggregate with multiple levels, degenerate") {
vector<uint8_t> message1 = {100, 2, 254, 88, 90, 45, 23};
PrivateKey sk1 = AugSchemeMPL().KeyGen(getRandomSeed());
G1Element pk1 = sk1.GetG1Element();
G2Element aggSig = AugSchemeMPL().Sign(sk1, message1);
vector<G1Element> pks = {pk1};
vector<vector<uint8_t>> ms = {message1};
for (size_t i = 0; i < 10; i++) {
PrivateKey sk = AugSchemeMPL().KeyGen(getRandomSeed());
G1Element pk = sk.GetG1Element();
pks.push_back(pk);
ms.push_back(message1);
G2Element sig = AugSchemeMPL().Sign(sk, message1);
aggSig = AugSchemeMPL().Aggregate({aggSig, sig});
}
REQUIRE(AugSchemeMPL().AggregateVerify(pks, ms, aggSig));
}
SECTION("Should aggregate with multiple levels, different messages") {
vector<uint8_t> message1 = {100, 2, 254, 88, 90, 45, 23};
vector<uint8_t> message2 = {192, 29, 2, 0, 0, 45, 23};
vector<uint8_t> message3 = {52, 29, 2, 0, 0, 45, 102};
vector<uint8_t> message4 = {99, 29, 2, 0, 0, 45, 222};
PrivateKey sk1 = AugSchemeMPL().KeyGen(getRandomSeed());
PrivateKey sk2 = AugSchemeMPL().KeyGen(getRandomSeed());
G1Element pk1 = sk1.GetG1Element();
G1Element pk2 = sk2.GetG1Element();
G2Element sig1 = AugSchemeMPL().Sign(sk1, message1);
G2Element sig2 = AugSchemeMPL().Sign(sk2, message2);
G2Element sig3 = AugSchemeMPL().Sign(sk2, message3);
G2Element sig4 = AugSchemeMPL().Sign(sk1, message4);
vector<G2Element> const sigsL = {sig1, sig2};
vector<G1Element> const pksL = {pk1, pk2};
vector<vector<uint8_t>> messagesL = {message1, message2};
const G2Element aggSigL = AugSchemeMPL().Aggregate(sigsL);
vector<G2Element> const sigsR = {sig3, sig4};
vector<G1Element> const pksR = {pk2, pk1};
const G2Element aggSigR = AugSchemeMPL().Aggregate(sigsR);
vector<G2Element> sigs = {aggSigL, aggSigR};
const G2Element aggSig = AugSchemeMPL().Aggregate(sigs);
vector<G1Element> allPks = {pk1, pk2, pk2, pk1};
vector<vector<uint8_t>> allMessages = {
message1, message2, message3, message4};
REQUIRE(AugSchemeMPL().AggregateVerify(allPks, allMessages, aggSig));
}
SECTION("README")
{
// Example seed, used to generate private key. Always use
// a secure RNG with sufficient entropy to generate a seed (at least 32 bytes).
vector<uint8_t> seed = {0, 50, 6, 244, 24, 199, 1, 25, 52, 88, 192,
19, 18, 12, 89, 6, 220, 18, 102, 58, 209, 82,
12, 62, 89, 110, 182, 9, 44, 20, 254, 22};
PrivateKey sk = AugSchemeMPL().KeyGen(seed);
G1Element pk = sk.GetG1Element();
vector<uint8_t> message = {1, 2, 3, 4, 5}; // Message is passed in as a byte vector
G2Element signature = AugSchemeMPL().Sign(sk, message);
vector<uint8_t> skBytes = sk.Serialize();
vector<uint8_t> pkBytes = pk.Serialize();
vector<uint8_t> signatureBytes = signature.Serialize();
cout << Util::HexStr(skBytes) << endl; // 32 bytes
cout << Util::HexStr(pkBytes) << endl; // 48 bytes
cout << Util::HexStr(signatureBytes) << endl; // 96 bytes
// Takes array of 32 bytes
PrivateKey skc = PrivateKey::FromByteVector(skBytes);
// Takes array of 48 bytes
pk = G1Element::FromByteVector(pkBytes);
// Takes array of 96 bytes
signature = G2Element::FromByteVector(signatureBytes);
REQUIRE(AugSchemeMPL().Verify(pk, message, signature));
// Generate some more private keys
seed[0] = 1;
PrivateKey sk1 = AugSchemeMPL().KeyGen(seed);
seed[0] = 2;
PrivateKey sk2 = AugSchemeMPL().KeyGen(seed);
vector<uint8_t> message2 = {1, 2, 3, 4, 5, 6, 7};
// Generate first sig
G1Element pk1 = sk1.GetG1Element();
G2Element sig1 = AugSchemeMPL().Sign(sk1, message);
// Generate second sig
G1Element pk2 = sk2.GetG1Element();
G2Element sig2 = AugSchemeMPL().Sign(sk2, message2);
// Signatures can be noninteractively combined by anyone
G2Element aggSig = AugSchemeMPL().Aggregate({sig1, sig2});
REQUIRE(AugSchemeMPL().AggregateVerify({pk1, pk2}, vector<vector<uint8_t>>{message, message2}, aggSig));
seed[0] = 3;
PrivateKey sk3 = AugSchemeMPL().KeyGen(seed);
G1Element pk3 = sk3.GetG1Element();
vector<uint8_t> message3 = {100, 2, 254, 88, 90, 45, 23};
G2Element sig3 = AugSchemeMPL().Sign(sk3, message3);
// Arbitrary trees of aggregates
G2Element aggSigFinal = AugSchemeMPL().Aggregate({aggSig, sig3});
REQUIRE(AugSchemeMPL().AggregateVerify({pk1, pk2, pk3}, vector<vector<uint8_t>>{message, message2, message3}, aggSigFinal));
// If the same message is signed, you can use Proof of Posession (PopScheme) for efficiency
// A proof of possession MUST be passed around with the PK to ensure security.
