/* Copyright (c) 2023, Google LLC * * Permission to use, copy, modify, and/or distribute this software for any * purpose with or without fee is hereby granted, provided that the above * copyright notice and this permission notice appear in all copies. * * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ #define OPENSSL_UNSTABLE_EXPERIMENTAL_DILITHIUM #include #include #include #include #include #include #include #include "../internal.h" #include "../test/file_test.h" #include "../test/test_util.h" #include "./internal.h" // This test is very slow, so it is disabled by default. TEST(DilithiumTest, DISABLED_BitFlips) { std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES); auto priv = std::make_unique(); EXPECT_TRUE(DILITHIUM_generate_key(encoded_public_key.data(), priv.get())); std::vector encoded_signature(DILITHIUM_SIGNATURE_BYTES); static const uint8_t kMessage[] = {'H', 'e', 'l', 'l', 'o', ' ', 'w', 'o', 'r', 'l', 'd'}; EXPECT_TRUE(DILITHIUM_sign(encoded_signature.data(), priv.get(), kMessage, sizeof(kMessage))); auto pub = std::make_unique(); CBS cbs = bssl::MakeConstSpan(encoded_public_key); ASSERT_TRUE(DILITHIUM_parse_public_key(pub.get(), &cbs)); EXPECT_EQ(DILITHIUM_verify(pub.get(), encoded_signature.data(), kMessage, sizeof(kMessage)), 1); for (size_t i = 0; i < DILITHIUM_SIGNATURE_BYTES; i++) { for (int j = 0; j < 8; j++) { encoded_signature[i] ^= 1 << j; EXPECT_EQ(DILITHIUM_verify(pub.get(), encoded_signature.data(), kMessage, sizeof(kMessage)), 0) << "Bit flip in signature at byte " << i << " bit " << j << " didn't cause a verification failure"; encoded_signature[i] ^= 1 << j; } } } TEST(DilithiumTest, SignatureIsRandomized) { std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES); auto priv = std::make_unique(); EXPECT_TRUE(DILITHIUM_generate_key(encoded_public_key.data(), priv.get())); auto pub = std::make_unique(); CBS cbs = bssl::MakeConstSpan(encoded_public_key); ASSERT_TRUE(DILITHIUM_parse_public_key(pub.get(), &cbs)); std::vector encoded_signature1(DILITHIUM_SIGNATURE_BYTES); std::vector encoded_signature2(DILITHIUM_SIGNATURE_BYTES); static const uint8_t kMessage[] = {'H', 'e', 'l', 'l', 'o', ' ', 'w', 'o', 'r', 'l', 'd'}; EXPECT_TRUE(DILITHIUM_sign(encoded_signature1.data(), priv.get(), kMessage, sizeof(kMessage))); EXPECT_TRUE(DILITHIUM_sign(encoded_signature2.data(), priv.get(), kMessage, sizeof(kMessage))); EXPECT_NE(Bytes(encoded_signature1), Bytes(encoded_signature2)); // Even though the signatures are different, they both verify. EXPECT_EQ(DILITHIUM_verify(pub.get(), encoded_signature1.data(), kMessage, sizeof(kMessage)), 1); EXPECT_EQ(DILITHIUM_verify(pub.get(), encoded_signature2.data(), kMessage, sizeof(kMessage)), 1); } TEST(DilithiumTest, PublicFromPrivateIsConsistent) { std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES); auto priv = std::make_unique(); EXPECT_TRUE(DILITHIUM_generate_key(encoded_public_key.data(), priv.get())); auto pub = std::make_unique(); EXPECT_TRUE(DILITHIUM_public_from_private(pub.get(), priv.get())); std::vector encoded_public_key2(DILITHIUM_PUBLIC_KEY_BYTES); CBB cbb; CBB_init_fixed(&cbb, encoded_public_key2.data(), encoded_public_key2.size()); ASSERT_TRUE(DILITHIUM_marshal_public_key(&cbb, pub.get())); EXPECT_EQ(Bytes(encoded_public_key2), Bytes(encoded_public_key)); } TEST(DilithiumTest, InvalidPublicKeyEncodingLength) { // Encode a public key with a trailing 0 at the end. std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES + 1); auto priv = std::make_unique(); EXPECT_TRUE(DILITHIUM_generate_key(encoded_public_key.data(), priv.get())); // Public key is 1 byte too short. CBS cbs = bssl::MakeConstSpan(encoded_public_key) .first(DILITHIUM_PUBLIC_KEY_BYTES - 1); auto parsed_pub = std::make_unique(); EXPECT_FALSE(DILITHIUM_parse_public_key(parsed_pub.get(), &cbs)); // Public key has the correct length. cbs = bssl::MakeConstSpan(encoded_public_key).first(DILITHIUM_PUBLIC_KEY_BYTES); EXPECT_TRUE(DILITHIUM_parse_public_key(parsed_pub.get(), &cbs)); // Public key is 1 byte too long. cbs = bssl::MakeConstSpan(encoded_public_key); EXPECT_FALSE(DILITHIUM_parse_public_key(parsed_pub.get(), &cbs)); } TEST(DilithiumTest, InvalidPrivateKeyEncodingLength) { std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES); auto priv = std::make_unique(); EXPECT_TRUE(DILITHIUM_generate_key(encoded_public_key.data(), priv.get())); CBB cbb; std::vector malformed_private_key(DILITHIUM_PRIVATE_KEY_BYTES + 1, 0); CBB_init_fixed(&cbb, malformed_private_key.data(), DILITHIUM_PRIVATE_KEY_BYTES); ASSERT_TRUE(DILITHIUM_marshal_private_key(&cbb, priv.get())); CBS cbs; auto parsed_priv = std::make_unique(); // Private key is 1 byte too short. CBS_init(&cbs, malformed_private_key.data(), DILITHIUM_PRIVATE_KEY_BYTES - 1); EXPECT_FALSE(DILITHIUM_parse_private_key(parsed_priv.get(), &cbs)); // Private key has the correct length. CBS_init(&cbs, malformed_private_key.data(), DILITHIUM_PRIVATE_KEY_BYTES); EXPECT_TRUE(DILITHIUM_parse_private_key(parsed_priv.get(), &cbs)); // Private key is 1 byte too long. CBS_init(&cbs, malformed_private_key.data(), DILITHIUM_PRIVATE_KEY_BYTES + 1); EXPECT_FALSE(DILITHIUM_parse_private_key(parsed_priv.get(), &cbs)); } static void DilithiumFileTest(FileTest *t) { std::vector seed, message, public_key_expected, private_key_expected, signed_message_expected; t->IgnoreAttribute("count"); ASSERT_TRUE(t->GetBytes(&seed, "seed")); t->IgnoreAttribute("mlen"); ASSERT_TRUE(t->GetBytes(&message, "msg")); ASSERT_TRUE(t->GetBytes(&public_key_expected, "pk")); ASSERT_TRUE(t->GetBytes(&private_key_expected, "sk")); t->IgnoreAttribute("smlen"); ASSERT_TRUE(t->GetBytes(&signed_message_expected, "sm")); uint8_t gen_key_entropy[DILITHIUM_GENERATE_KEY_ENTROPY]; // The test vectors provide a CTR-DRBG seed which is used to generate the // input entropy. ASSERT_EQ(seed.size(), size_t{CTR_DRBG_ENTROPY_LEN}); { bssl::UniquePtr state( CTR_DRBG_new(seed.data(), nullptr, 0)); ASSERT_TRUE(state); ASSERT_TRUE(CTR_DRBG_generate(state.get(), gen_key_entropy, DILITHIUM_GENERATE_KEY_ENTROPY, nullptr, 0)); CONSTTIME_SECRET(gen_key_entropy, sizeof(gen_key_entropy)); } // Reproduce key generation. auto parsed_pub = std::make_unique(); auto priv = std::make_unique(); std::vector encoded_private_key(DILITHIUM_PRIVATE_KEY_BYTES); std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES); EXPECT_TRUE(DILITHIUM_generate_key_external_entropy( encoded_public_key.data(), priv.get(), gen_key_entropy)); CBB cbb; CBB_init_fixed(&cbb, encoded_private_key.data(), encoded_private_key.size()); ASSERT_TRUE(DILITHIUM_marshal_private_key(&cbb, priv.get())); CONSTTIME_DECLASSIFY(encoded_private_key.data(), encoded_private_key.size()); EXPECT_EQ(Bytes(encoded_public_key), Bytes(public_key_expected)); EXPECT_EQ(Bytes(encoded_private_key), Bytes(private_key_expected)); // Reproduce signature. std::vector encoded_signature(DILITHIUM_SIGNATURE_BYTES); EXPECT_TRUE(DILITHIUM_sign_deterministic(encoded_signature.data(), priv.get(), message.data(), message.size())); ASSERT_GE(signed_message_expected.size(), size_t{DILITHIUM_SIGNATURE_BYTES}); EXPECT_EQ(Bytes(encoded_signature), Bytes(bssl::MakeConstSpan(signed_message_expected) .first(DILITHIUM_SIGNATURE_BYTES))); EXPECT_EQ(Bytes(message), Bytes(bssl::MakeConstSpan(signed_message_expected) .subspan(DILITHIUM_SIGNATURE_BYTES))); // Check that verification matches. CBS cbs; CBS_init(&cbs, encoded_public_key.data(), encoded_public_key.size()); ASSERT_TRUE(DILITHIUM_parse_public_key(parsed_pub.get(), &cbs)); EXPECT_EQ(DILITHIUM_verify(parsed_pub.get(), encoded_signature.data(), message.data(), message.size()), 1); // Test that parsing the encoded private key yields a functional object. auto parsed_priv = std::make_unique(); std::vector encoded_signature2(DILITHIUM_SIGNATURE_BYTES); CBS_init(&cbs, encoded_private_key.data(), encoded_private_key.size()); ASSERT_TRUE(DILITHIUM_parse_private_key(parsed_priv.get(), &cbs)); EXPECT_TRUE(DILITHIUM_sign_deterministic(encoded_signature2.data(), parsed_priv.get(), message.data(), message.size())); EXPECT_EQ(Bytes(encoded_signature2), Bytes(encoded_signature)); // Test that parsing + encoding is idempotent. std::vector encoded_private_key2(DILITHIUM_PRIVATE_KEY_BYTES); std::vector