[Kernel] Replace BCrypt RSA with portable bignum implementation
Removes the Windows-only BCrypt dependency from XeCryptBnQwNeRsaPubCrypt and replaces it with a portable modular exponentiation implementation using 64-bit arithmetic, enabling RSA signature verification on all platforms. Adds Catch2 tests validating the implementation with a 2048-bit RSA key.
This commit is contained in:
Herman S.
@@ -21,3 +21,8 @@ target_link_libraries(xenia-kernel PUBLIC
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aes_128 fmt zlib-ng pugixml xenia-apu xenia-base xenia-cpu xenia-hid xenia-vfs
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)
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xe_target_defaults(xenia-kernel)
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if(XENIA_BUILD_TESTS)
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set(CMAKE_FOLDER "tests")
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add_subdirectory(testing)
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endif()
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3
src/xenia/kernel/testing/CMakeLists.txt
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3
src/xenia/kernel/testing/CMakeLists.txt
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@@ -0,0 +1,3 @@
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xe_test_suite(xenia-kernel-tests ${CMAKE_CURRENT_SOURCE_DIR}
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LINKS fmt xenia-base
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)
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159
src/xenia/kernel/testing/bignum_rsa_test.cc
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159
src/xenia/kernel/testing/bignum_rsa_test.cc
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@@ -0,0 +1,159 @@
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#include "third_party/catch/include/catch.hpp"
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#include "xenia/kernel/xboxkrnl/xecrypt_rsa.h"
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namespace {
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// Helper to build an XECRYPT_RSA-compatible blob in memory.
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// Layout: [4 bytes size BE][4 bytes exponent BE][8 bytes pad][modulus limbs...]
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std::vector<uint8_t> build_rsa_blob(uint32_t num_qwords, uint32_t exponent,
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const uint8_t* modulus_limbs) {
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std::vector<uint8_t> blob(0x10 + num_qwords * 8);
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// size (big-endian)
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blob[0] = (num_qwords >> 24) & 0xFF;
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blob[1] = (num_qwords >> 16) & 0xFF;
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blob[2] = (num_qwords >> 8) & 0xFF;
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blob[3] = num_qwords & 0xFF;
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// exponent (big-endian)
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blob[4] = (exponent >> 24) & 0xFF;
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blob[5] = (exponent >> 16) & 0xFF;
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blob[6] = (exponent >> 8) & 0xFF;
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blob[7] = exponent & 0xFF;
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// pad = 0
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// modulus data
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std::memcpy(blob.data() + 0x10, modulus_limbs, num_qwords * 8);
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return blob;
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}
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// Pirs public key modulus (32 qwords = 2048 bits), exponent = 3
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static const uint8_t pirs_modulus[] = {
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0xE6, 0x3B, 0x32, 0xB2, 0x8D, 0x9E, 0x9E, 0xE7, 0x9D, 0xFC, 0x5C, 0x72,
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0x41, 0x94, 0x58, 0x47, 0xDE, 0x0D, 0x18, 0x40, 0x72, 0xD6, 0xE3, 0x46,
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0x8E, 0xBA, 0x8E, 0xBC, 0x1A, 0x90, 0xAC, 0x20, 0xBA, 0x03, 0x85, 0xB5,
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0x1A, 0x3E, 0x25, 0xF9, 0xA6, 0x58, 0xEB, 0xB6, 0xA3, 0xC4, 0xA3, 0xEE,
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0xB2, 0xB0, 0xAE, 0x97, 0x69, 0xEB, 0xFE, 0x71, 0xFC, 0x02, 0xAB, 0x77,
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0xBA, 0xC8, 0xE6, 0x74, 0xE6, 0x7C, 0x63, 0x0E, 0xAF, 0x4C, 0xF7, 0xE7,
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0x11, 0x4A, 0x80, 0x24, 0x72, 0x05, 0x7A, 0x63, 0xD0, 0xF8, 0x91, 0x02,
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0xA6, 0xE7, 0x7D, 0x77, 0xC5, 0xA7, 0x9B, 0x08, 0x11, 0x2E, 0xA0, 0x64,
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0x45, 0x60, 0x46, 0xBC, 0x36, 0xE1, 0x17, 0x71, 0xBE, 0x66, 0x49, 0x2F,
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0xAE, 0x20, 0xA4, 0x76, 0x9C, 0x27, 0x51, 0xCF, 0x4B, 0x34, 0x7A, 0x35,
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0xBC, 0xA4, 0xAA, 0x1C, 0x47, 0x4B, 0xF4, 0x97, 0x22, 0x4E, 0x13, 0x24,
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0xD3, 0xC1, 0x57, 0xDF, 0x4D, 0x84, 0xB9, 0x18, 0x97, 0x99, 0xAC, 0x00,