G2Element popSig1 = PopSchemeMPL().Sign(sk1, message);
G2Element popSig2 = PopSchemeMPL().Sign(sk2, message);
G2Element popSig3 = PopSchemeMPL().Sign(sk3, message);
G2Element pop1 = PopSchemeMPL().PopProve(sk1);
G2Element pop2 = PopSchemeMPL().PopProve(sk2);
G2Element pop3 = PopSchemeMPL().PopProve(sk3);
REQUIRE(PopSchemeMPL().PopVerify(pk1, pop1));
REQUIRE(PopSchemeMPL().PopVerify(pk2, pop2));
REQUIRE(PopSchemeMPL().PopVerify(pk3, pop3));
G2Element popSigAgg = PopSchemeMPL().Aggregate({popSig1, popSig2, popSig3});
REQUIRE(PopSchemeMPL().FastAggregateVerify({pk1, pk2, pk3}, message, popSigAgg));
// Aggregate public key, indistinguishable from a single public key
G1Element popAggPk = pk1 + pk2 + pk3;
REQUIRE(PopSchemeMPL().Verify(popAggPk, message, popSigAgg));
// Aggregate private keys
PrivateKey aggSk = PrivateKey::Aggregate({sk1, sk2, sk3});
REQUIRE(PopSchemeMPL().Sign(aggSk, message) == popSigAgg);
PrivateKey masterSk = AugSchemeMPL().KeyGen(seed);
PrivateKey child = AugSchemeMPL().DeriveChildSk(masterSk, 152);
PrivateKey grandchild = AugSchemeMPL().DeriveChildSk(child, 952);
G1Element masterPk = masterSk.GetG1Element();
PrivateKey childU = AugSchemeMPL().DeriveChildSkUnhardened(masterSk, 22);
PrivateKey grandchildU = AugSchemeMPL().DeriveChildSkUnhardened(childU, 0);
G1Element childUPk = AugSchemeMPL().DeriveChildPkUnhardened(masterPk, 22);
G1Element grandchildUPk = AugSchemeMPL().DeriveChildPkUnhardened(childUPk, 0);
REQUIRE(grandchildUPk == grandchildU.GetG1Element());
}
SECTION("Bytes overloads")
{
std::vector<uint8_t> vecHash = getRandomSeed();
PrivateKey pk1 = BasicSchemeMPL().KeyGen(Bytes(getRandomSeed()));
PrivateKey pk2 = AugSchemeMPL().KeyGen(Bytes(getRandomSeed()));
PrivateKey pk3 = PopSchemeMPL().KeyGen(Bytes(getRandomSeed()));
std::vector<uint8_t> vecG1Element = pk1.GetG1Element().Serialize();
G1Element g1Vector = G1Element::FromByteVector(vecG1Element);
G1Element g1Bytes = G1Element::FromBytes(Bytes(vecG1Element));
REQUIRE(g1Vector == g1Bytes);
std::vector<uint8_t> vecG2Element = pk1.GetG2Element().Serialize();
G2Element g2Vector = G2Element::FromByteVector(vecG2Element);
G2Element g2Bytes = G2Element::FromBytes(Bytes(vecG2Element));
REQUIRE(g2Vector == g2Bytes);
G1Element g1MessageVector = G1Element::FromMessage(vecHash, vecHash.data(), vecHash.size());
G1Element g1MessageBytes = G1Element::FromMessage(Bytes(vecHash), vecHash.data(), vecHash.size());
REQUIRE(g1MessageVector == g1MessageBytes);
G2Element g2MessageVector = G2Element::FromMessage(vecHash, vecHash.data(), vecHash.size());
G2Element g2MessageBytes = G2Element::FromMessage(Bytes(vecHash), vecHash.data(), vecHash.size());
REQUIRE(g2MessageVector == g2MessageBytes);
G1Element g1_1 = pk1.GetG1Element();
G1Element g1_2 = pk2.GetG1Element();
G1Element g1_3 = pk3.GetG1Element();
G2Element g2BasicSignVector1 = BasicSchemeMPL().Sign(pk1, vecHash);
G2Element g2BasicSignBytes1 = BasicSchemeMPL().Sign(pk1, Bytes(vecHash));