encoded_public_key2(DILITHIUM_PUBLIC_KEY_BYTES); CBB_init_fixed(&cbb, encoded_private_key2.data(), encoded_private_key2.size()); ASSERT_TRUE(DILITHIUM_marshal_private_key(&cbb, parsed_priv.get())); CBB_init_fixed(&cbb, encoded_public_key2.data(), encoded_public_key2.size()); ASSERT_TRUE(DILITHIUM_marshal_public_key(&cbb, parsed_pub.get())); EXPECT_EQ(Bytes(encoded_public_key2), Bytes(encoded_public_key)); EXPECT_EQ(Bytes(encoded_private_key2), Bytes(encoded_private_key)); } static void DilithiumSignFileTest(FileTest *t) { std::string description, valid; std::vector message, private_key, signed_message_expected; ASSERT_TRUE(t->GetAttribute(&description, "description")); t->IgnoreAttribute("mlen"); ASSERT_TRUE(t->GetBytes(&message, "msg")); ASSERT_TRUE(t->GetBytes(&private_key, "sk")); ASSERT_TRUE(t->GetAttribute(&valid, "valid")); t->IgnoreAttribute("smlen"); ASSERT_TRUE(t->GetBytes(&signed_message_expected, "sm")); bool is_valid = valid == "true"; // Parse private key. DILITHIUM_private_key priv; CBS cbs; CBS_init(&cbs, private_key.data(), private_key.size()); if (!DILITHIUM_parse_private_key(&priv, &cbs)) { EXPECT_FALSE(is_valid) << "Unexpected signing result for edge case: " << description; return; } // Reproduce signature. uint8_t encoded_signature[DILITHIUM_SIGNATURE_BYTES]; DILITHIUM_sign_deterministic(encoded_signature, &priv, message.data(), message.size()); ASSERT_GE(signed_message_expected.size(), size_t{DILITHIUM_SIGNATURE_BYTES}); EXPECT_EQ(Bytes(encoded_signature), Bytes(signed_message_expected.data(), DILITHIUM_SIGNATURE_BYTES)) << "Unexpected signing result for edge case: " << description; EXPECT_EQ(Bytes(message), Bytes(&signed_message_expected[DILITHIUM_SIGNATURE_BYTES], signed_message_expected.size() - DILITHIUM_SIGNATURE_BYTES)) << "Unexpected signing result for edge case: " << description; EXPECT_TRUE(is_valid) << "Unexpected signing result for edge case: " << description; } static void DilithiumVerifyFileTest(FileTest *t) { std::string description, valid; std::vector message, public_key, signed_message; ASSERT_TRUE(t->GetAttribute(&description, "description")); t->IgnoreAttribute("mlen"); ASSERT_TRUE(t->GetBytes(&message, "msg")); ASSERT_TRUE(t->GetBytes(&public_key, "pk")); ASSERT_TRUE(t->GetAttribute(&valid, "valid")); t->IgnoreAttribute("smlen"); ASSERT_TRUE(t->GetBytes(&signed_message, "sm")); bool is_valid = valid == "true"; // Parse public key. DILITHIUM_public_key pub; CBS cbs; CBS_init(&cbs, public_key.data(), public_key.size()); if (!DILITHIUM_parse_public_key(&pub, &cbs)) { EXPECT_FALSE(is_valid) << "Unexpected verification result for edge case: " << description; return; } // Verify signature. ASSERT_GE(signed_message.size(), size_t{DILITHIUM_SIGNATURE_BYTES}); EXPECT_EQ(DILITHIUM_verify(&pub, signed_message.data(), &signed_message[DILITHIUM_SIGNATURE_BYTES], signed_message.size() - DILITHIUM_SIGNATURE_BYTES), is_valid) << "Unexpected verification result for edge case: " << description; } TEST(DilithiumTest, TestVectors) { FileTestGTest("crypto/dilithium/dilithium_tests.txt", DilithiumFileTest); } TEST(DilithiumTest, EdgeCaseSigningTests) { FileTestGTest("crypto/dilithium/edge_cases_draft_dilithium3_sign.txt", DilithiumSignFileTest); } TEST(DilithiumTest, EdgeCaseVerifyTests) { FileTestGTest("crypto/dilithium/edge_cases_draft_dilithium3_verify.txt", DilithiumVerifyFileTest); } TEST(DilithiumTest, KeyGenerationHardCodedNIST) { // Published on // https://csrc.nist.gov/Projects/post-quantum-cryptography/post-quantum-cryptography-standardization/example-files uint8_t entropy[DILITHIUM_GENERATE_KEY_ENTROPY] = { 0x72, 0xC3, 0xC5, 0xE0, 0xCC, 0x9F, 0x33, 0x2F, 0x49, 0xD0, 0xFC, 0x0F, 0xD6, 0x39, 0x9D, 0xA7, 0x56, 0x45, 0xA3, 0xE3, 0x3D, 0xBF, 0x56, 0xF1, 0xE9, 0x68, 0x97, 0x66, 0x2D, 0x0A, 0x9B, 0x37}; std::vector encoded_public_key(DILITHIUM_PUBLIC_KEY_BYTES); auto priv = std::make_unique(); EXPECT_TRUE(DILITHIUM_generate_key_external_entropy(encoded_public_key.data(), priv.get(), entropy)); static const uint8_t expected_public_key[DILITHIUM_PUBLIC_KEY_BYTES] = { 0x88, 0xC9, 0x3D, 0xEB, 0x90, 0x1A, 0x24, 0xA9, 0x45, 0xFA, 0x94, 0xAE, 0x54, 