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0xB3, 0x3D, 0x03, 0x25, 0x60, 0xC8, 0x7A, 0x59, 0xFE, 0x48, 0xFF, 0x28,
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0x3D, 0x10, 0xBB, 0x9E, 0x09, 0x06, 0x2A, 0x61, 0x20, 0x2C, 0xF8, 0x72,
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0xEB, 0x87, 0xE6, 0xD1, 0xFB, 0xB3, 0x66, 0xFC, 0x4A, 0x02, 0xAE, 0xD4,
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0xD8, 0x37, 0xCF, 0xA6, 0x32, 0x25, 0x79, 0x36, 0x0E, 0xF4, 0xED, 0x19,
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0xA2, 0x10, 0x27, 0x96, 0x2F, 0x9F, 0xA9, 0x3D, 0xA4, 0x37, 0x30, 0x11,
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0x51, 0x83, 0xBD, 0xF7, 0xC7, 0xE5, 0xCE, 0xAA, 0xEC, 0xDE, 0x48, 0xA0,
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0x84, 0xF7, 0xB0, 0xF6, 0x4B, 0x8E, 0xF0, 0x89, 0xBD, 0x47, 0x7C, 0x90,
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0xDD, 0x88, 0x12, 0x17, 0x40, 0xD2, 0x4E, 0xA6, 0xC6, 0x11, 0x04, 0x1B,
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0x57, 0xA8, 0x68, 0xB4, 0x61, 0xF4, 0x1B, 0xC6, 0x8B, 0xE8, 0xD9, 0x20,
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0xF2, 0x05, 0xE0, 0x70,
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};
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} // namespace
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TEST_CASE("XeCryptBnQwNeRsaPubCrypt_rejects_small_keys", "[crypt]") {
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// Keys below 512 bits (8 qwords) must be rejected
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const uint8_t modulus[] = {
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07,
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};
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const uint8_t input[] = {
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02,
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};
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uint8_t output[8] = {};
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REQUIRE(XeCryptBnQwNeRsaPubCrypt(input, output, modulus, 1, 3) == 0);
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const uint8_t modulus2[] = {
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x11,
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};
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const uint8_t input2[] = {
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01,
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0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
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};
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uint8_t output2[16] = {};
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REQUIRE(XeCryptBnQwNeRsaPubCrypt(input2, output2, modulus2, 2, 65537) == 0);
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}
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TEST_CASE("XeCryptBnQwNeRsaPubCrypt_2048bit_identity", "[crypt]") {
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// 1^3 mod modulus = 1
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uint8_t input[256] = {};
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input[7] = 0x01;
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uint8_t output[256] = {};
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uint32_t ret = XeCryptBnQwNeRsaPubCrypt(input, output, pirs_modulus, 0x20, 3);
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REQUIRE(ret == 1);
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uint8_t expected[256] = {};
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expected[7] = 0x01;
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REQUIRE(std::memcmp(output, expected, 256) == 0);
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}
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TEST_CASE("XeCryptBnQwNeRsaPubCrypt_2048bit_small_base", "[crypt]") {
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// 2^3 = 8 < modulus, so result is 8
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uint8_t input[256] = {};
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input[7] = 0x02;
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uint8_t output[256] = {};
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uint32_t ret = XeCryptBnQwNeRsaPubCrypt(input, output, pirs_modulus, 0x20, 3);
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REQUIRE(ret == 1);
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uint8_t expected[256] = {};
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expected[7] = 0x08;
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REQUIRE(std::memcmp(output, expected, 256) == 0);
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}
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TEST_CASE("XeCryptBnQwNeRsaPubCrypt_2048bit_large_base", "[crypt]") {
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// Large base that exercises modular reduction
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uint8_t input[256];
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for (int i = 0; i < 256; i++) {
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input[i] = static_cast<uint8_t>(i + 1);
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}
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// Ensure top limb is smaller than modulus top limb (0xF2...)
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input[248] = 0x01;
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input[249] = 0x02;
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input[250] = 0x03;
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input[251] = 0x04;
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input[252] = 0x05;
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input[253] = 0x06;
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input[254] = 0x07;
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input[255] = 0x08;
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uint8_t output[256] = {};
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uint32_t ret = XeCryptBnQwNeRsaPubCrypt(input, output, pirs_modulus, 0x20, 3);
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REQUIRE(ret == 1);
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// Deterministic: same input produces same output
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uint8_t output2[256] = {};
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uint32_t ret2 =
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XeCryptBnQwNeRsaPubCrypt(input, output2, pirs_modulus, 0x20, 3);
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REQUIRE(ret2 == 1);
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REQUIRE(std::memcmp(output, output2, 256) == 0);
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// Non-trivial result
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bool all_zero = true;
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for (int i = 0; i < 256; i++) {
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if (output[i] != 0) {
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all_zero = false;
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break;
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}
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}
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REQUIRE_FALSE(all_zero);
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}
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TEST_CASE("XeCryptBnQwNeRsaPubCrypt_2048bit_zero_base", "[crypt]") {
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// 0^e mod m = 0
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uint8_t input[256] = {};
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uint8_t output[256];
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std::memset(output, 0xFF, 256);
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uint32_t ret =
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XeCryptBnQwNeRsaPubCrypt(input, output, pirs_modulus, 0x20, 65537);
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REQUIRE(ret == 1);
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for (int i = 0; i < 256; i++) {
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REQUIRE(output[i] == 0x00);
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}
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}
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@@ -15,10 +15,6 @@
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#include "xenia/kernel/util/shim_utils.h"
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#include "xenia/kernel/xboxkrnl/xboxkrnl_private.h"
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#ifdef XE_PLATFORM_WIN32
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#include "xenia/base/platform_win.h" // for bcrypt.h
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#endif
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#include "third_party/crypto/TinySHA1.hpp"
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#include "third_party/crypto/des/des.cpp"
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#include "third_party/crypto/des/des.h"
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@@ -26,6 +22,7 @@
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#include "third_party/crypto/des/descbc.h"
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#include "third_party/crypto/sha256.cpp"
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#include "third_party/crypto/sha256.h"
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#include "xenia/kernel/xboxkrnl/xecrypt_rsa.h"
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extern "C" {
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#include "third_party/FFmpeg/libavutil/md5.h"
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@@ -697,105 +694,17 @@ DECLARE_XBOXKRNL_EXPORT1(XeCryptBnQw_SwapDwQwLeBe, kNone, kImplemented);
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dword_result_t XeCryptBnQwNeRsaPubCrypt_entry(pointer_t<uint64_t> qw_a,
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pointer_t<uint64_t> qw_b,
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pointer_t<XECRYPT_RSA> rsa) {
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// 0 indicates failure (but not a BOOL return value)
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#ifndef XE_PLATFORM_WIN32
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XELOGE(
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"XeCryptBnQwNeRsaPubCrypt called but no implementation available for "
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"this platform!");
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assert_always();
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return 1;
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#else
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uint32_t modulus_size = rsa->size * 8;
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uint32_t num_qwords = rsa->size;
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uint32_t exponent = rsa->public_exponent;
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const uint8_t* input_bytes = reinterpret_cast<const uint8_t*>(&qw_a[0]);
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uint8_t* output_bytes = reinterpret_cast<uint8_t*>(&qw_b[0]);
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const uint8_t* mod_bytes =
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reinterpret_cast<const uint8_t*>(&rsa[1]); // modulus follows header
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// Convert XECRYPT blob into BCrypt format
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ULONG key_size = sizeof(BCRYPT_RSAKEY_BLOB) + sizeof(uint32_t) + modulus_size;
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auto key_buf = std::make_unique<uint8_t[]>(key_size);
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auto* key_header = reinterpret_cast<BCRYPT_RSAKEY_BLOB*>(key_buf.get());
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key_header->Magic = BCRYPT_RSAPUBLIC_MAGIC;
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key_header->BitLength = modulus_size * 8;
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key_header->cbPublicExp = sizeof(uint32_t);
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key_header->cbModulus = modulus_size;
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key_header->cbPrime1 = key_header->cbPrime2 = 0;
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// Copy in exponent/modulus, luckily these are BE inside BCrypt blob
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uint32_t* key_exponent = reinterpret_cast<uint32_t*>(&key_header[1]);
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*key_exponent = rsa->public_exponent.value;
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// ...except modulus needs to be reversed in 64-bit chunks for BCrypt to make
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// use of it properly for some reason
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uint64_t* key_modulus = reinterpret_cast<uint64_t*>(&key_exponent[1]);
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uint64_t* xecrypt_modulus = reinterpret_cast<uint64_t*>(&rsa[1]);
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std::reverse_copy(xecrypt_modulus, xecrypt_modulus + rsa->size, key_modulus);
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BCRYPT_ALG_HANDLE hAlgorithm = NULL;
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NTSTATUS status = BCryptOpenAlgorithmProvider(
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&hAlgorithm, BCRYPT_RSA_ALGORITHM, MS_PRIMITIVE_PROVIDER, 0);
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if (!BCRYPT_SUCCESS(status)) {