0xDB, 0xAF, 0x46, 0xD8, 0x1C, 0xAC, 0xA9, 0x43, 0xFB, 0xE3, 0x20, 0x42, 0x1C, 0x61, 0xB3, 0x32, 0x04, 0x84, 0x9F, 0x65, 0xE8, 0x33, 0xB5, 0xEB, 0x94, 0xC6, 0x0E, 0x74, 0xA6, 0x0D, 0xD2, 0xC8, 0xEA, 0x1D, 0xE7, 0xFE, 0x99, 0x60, 0x93, 0x55, 0x87, 0x5F, 0xFC, 0x40, 0x0E, 0xCD, 0x83, 0xF1, 0x2C, 0xDD, 0xD1, 0xB0, 0x15, 0xAC, 0x75, 0x0D, 0xF7, 0x75, 0x9D, 0x3D, 0x0F, 0xEC, 0xE7, 0x95, 0x42, 0xF1, 0x2B, 0xE3, 0x0A, 0x47, 0x39, 0x21, 0x49, 0x9A, 0x92, 0x7C, 0xDE, 0xED, 0xF9, 0xC6, 0x2F, 0x0A, 0x75, 0x58, 0x35, 0xB9, 0xFF, 0x46, 0x40, 0x40, 0xEF, 0x40, 0x97, 0x84, 0xBA, 0x7D, 0x50, 0x91, 0xBC, 0x92, 0xC7, 0xA0, 0xC6, 0x23, 0xDE, 0xC0, 0x17, 0xE9, 0x5C, 0x3A, 0xD4, 0x3C, 0x86, 0x5B, 0x59, 0x5D, 0x04, 0x09, 0x16, 0x29, 0xA5, 0x61, 0x14, 0xA3, 0x19, 0x7B, 0x0A, 0x21, 0x17, 0xE9, 0xEC, 0xC8, 0xF3, 0xE4, 0x8E, 0x1E, 0x9C, 0x77, 0x2B, 0xA6, 0x1E, 0x5A, 0xE3, 0x13, 0x81, 0x89, 0xDF, 0x4A, 0x9E, 0x14, 0x92, 0x91, 0xA6, 0x69, 0x4A, 0xBB, 0x10, 0x05, 0xCF, 0xA8, 0xED, 0x76, 0x6D, 0xCD, 0x8C, 0x8C, 0xF7, 0x2A, 0xE9, 0xC4, 0x55, 0x03, 0xBB, 0x71, 0x65, 0xB8, 0x41, 0x40, 0xB0, 0xCB, 0x5C, 0xBD, 0x33, 0xFF, 0xC4, 0x3E, 0x63, 0x84, 0xCD, 0x90, 0x59, 0x95, 0xB5, 0xA7, 0x87, 0xFE, 0x48, 0x4B, 0xFE, 0x17, 0xD2, 0xBF, 0x30, 0x25, 0x0F, 0x78, 0xBE, 0x5C, 0xEA, 0x26, 0xE2, 0x01, 0xFF, 0x1F, 0x20, 0x57, 0x4B, 0xB6, 0x77, 0xF4, 0xD2, 0x08, 0xE7, 0xC5, 0xB9, 0x6C, 0xAB, 0xD6, 0x41, 0x6E, 0xEC, 0x1E, 0x21, 0xE0, 0x81, 0x6F, 0x35, 0x2C, 0x84, 0x8E, 0xEA, 0xA4, 0x7C, 0xDD, 0x8E, 0x02, 0xB4, 0x71, 0x58, 0xBC, 0xB4, 0x44, 0x51, 0xD3, 0x60, 0xAC, 0xBD, 0x9D, 0xCF, 0x52, 0x3E, 0xB9, 0x69, 0x4F, 0xD5, 0xE1, 0x55, 0x7D, 0xA8, 0xF2, 0xBE, 0xED, 0x0A, 0x0A, 0xEE, 0x52, 0xE2, 0x3A, 0xEF, 0x1B, 0xEB, 0x44, 0x9D, 0x91, 0x32, 0x76, 0xE8, 0x8A, 0xF1, 0x88, 0x15, 0x1F, 0x68, 0x76, 0xE4, 0xA5, 0xF5, 0x70, 0xA2, 0x40, 0xA6, 0x95, 0xB0, 0x6E, 0x4D, 0x60, 0x13, 0x2D, 0xA2, 0xB6, 0x2F, 0x4C, 0xAB, 0x5C, 0x88, 0x1F, 0x72, 0x77, 0xAC, 0xD1, 0xDA, 0x48, 0x68, 0x73, 0x68, 0xCB, 0x8E, 0xD4, 0x9F, 0xAE, 0x2A, 0x4B, 0x2E, 0x5E, 0xF3, 0xDE, 0x02, 0x60, 0xA7, 0x31, 0xD6, 0x59, 0xA3, 0xF4, 0x2A, 0x19, 0xF4, 0x66, 0xC9, 0xF0, 0xD4, 0x3A, 0x10, 0x2B, 0x12, 0x9C, 0xDA, 0xE4, 0xA6, 0xBF, 0x08, 0x41, 0x96, 0xD6, 0xFE, 0xA7, 0xEE, 0xB3, 0x83, 0x36, 0xEF, 0x1F, 0x25, 0x65, 0x02, 0xEE, 0xC8, 0x0A, 0x49, 0x2F, 0x0A, 0x4F, 0x8A, 0x18, 0x23, 0x45, 0xCC, 0x78, 0x97, 0x8C, 0x06, 0x1C, 0x56, 0x3D, 0x03, 0xE0, 0x7A, 0xC6, 0xFC, 0x2A, 0x1C, 0xF5, 0xCB, 0x8D, 0x25, 0xC0, 0x48, 0x87, 0xE5, 0xD1, 0x13, 0x91, 0xE0, 0xB3, 0xCD, 0x1D, 0xB1, 0x05, 0xC7, 0x34, 0x5C, 0xB3, 0xC8, 0x26, 0xFF, 0x05, 0x8C, 0x30, 0xE0, 0x22, 0x8C, 0x3A, 0x85, 0x7B, 0x7C, 0xE2, 0xF0, 0x64, 0xA5, 0x08, 0xAE, 0x80, 0xE3, 0x3C, 0xE2, 0xCA, 0x82, 0xFE, 0x36, 0x24, 0x6D, 0x61, 0x57, 0x8C, 0x52, 0xD6, 0x9A, 0x8F, 0x8B, 0x84, 0x4F, 0x99, 0x7D, 0x8B, 0x4A, 0x33, 0x41, 0xC9, 0x16, 0x2F, 0xF5, 0x32, 0x02, 0x28, 0xDD, 0x59, 0xC0, 0x91, 0x1F, 0xE4, 0x79, 0xE7, 0x2F, 0xF6, 0xAB, 0x43, 0xF4, 0xA7, 0xB9, 0xF8, 0x05, 0xA8, 0x6F, 0x98, 0x45, 0x12, 0xF9, 0x73, 0xD0, 0x91, 0x37, 0x0F, 0x68, 0x1F, 0x49, 0x82, 0x72, 0x96, 0x96, 0x43, 0x41, 0xAC, 0xAE, 0xD3, 0xE3, 0x11, 0xA3, 0x2B, 0xEC, 0x51, 0x74, 0xA7, 0x76, 0x89, 0xA4, 0x92, 0x1D, 0x02, 0x9F, 0x21, 0xF6, 0xC4, 0x0E, 0xA5, 0x5F, 0x1E, 0x73, 0xC1, 0xAF, 0xF2, 0x14, 0x3A, 0xCD, 0x3E, 0x50, 0x37, 0xFC, 0xD5, 0xB3, 0x11, 0xCD, 0x82, 0x5F, 0x33, 0x26, 0x71, 0x0C, 0x32, 0x63, 0xA0, 0xCF, 0x60, 0x16, 0xD9, 0xEA, 0xE3, 0xE5, 0x0F, 0xE2, 0x57, 0x5E, 0x0A, 0xAB, 0xED, 0xFC, 0xB3, 0x49, 0x5B, 0x9E, 0x77, 0x76, 0x4E, 0x97, 0xA2, 0x63, 0xD0, 0x94, 0x80, 0x6F, 0xA1, 0x24, 0xA8, 0xC1, 0x53, 0xE5, 0x97, 0x5D, 0x35, 0xFA, 0x42, 0x59, 0x76, 0x83, 0xC9, 0x5D, 0x83, 0x80, 0x67, 0x02, 0x8E, 0xBD, 0xA9, 0x76, 0x58, 0xE6, 0x44, 0x78, 0x58, 0x0C, 0xEC, 0xAA, 0x77, 0x2E, 0xC6, 0xCA, 0x31, 0x9F, 0x11, 0x80, 0x3A, 0x64, 0x8D, 0x6A, 0xF0, 0xF9, 0x48, 0x4B, 0x15, 0x82, 0xDE, 0x0C, 0x72, 0xAF, 0x6C, 0x49, 0x12, 0xEA, 0x79, 0x15, 0xFF, 0xEC, 0x90, 0x0A, 0x95, 0xDE, 0x23, 0x5D, 0xEF, 0xFC, 0x4F, 0x75, 0x4B, 0xED, 0x72, 0x4E, 0x36, 0x12, 0xF0, 0x69, 0x6A, 0x1A, 0xE1, 0xFF, 0x05, 0xE8, 0xBE, 0x25, 0x90, 0x02, 0x9C, 0xC0, 0xD3, 0x4E, 0xDD, 0x83, 0x98, 0x25, 0x0B, 0xC0, 0xD3, 0x91, 0xDE, 0xE8, 0x71, 0xA5, 0x4F, 0x15, 0x68, 0x5D, 0x9C, 0xD6, 0x7F, 0x85, 0xEB, 0x1B, 0xB5, 0x0F, 0x39, 0xA8, 0xA1, 0x94, 0x15, 0xF8, 0x63, 0x52, 0x74, 0x30, 0xF4, 0xEF, 0xC2, 0x97, 0xBC, 0x08, 0xA0, 0x3D, 0xB9, 0xDF, 0x86, 0xD2, 0x4C, 0x6D, 0x0F, 0x63, 0xD0, 0x39, 0x9D, 0x2E, 0x86, 0x42, 0x63, 0x31, 0x57, 0x4D, 0x1C, 0x67, 0x98, 0xFB, 0xAF, 0x46, 0x33, 0xCF, 0xBE, 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0x0A, 0xCB, 0x3F, 0x5F, 0x9B, 0x7B, 0x60, 0xEA, 0x43, 0x66, 0x4D, 0x05, 0x3C, 0xA4, 0x18, 0x65, 0xD0, 0x68, 0x85, 0x4A, 0xEE, 0xF2, 0xAD, 0x80, 0xA5, 0x62, 0x6D, 0xF6, 0x6A, 0xC0, 0x03, 0x2B, 0x22, 0x51, 0x97, 0xD5, 0x2C, 0x7A, 0x55, 0xF6, 0xDD, 0x56, 0xD3, 0x75, 0xA4, 0x4D, 0xC2, 0x34, 0xE3, 0x55, 0xE6, 0xB7, 0xF1, 0x00, 0xCD, 0x5D, 0xF2, 0xE3, 0x07, 0xC2, 0x0C, 0x8E, 0xF4, 0x4C, 0x77, 0x97, 0x6A, 0xBF, 0xC4, 0x54, 0x2A, 0x0E, 0xBF, 0xBD, 0xB7, 0x9A, 0xFF, 0x5E, 0x79, 0xB4, 0x9A, 0x3F, 0x08, 0xEE, 0x63, 0xC0, 0xF7, 0x8D, 0x12, 0x4B, 0x62, 0x1B, 0x7B, 0xF4, 0xBD, 0x35, 0x50, 0xAD, 0x63, 0x24, 0x6F, 0xAF, 0x74, 0x8C, 0x46, 0xE9, 0x40, 0x91, 0xE4, 0xCC, 0x1A, 0x98, 0x1B, 0x41, 0x46, 0x4B, 0xD2, 0x7C, 0xF6, 0xED, 0xA5, 0xDE, 0xD5, 0xE9, 0x2C, 0x0A, 0x83, 0x8E, 0x59, 0xE2, 0xEC, 0x6F, 0xD2, 0x0C, 0x02, 0x59, 0x0E, 0xA2, 0x80, 0x7E, 0x1B, 0xEE, 0xBA, 0xA9, 0x1B, 0x5A, 0x5F, 0x03, 0x12, 0x54, 0x3F, 0x6F, 0xC6, 0x3C, 0x0B, 0x82, 0x24, 0x15, 0x32, 0xD2, 0xC4, 0x97, 0xEC, 0xEE, 0x54, 0xC0, 0xE6, 0x5E, 0x4F, 0x93, 0x83, 0x6A, 0x8A, 0x69, 0x09, 0x42, 0x67, 0x3A, 0x6C, 0x61, 0x11, 0x39, 0x66, 0xCA, 0x56, 0x6C, 0x2C, 0xE9, 0x60, 0x6B, 0xD8, 0x97, 0xB9, 0x00, 0xD7, 0x66, 0x1B, 0x9A, 0x0C, 0xB5, 0x36, 0x0C, 0x0A, 0x8D, 0x65, 0x5F, 0x7A, 0x5D, 0x99, 0x91, 0x36, 0xAD, 0x8E, 0xCD, 0xDA, 0xE0, 0x6C, 0x11, 0xF2, 0x14, 0x4D, 0xD6, 0x45, 0x29, 0xB6, 0x2C, 0xB1, 0xF1, 0x29, 0x4D, 0xF2, 0x22, 0xBF, 0xA6, 0xE5, 0x78, 0x0F, 0xEC, 0x07, 0xFB, 0xA3, 0xF7, 0xEC, 0xA8, 0x6B, 0x59, 0x3C, 0x26, 0x11, 0xA7, 0x45, 0xBC, 0x20, 0x6F, 0xE3, 0x07, 0xD4, 0x10, 0x3A, 0x3B, 0x68, 0xD3, 0xCA, 0x41, 0xA7, 0x72, 0x95, 0x41, 0x1D, 0x44, 0x85, 0x3B, 0x08, 0xF5, 0x2B, 0xC7, 0x46, 0x78, 0xE6, 0xC2, 0x2C, 0x17, 0x00, 0x76, 0x45, 0x64, 0xF3, 0xA3, 0x91, 0xF7, 0x87, 0xFF, 0x5F, 0x97, 0xA9, 0x50, 0xC7, 0x2F, 0x27, 0x1F, 0x49, 0x3C, 0xF6, 0x4E, 0x80, 0x89, 0x25, 0x23, 0x12, 0x09, 0xB8, 0xBE, 0x77, 0xC8, 0x62, 0xC7, 0x7B, 0x7C, 0x04, 0xC3, 0x61, 0x1C, 0x86, 0x39, 0x7A, 0xF4, 0x9D, 0xAF, 0x0B, 0xAA, 0x4E, 0xDE, 0x81, 0x71, 0x45, 0x86, 0xC0, 0xA6, 0xC5, 0x21, 0x0E, 0x46, 0xAB, 0x49, 0xAA, 0x56, 0xAD, 0x0D, 0xC8, 0x6B, 0x02, 0x07, 0xE5, 0xA2, 0xF8, 0xDE, 0x98, 0x85, 0xB8, 0x40, 0x76, 0xC3, 0x10, 0xD0, 0x9C, 0xE3, 0x24, 0xE9, 0xCC, 0x27, 0x56, 0x87, 0xB0, 0x54, 0xA0, 0xB4, 0xC6, 0x19, 0x76, 0x0A, 0x5F, 0x3C, 0x4E, 0x73, 0xA6, 0x1C, 0xDF, 0x37, 0xC2, 0x76, 0x26, 0x1D, 0xB1, 0xE0, 0x7F, 0x53, 0x61, 0x04, 0x4E, 0xEC, 0x1E, 0x69, 0xCC, 0xA9, 0xBD, 0x48, 0xC3, 0xAD, 0xCF, 0x68, 0x0B, 0x9E, 0x47, 0xD1, 0x5A, 0x2F, 0x39, 0x23, 0x54, 0x37, 0xCD, 0x40, 0xE7, 0xC9, 0x54, 0x1A, 0x06, 0xC0, 0xDA, 0xB1, 0x3A, 0x30, 0x29, 0x43, 0x38, 0x56, 0x1F, 0xB3, 0x26, 0xE8, 0x27, 0x5E, 0xD2, 0x83, 0x2F, 0x77, 0xD9, 0x5C, 0x63, 0x91, 0x5C, 0x06, 0x9F, 0xD4, 0xF5, 0x9A, 0xFF, 0x38, 0x84, 0x58, 0xB9, 0xB3, 0x9E, 0x4E, 0x0E, 0x24, 0xC9, 0x93, 0x24, 0x77, 0xDD, 0x52, 0xFF, 0x83, 0xDB, 0xDD, 0x24, 0xF2, 0xB6, 0x39, 0xFF, 0x9A, 0x32, 0x15, 0x66, 0x73, 0xDF, 0x05, 0x1C, 0x35, 0xB6, 0xF4, 0xF3, 0x2F, 0x21, 0x78, 0xB2, 0xEC, 0xD0, 0x9E, 0x7E, 0x9A, 0xFD, 0x4B, 0x62, 0xDD, 0x55, 0x16, 0xA0, 0xE2, 0xBE, 0x2C, 0x89, 0x53, 0x87, 0x28, 0x4B, 0xAF, 0x82, 0x8F, 0x88, 0x6C, 0x0C, 0xF4, 0x67, 0x40, 0x5B, 0x0A, 0x67, 0xFA, 0xF7, 0x6E, 0x4D, 0x1A, 0xD9, 0x33, 0x11, 0xC8, 0xAF, 0x07, 0xEE, 0xF1, 0x6F, 0x17, 0x29, 0xF6, 0x06, 0x46, 0xF3, 0xDB, 0xB9, 0x2D, 0xB0, 0x20, 0x44, 0xF9, 0xFE, 0x56, 0x33, 0x38, 0xDA, 0xC3, 0x0E, 0xC1, 0x65, 0x8A, 0xFF, 0xEA, 0xAC, 0xC7, 0xBC, 0x42, 0x12, 0x58, 0x8C, 0x32, 0x25, 0x19, 0xB3, 0xB9, 0x0B, 0x66, 0x55, 0xC2, 0xEC, 0x50, 0x9C, 0x73, 0xE9, 0x9E, 0x4B, 0x27, 0x50, 0xBB, 0x71, 0x1B, 0xBC, 0xD3, 0x9F, 0xBD, 0xC5, 0x39, 0x9C, 0xA9, 0x3E, 0xFE, 0xEF, 0x0C, 0xE8, 0x2E, 0x51, 0xD0, 0x8A, 0xC3, 0x50, 0xBC, 0x0B, 0x5E, 0x50, 0x38, 0x35, 0xEB, 0xE1, 0xB6, 0xF8, 0x4C, 0x42, 0xE1, 0xAB, 0x43, 0xC9, 0xD8, 0x86, 0xD1, 0x4A, 0xFA, 0xAB, 0x89, 0xA0, 0xBA, 0x4A, 0x7C, 0x94, 0x9B, 0x9D, 0x11, 0x5C, 0x7F, 0x83, 0x7D, 0x74, 0x95, 0xA7, 0x80, 0x10, 0x3B, 0xE8, 0xBE, 0x9F, 0x51, 0x4A, 0x34, 0x97, 0x03, 0xFD, 0x0E, 0x41, 0x8D, 0xBE, 0x88, 0xF2, 0x27, 0x88, 0x0C, 0xE5, 0xB2, 0xDD, 0x54, 0xC0, 0xBC, 0xE1, 0xFF, 0x61, 0x89, 0xC3, 0xCA, 0x89, 0x21, 0x6C, 0xDD, 0x23, 0x0D, 0x59, 0x87, 0xBC, 0xD4, 0x6C, 0x3B, 0x6C, 0x2D, 0xE7, 0xEE, 0x54, 0xB7, 0xDC, 0x96, 0x12, 0x3B, 0xAD, 0x7A, 0x9E, 0x2F, 0x92, 0x6A, 0xF1, 0x95, 0x2F, 0x42, 0x4F, 0x39, 0xC8, 0x90, 0xD6, 0x1A, 0x9D, 0xA8, 0xCF, 0xEB, 0xE1, 0x77, 0x08, 0x5D, 0x1A, 0x87, 0x60, 0x87, 0x6F, 0x68, 0x64, 0x8A, 0x82, 0xDD, 0xB7, 0x99, 0x95, 0x1A, 0x10, 0x1B, 0x82, 0x8F, 0x57, 0xE0, 0xCF, 0xE0, 0xFA, 0xC6, 0xD9, 0x08, 0x59, 0x62, 0xCF, 0x45, 0x11, 0x3C, 0xC5, 0xBF, 0x6D, 0x7F, 0xC2, 0xAC, 0xBC, 0xEE, 0xB5, 0x56, 0xDF, 0x2B, 0xC3, 0xD2, 0xFE, 0x67, 0xA8, 0x63, 0x31, 0x21, 0x34, 0xE7, 0x3E, 0x50, 0x6D, 0xA9, 0xDC, 0x78, 0xB7, 0xC9, 0x43, 0x47, 0x21, 0x7E, 0xAB, 0xB7, 0x3E, 0x24, 0x98, 0xD5, 0xF3, 0xA5, 0x29, 0x7F, 0x18, 0x59, 0xBD, 0x13, 0x74, 0x8C, 0xDB, 0x3B, 0x70, 0xE5, 0x19, 0x71, 0xCC, 0x01, 0xF0, 0x5B, 0x04, 0xEB, 0x08, 0x02, 0x28, 0xD5, 0x95, 0x9C, 0xC8, 0xFE, 0x59, 0x61, 0xA0, 0x20, 0x92, 0xEC, 0x8D, 0x0A, 0x4D, 0x16, 0x80, 0x6E, 0xB5, 0xD6, 0x08, 0x64, 0xC3, 0xEC, 0xF8, 0x01, 0x24, 0x42, 0x94, 0x02, 0x2A, 0x08, 0x23, 0x87, 0x3D, 0xBE, 0x8D, 0xFB, 0x6D, 0x06, 0xB6, 0xBA, 0xF6, 0x9C, 0xDD, 0x10, 0x7C, 0x96, 0x0A, 0xA4, 0xB2, 0xC3, 0x53, 0x6B, 0xB4, 0x42, 0x46, 0x13, 0x74, 0xF8, 0xFC, 0xB0, 0x48, 0x32, 0x64, 0x8B, 0x60, 0x03, 0x28, 0x64, 0xFA, 0x6F, 0x0A, 0xF7, 0x6F, 0x34, 0x35, 0x5B, 0x93, 0x43, 0xDC, 0xF3, 0xC8, 0xF9, 0x9F, 0xED, 0xD8, 0x8C, 0xA3, 0xD8, 0x3C, 0xAD, 0x67, 0x35, 0x1B, 0x45, 0x62, 0x06, 0x4E, 0xA1, 0x32, 0x51, 0x80, 0x60, 0x63, 0x62, 0xD7, 0x9A, 0x76, 0xA1, 0xB3, 0xC6, 0x76, 0x15, 0x2B, 0xA8, 0x0E, 0x82, 0xB8, 0x43, 0xD8, 0x5D, 0x53, 0x7E, 0xCE, 0xFF, 0xDD, 0xCC, 0x95, 0xB4, 0x66, 0x1C, 0xFA, 0x4A, 0x70, 0xB0, 0x6F, 0x92, 0x4D, 0x69, 0x2D, 0x87, 0xE1, 0xFB, 0x8E, 0x1C, 0xED, 0xD8, 0x5F, 0x7A, 0xB9, 0x32, 0x4F, 0xF5, 0xD0, 0xA7, 0x53, 0xD8, 0x62, 0x59, 0x1B, 0xE2, 0x39, 0xAB, 0xC9, 0x63, 0xB5, 0x0A, 0x7E, 0xF8, 0x70, 0xB0, 0x5F, 0x27, 0x21, 0x21, 0x5E, 0xB9, 0x0A, 0x60, 0xE4, 0x66, 0x95, 0x5D, 0x52, 0x2C, 0xA4, 0x21, 0x69, 0x44, 0x69, 0x35, 0x46}; EXPECT_EQ(Bytes(encoded_public_key), Bytes(expected_public_key)); static const uint8_t expected_private_key[DILITHIUM_PRIVATE_KEY_BYTES] = { 0x88, 0xC9, 0x3D, 0xEB, 0x90, 0x1A, 0x24, 0xA9, 0x45, 0xFA, 0x94, 0xAE, 0x54, 0xDB, 0xAF, 0x46, 0xD8, 0x1C, 0xAC, 0xA9, 0x43, 0xFB, 0xE3, 0x20, 0x42, 0x1C, 0x61, 0xB3, 0x32, 0x04, 0x84, 0x9F, 0x9B, 0x2E, 0x34, 0x8E, 0x48, 0x65, 0x61, 0x66, 0x80, 0xFC, 0x18, 0x43, 0x76, 0xA8, 0xCC, 0xB8, 0xDB, 0xE5, 0x98, 0x36, 0x5A, 0x23, 0xA2, 0x72, 0x39, 0x44, 0xF5, 0x35, 0x1F, 0x42, 0xF4, 0x74, 0x20, 0x77, 0x58, 0x21, 0x02, 0xF6, 0xF3, 0x13, 0xC2, 0x25, 0x64, 0xF8, 0x41, 0x4E, 0x37, 0x66, 0x70, 0x4F, 0xFD, 0x18, 0x01, 0x7F, 0xDC, 0xAE, 0x57, 0x0D, 0xB8, 0xC8, 0xFC, 0xB5, 0x67, 0xE4, 0x13, 0x21, 0x9C, 0xB4, 0xB4, 0x51, 0x75, 0xB8, 0x3E, 0x6B, 0xA5, 0xE3, 0x22, 0xA1, 0x12, 0xD1, 0x8C, 0xF9, 0xF3, 0x56, 0xB5, 0x76, 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0xE4, 0xA3, 0x5B, 0x30, 0x8A, 0xF2, 0x76, 0x87, 0xE6, 0xFB, 0x1A, 0xBE, 0x6C, 0x90, 0x17, 0xCA, 0xA6, 0xE4, 0x77, 0x88, 0x92, 0x54, 0x68, 0x92, 0x6F, 0xEF, 0x07, 0x84, 0x1D, 0x1B, 0xF4, 0x99, 0x6F, 0xB9, 0xD3, 0xBB, 0x0E, 0x81, 0x97, 0x73, 0xE8, 0x49, 0x29, 0xE4, 0x3C, 0x28, 0xE4, 0xB5, 0x06, 0x96, 0xC0, 0x8E, 0x1C, 0x7E, 0xF5, 0x1E, 0x46, 0xC9, 0x4C, 0x99, 0x40, 0x1F, 0xE6, 0xB2, 0x81, 0x25, 0xDA, 0x89, 0xA6, 0x6D, 0x65, 0xD3, 0x8B, 0x7A, 0x9D, 0xE8, 0xB0, 0x2B, 0x59, 0x57, 0x2A, 0x0F, 0x72, 0x46, 0x67, 0x35, 0x8C, 0x69, 0x6B, 0x9E, 0xBE, 0x5D, 0xFC, 0x51, 0x1B, 0x1A}; bssl::ScopedCBB cbb; EXPECT_TRUE(CBB_init(cbb.get(), DILITHIUM_PRIVATE_KEY_BYTES)); EXPECT_TRUE(DILITHIUM_marshal_private_key(cbb.get(), priv.get())); EXPECT_EQ(CBB_len(cbb.get()), size_t{DILITHIUM_PRIVATE_KEY_BYTES}); EXPECT_EQ(Bytes(CBB_data(cbb.get()), CBB_len(cbb.get())), Bytes(expected_private_key)); } TEST(DilithiumTest, SignatureHardCodedNIST) { // Published on // https://csrc.nist.gov/Projects/post-quantum-cryptography/post-quantum-cryptography-standardization/example-files static const uint8_t encoded_private_key[DILITHIUM_PRIVATE_KEY_BYTES] = { 0xD2, 0x6E, 0xE5, 0x9A, 0x89, 0xF6, 0x7C, 0x98, 0xB2, 0x0F, 0x89, 0x0B, 0x03, 0x42, 0x2C, 0x80, 0x27, 0xB7, 0x76, 0xFC, 0x30, 0x5B, 0xEF, 0x42, 0x2C, 0xDE, 0xD4, 0x03, 0xAA, 0x70, 0x5D, 0xA5, 0xDC, 0x38, 0x0A, 0xD9, 0x09, 0xE3, 0xC1, 0x3A, 0x76, 0xF7, 0xF5, 0x9B, 0xDD, 0x27, 0xA8, 0x43, 0xF5, 0xF9, 0xA1, 0xB8, 0xE5, 0xB7, 0xB5, 0x24, 0xEC, 0x44, 0x5A, 0x91, 0x6B, 0x7A, 0x44, 0xA1, 0x51, 0x67, 0x71, 0x6B, 0xC6, 0x09, 0xB3, 0xEC, 0x0C, 0x65, 0x3B, 0x21, 0x0C, 0x65, 0x69, 0xBA, 0x2F, 0x82, 0x33, 0xE7, 0xF6, 0xE4, 0x04, 0xB9, 0x2E, 0xB2, 0x1F, 0x39, 0x72, 0x9F, 0xEB, 0xC0, 0x6A, 0x64, 0x40, 0x87, 0xC7, 0x5F, 0xA7, 0xDA, 0x3D, 0xDC, 0x5B, 0x85, 0xA8, 0x9F, 0x55, 0xC9, 0xF8, 0x7A, 0x15, 0x01, 0x4E, 0x27, 0xAB, 0x32, 0x5E, 0xBE, 0xE0, 0xFE, 0x47, 0x2B, 0x2F, 0x56, 0x20, 0x58, 0x44, 0x86, 0x03, 0x82, 0x53, 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0xD3, 0xD8, 0x15, 0xBF, 0x73, 0xFB, 0xEC, 0xF1, 0xC9, 0xD4, 0x37, 0xD3, 0xA4, 0x7A, 0x78, 0x62, 0xC2, 0x86, 0x88, 0x4B, 0x63, 0x8D, 0xD7, 0xFB, 0x64, 0xBE, 0x01, 0xB7, 0x98, 0x1D, 0x7C, 0xC8, 0x2A, 0x90, 0x93, 0x8E, 0xBD, 0xD9, 0x66, 0x4D, 0xEB, 0xAF, 0x0E, 0x03, 0xA5, 0x95, 0x36, 0x8B, 0x89, 0x33, 0x8A, 0xB0, 0x76, 0xBD, 0x22, 0xAD, 0x57, 0x9D, 0x04, 0xF1, 0xC7, 0xEA, 0x07, 0x5D, 0x22, 0x0F, 0x8C, 0xCD, 0xC0, 0xB9, 0xE3, 0x72, 0xF5, 0x19, 0x4A, 0xFE, 0x83, 0x4D, 0x28}; CBS cbs; auto priv = std::make_unique(); CBS_init(&cbs, encoded_private_key, sizeof(encoded_private_key)); ASSERT_TRUE(DILITHIUM_parse_private_key(priv.get(), &cbs)); static const uint8_t message[] = { 0x4D, 0x3C, 0x4D, 0x95, 0x2A, 0x1D, 0xAC, 0x15, 0x17, 0x36, 0xAE, 0x9D, 0x0A, 0xD8, 0x1C, 0xD3, 0x7F, 0x7C, 0x49, 0x25, 0x39, 0xFC, 0xC9, 0x16, 0xA4, 0xB2, 0x25, 0x13, 0x09, 0xE0, 0x6C, 0xED, 0x54, 0xD7, 0x14, 0x58, 0x68, 0xD1, 0x45, 0xBC, 0x8D, 0x16, 0xF8, 0xB3, 0x64, 0xE5, 0xD6, 0x02, 0x6E, 0x11, 0x3B, 0xEC, 0x48, 0x24, 0xF6, 0xBF, 0xAE, 0x3C, 0x9F, 0x6C, 0x8B, 0x88, 0x8E, 0xC6, 0xB8, 0x25, 0x4C, 0xE5, 0x9E, 0x9E, 0x8E, 0x15, 0x8E, 0xB0, 0x40, 0x77, 0x84, 0x12, 0x43, 0xEE, 0x3A, 0x89, 0xD2, 0x5C, 0x0B, 0x30, 0xB4, 0xA6, 0x4B, 0x72, 0x36, 0x97, 0x33, 0x0A, 0xA8, 0x76, 0x63, 0xB2, 0x0E, 0xA4, 0x51, 0x31, 0x89, 0x55, 0x84, 0x66, 0xD2, 0x64, 0xC7, 0x90, 0x88, 0x41, 0x5E, 0xFA, 0x09, 0xDE, 0x9B, 0x64, 0xAB, 0x01, 0xB6, 0x40, 0xB2, 0x88, 0xD1, 0xD5, 0x56, 0x2E, 0xD7, 0x44, 0xE8, 0x0C, 0xAF, 0x0B, 0x6E, 0x2C, 0x29, 0xFF, 0xA1, 0xC3, 0x21, 0x12, 0x9E, 0xBC, 0x70, 0xCA, 0xA7, 0x3D, 0xCA, 0x7D, 0xCE, 0x89, 0x95, 0x71, 0x26, 0x0B, 0x2E, 0x7D, 0xA1, 0xB4, 0x7C, 0xEC, 0x5B, 0xB0, 0x0F, 0xD6, 0x6A, 0xF8, 0xB8, 0x9B, 0xB8, 0x43, 0x92, 0x89, 0x7B, 0xDD, 0x1A, 0x5E, 0xC7, 0x18, 0x66, 0x70, 0xDB, 0x81, 0x60, 0x4E, 0x0B, 0x94, 0x9B, 0x5A, 0xB1, 0xD1, 0x95, 0x22, 0xA3, 0xF0, 0x82, 0x8D, 0x0E, 0x77, 0xB3, 0x00, 0xA6, 0x3E, 0xDC, 0xB7, 0x4C, 0x48, 0xF9, 0xA0, 0x1C, 0xA9, 0x18, 0x16, 0xFB, 0xEE, 0x01, 0x1A, 0x5B, 0x01, 0x45, 0xC6, 0xA0, 0xB4, 0xEF, 0xD5, 0xA3, 0x00, 0x8A, 0x91, 0xE0, 0xB1, 0xAC, 0x96, 0xDD, 0x8C, 0xB9, 0x41, 0x0D, 0x56, 0xA9, 0x52, 0xE7, 0x4B, 0x7F, 0xB6, 0x84, 0xA0, 0xB1, 0x66, 0xE5, 0xF0, 0xDF, 0x9A, 0xD1, 0x00, 0xEE, 0x1C, 0x9E, 0x3B, 0x7B, 0x85, 0x1B, 0x4C, 0xBF, 0x33, 0x7A, 0x33, 0x28, 0xDB, 0x13, 0x97, 0x74, 0x51, 0xE9, 0x92, 0xC4, 0xA0, 0xB4, 0x54, 0xBA, 0xC5, 0xE3, 0xA2, 0xD0, 0xE6, 0x4D, 0x10, 0x6D, 0xC4, 0x7C, 0x21, 0x6E, 0x0C, 0x0A, 0xC1, 0x1B, 0x0F, 0x7C, 0x48, 0x58, 0x9E, 0x57, 0x30, 0x51, 0x13, 0x3D, 0x01, 0xF2, 0x95, 0x79, 0xC7, 0xE6, 0x59, 0xF8, 0xFB, 0x8E, 0x65, 0x39, 0xB0, 0xF6, 0x18, 0xD0, 0x53, 0xF4, 0x32, 0x3A, 0xD0, 0x23, 0x7A, 0x58, 0x94, 0x9F, 0x68, 0x94, 0x58, 0xAC, 0xC1, 0x09, 0xBE, 0xB7, 0xC8, 0x19, 0x52, 0xA8, 0x79, 0xA1, 0x0B, 0xF8, 0xBC, 0x01, 0xCE, 0x05, 0x7E, 0x93, 0x6B, 0x62, 0x01, 0x7E, 0x22, 0x6D, 0xD6, 0x6A, 0xB2, 0x47, 0x08, 0x52, 0xC0, 0x00, 0xA6, 0x18, 0xB9, 0xB1, 0x30, 0x05, 0x0F, 0x6B, 0x04, 0x77, 0x46, 0xD0, 0x68, 0xFE, 0x7D, 0x3C, 0xC1, 0x27, 0x7E, 0x4F, 0xF4, 0x40, 0x0F, 0x37, 0x2D, 0x50, 0xA8, 0x5F, 0x46, 0x9B, 0x4C, 0x7A, 0x35, 0xAA, 0x7F, 0xE8, 0x8D, 0xD9, 0x23, 0xAC, 0xEF, 0x5F, 0xFF, 0x47, 0xA9, 0x5F, 0x97, 0x1E, 0xFE, 0xA6, 0xB6, 0x5D, 0x33, 0xE6, 0x5F, 0x20, 0x17, 0x3C, 0x5B, 0xA5, 0xA3, 0x20, 0xDD, 0x16, 0xCA, 0xAB, 0x59, 0xAA, 0x7A, 0x7B, 0xB9, 0x99, 0x56, 0xEB, 0x5E, 0xD5, 0x4E, 0xB9, 0x3E, 0x89, 0xC8, 0x87, 0xA3, 0x0D, 0x6D, 0x38, 0x43, 0x45, 0xE2, 0x12, 0x91, 0xB8, 0xE9, 0xC6, 0xCD, 0xCB, 0xE2, 0x67, 0x1F, 0x81, 0x0A, 0x05, 0x8B, 0x85, 0x82, 0x20, 0x14, 0x6A, 0x21, 0x61, 0xB7, 0x41, 0x2C, 0xE2, 0xDB, 0x81, 0x7C, 0xC8, 0xC9, 0x95, 0x28, 0x19, 0x5F, 0x56, 0x7A, 0x92, 0xE1, 0x98, 0x33, 0x0A, 0xAA, 0x41, 0x8A, 0x5F, 0xAB, 0x75, 0x4E, 0x27, 0x22, 0x1A, 0x21, 0x65, 0xEC, 0x4D, 0x50, 0xB3, 0x91, 0xBB, 0x8A, 0xB2, 0xBE, 0xCC, 0xAA, 0x44, 0x9C, 0xA1, 0xD4, 0xD3, 0xD5, 0xC1, 0x7E, 0x28, 0x57, 0x30, 0x48, 0x45, 0x2E, 0xE4, 0x12, 0x06, 0x93, 0x50, 0x55, 0x15, 0xCF, 0x8D, 0x1E, 0x2F, 0x89, 0x84, 0xD3, 0x63, 0x46, 0x4D, 0xB7, 0x86, 0xE9, 0xB8, 0xB7, 0xBD, 0xED, 0xFA, 0x23, 0x01, 0xA2, 0x1F, 0x3C, 0x46, 0x9F, 0x01, 0x3E, 0x27, 0x74, 0x24, 0x05, 0xCF, 0xD0, 0xD1, 0x5E, 0x70, 0xBE, 0x05, 0x60, 0xE8, 0xB1, 0x8C, 0x82, 0x32, 0x78, 0x61, 0xA8, 0xDF, 0x64, 0x20, 0x0A, 0x51, 0xE6, 0x9D, 0x27, 0x91, 0xD4, 0x1E, 0x1E, 0x12, 0xBF, 0x37, 0x16, 0x64, 0x27, 0x0A, 0xFB, 0xBE, 0x1C, 0x84, 0xFF, 0x19, 0xD1, 0x1D, 0x4C, 0x23, 0x3E, 0xCD, 0xB8, 0x03, 0x3B, 0xC7, 0x9B, 0xC7, 0x96, 0x7C, 0x41, 0x0C, 0x13, 0xE8, 0xE3, 0xF9, 0x34, 0x0F, 0x84, 0x85, 0x10, 0x76, 0x0D, 0xAB, 0xCC, 0xAB, 0x6E, 0xF7, 0xBB, 0x87, 0x39, 0x8B, 0x14, 0x21, 0xE5, 0x80, 0x4F, 0x6D, 0x41, 0xAB, 0xC0, 0x9E, 0x65, 0x42, 0xD7, 0x2B, 0x87, 0x11, 0x5F, 0x12, 0x81, 0x45, 0x0C, 0x66, 0xAF, 0x3B, 0xF4, 0xFD, 0xC2, 0x1C, 0xB9, 0xB8, 0xC2, 0x7D, 0x0F, 0xC6, 0xDD, 0xFA, 0x73, 0x73, 0x2A, 0x87, 0x7C, 0xB7, 0xD7, 0xC0, 0x9B, 0x8E, 0x9F, 0x46, 0x03, 0xD9, 0x86, 0x5E, 0x4A, 0xF9, 0x1C, 0x58, 0xE9, 0xEF, 0x6F, 0xD9, 0xA3, 0x2C, 0x91, 0xEE, 0xAA, 0xEF, 0x17, 0x0B, 0xF4, 0xF4, 0x4B, 0xF5, 0x86, 0xD7, 0x89, 0xEF, 0x45, 0x71, 0xDE, 0xBE, 0x6F, 0xFF, 0x0C, 0x43, 0xE8, 0x42, 0x61, 0x7F, 0xA5, 0x0F, 0xA6, 0xEA, 0xC8, 0xC7, 0xF7, 0x0E, 0xB6, 0x80, 0xBE, 0x71, 0x76, 0x88, 0x18, 0x8A, 0x43, 0x04, 0x84, 0xF3, 0x38, 0x8F, 0x62, 0x19, 0xA7, 0x0E, 0xA3, 0x8B, 0xF3, 0xC6, 0xDB, 0xBC, 0x7F, 0xF3, 0xA7, 0x49, 0xD8, 0xC8, 0xE5, 0x1A, 0x13, 0x65, 0xAE, 0x37, 0x29, 0x88, 0xD2, 0x48, 0xF9, 0xFC, 0x0F, 0x2B, 0x67, 0xE8, 0x96, 0xCB, 0xC8, 0x6D, 0x2A, 0xED, 0x35, 0xF7, 0xAD, 0x8D, 0x4E, 0x93, 0xC2, 0x1D, 0xA0, 0x9E, 0x02, 0x04, 0xC7, 0xDB, 0x92, 0xFA, 0xFA, 0x71, 0x19, 0xA6, 0x3B, 0xD0, 0xCC, 0x00, 0xA0, 0x29, 0xCE, 0x7D, 0xB9, 0x3D, 0xF3, 0x4C, 0x33, 0xEC, 0xF6, 0x73, 0xD4, 0x8C, 0xE3, 0xF4, 0x09, 0x48, 0xDE, 0x86, 0xCA, 0x54, 0x67, 0xCC, 0x15, 0x99, 0x60, 0xB3, 0x29, 0xF5, 0x60, 0xB2, 0x0E, 0x5C, 0x8A, 0xC3, 0x7A, 0xC4, 0xC8, 0x96, 0x0B, 0x49, 0xB4, 0x55, 0x07, 0x54, 0x89, 0xE7, 0x21, 0x7D, 0x6B, 0xC5, 0x3A, 0xEE, 0x7C, 0x19, 0xB3, 0xFD, 0xE9, 0xFF, 0xF6, 0x67, 0xEA, 0xE8, 0x9A, 0xA6, 0xCE, 0x8C, 0x41, 0x5E, 0x80, 0x7B, 0x34, 0x8A, 0x14, 0x59, 0x83, 0x29, 0xA3, 0x2D, 0x9E, 0x50, 0x8C, 0x34, 0x09, 0xDF, 0x18, 0xEB, 0x42, 0x6B, 0xDB, 0xFD, 0xDD, 0x88, 0xAE, 0xB3, 0xA9, 0xBC, 0xB9, 0xD8, 0x4C, 0x23, 0x88, 0xAD, 0x79, 0xAA, 0xBF, 0xA3, 0x44, 0x5F, 0x80, 0xA9, 0xA6, 0x8E, 0xF7, 0x40, 0x96, 0xE3, 0x45, 0x16, 0xCB, 0x53, 0x16, 0xDF, 0x59, 0x9E, 0x58, 0x36, 0xF1, 0x23, 0x27, 0x1C, 0xF7, 0x29, 0x47, 0x29, 0x52, 0xE0, 0x6C, 0x81, 0x7A, 0x67, 0xC2, 0x19, 0x38, 0x2F, 0x22, 0xC4, 0xB0, 0xA1, 0x6F, 0x7B, 0x7D, 0xDE, 0x9E, 0xCF, 0x4A, 0xF6, 0x92, 0x7B, 0xBF, 0x44, 0x24, 0xF4, 0x3F, 0xCE, 0xB1, 0xA4, 0x8F, 0x1F, 0x2C, 0xBD, 0x98, 0xE7, 0x59, 0x34, 0x64, 0xEB, 0xDE, 0x45, 0xD6, 0x04, 0xB6, 0xAF, 0x95, 0xE3, 0x2A, 0xE7, 0x28, 0xD9, 0x21, 0xB3, 0x90, 0xF7, 0x12, 0xAD, 0xC2, 0x80, 0x25, 0x7F, 0x44, 0x20, 0x74, 0x1C, 0x0D, 0x29, 0xE0, 0xE6, 0xB9, 0x8E, 0xC1, 0x70, 0x85, 0x69, 0x38, 0x1B, 0xC8, 0x45, 0x42, 0x0D, 0xB0, 0xC1, 0xBD, 0xC9, 0xA2, 0x3D, 0xAE, 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