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XELOGE(
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"XeCryptBnQwNeRsaPubCrypt: BCryptOpenAlgorithmProvider failed with "
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"status {:#X}!",
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status);
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return 0;
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}
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BCRYPT_KEY_HANDLE hKey = NULL;
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status = BCryptImportKeyPair(hAlgorithm, NULL, BCRYPT_RSAPUBLIC_BLOB, &hKey,
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key_buf.get(), key_size, 0);
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if (!BCRYPT_SUCCESS(status)) {
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XELOGE(
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"XeCryptBnQwNeRsaPubCrypt: BCryptImportKeyPair failed with status "
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"{:#X}!",
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status);
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if (hAlgorithm) {
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BCryptCloseAlgorithmProvider(hAlgorithm, 0);
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}
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return 0;
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}
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// Byteswap & reverse the input into output, as BCrypt wants MSB first
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uint64_t* output = qw_b;
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uint8_t* output_bytes = reinterpret_cast<uint8_t*>(output);
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xe::copy_and_swap<uint64_t>(output, qw_a, rsa->size);
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std::reverse(output_bytes, output_bytes + modulus_size);
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// BCryptDecrypt only works with private keys, fortunately BCryptEncrypt
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// performs the right actions needed for us to decrypt the input
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ULONG result_size = 0;
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status =
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BCryptEncrypt(hKey, output_bytes, modulus_size, nullptr, nullptr, 0,
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output_bytes, modulus_size, &result_size, BCRYPT_PAD_NONE);
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assert(result_size == modulus_size);
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if (!BCRYPT_SUCCESS(status)) {
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XELOGE("XeCryptBnQwNeRsaPubCrypt: BCryptEncrypt failed with status {:#X}!",
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status);
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} else {
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// Reverse data & byteswap again so data is as game expects
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std::reverse(output_bytes, output_bytes + modulus_size);
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xe::copy_and_swap(output, output, rsa->size);
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}
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if (hKey) {
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BCryptDestroyKey(hKey);
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}
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if (hAlgorithm) {
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BCryptCloseAlgorithmProvider(hAlgorithm, 0);
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}
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return BCRYPT_SUCCESS(status) ? 1 : 0;
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#endif
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return XeCryptBnQwNeRsaPubCrypt(input_bytes, output_bytes, mod_bytes,
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num_qwords, exponent);
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}
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#ifdef XE_PLATFORM_WIN32
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DECLARE_XBOXKRNL_EXPORT1(XeCryptBnQwNeRsaPubCrypt, kNone, kImplemented);
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#else
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DECLARE_XBOXKRNL_EXPORT1(XeCryptBnQwNeRsaPubCrypt, kNone, kStub);
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#endif
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dword_result_t XeCryptBnQwBeSigVerify_entry(pointer_t<XECRYPT_SIG> sig,
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lpvoid_t hash, lpstring_t salt,
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430
src/xenia/kernel/xboxkrnl/xecrypt_rsa.h
Normal file
430
src/xenia/kernel/xboxkrnl/xecrypt_rsa.h
Normal file
@@ -0,0 +1,430 @@
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#ifndef XECRYPT_RSA_H_
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#define XECRYPT_RSA_H_
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#include <algorithm>
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#include <cstdint>
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#include <cstring>
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#include <vector>
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namespace xecrypt {
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namespace bignum {
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// Portable 128-bit unsigned helpers using only 64-bit arithmetic
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struct u128 {
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uint64_t lo;
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uint64_t hi;
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};
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static inline u128 u128_from(uint64_t v) { return {v, 0}; }
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static inline u128 u128_add(u128 a, uint64_t b) {
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u128 r;
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r.lo = a.lo + b;
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r.hi = a.hi + (r.lo < a.lo ? 1 : 0);
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return r;
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}
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static inline u128 u128_sub(u128 a, uint64_t b) {
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u128 r;
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r.hi = a.hi - (a.lo < b ? 1 : 0);
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r.lo = a.lo - b;
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return r;
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}
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static inline u128 u128_shl(u128 v, int s) {
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if (s == 0) return v;
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if (s >= 64) return {0, v.lo << (s - 64)};
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return {v.lo << s, (v.hi << s) | (v.lo >> (64 - s))};
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}
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static inline u128 u128_shr(u128 v, int s) {
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if (s == 0) return v;
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if (s >= 64) return {v.hi >> (s - 64), 0};
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return {(v.lo >> s) | (v.hi << (64 - s)), v.hi >> s};
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}
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static inline u128 u128_or64(u128 a, uint64_t b) { return {a.lo | b, a.hi}; }
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// Portable 64x64 -> 128 multiply
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static inline u128 u128_mul64(uint64_t a, uint64_t b) {
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uint64_t a_lo = a & 0xFFFFFFFF;
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uint64_t a_hi = a >> 32;
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uint64_t b_lo = b & 0xFFFFFFFF;
|
||||
uint64_t b_hi = b >> 32;
|
||||
|
||||
uint64_t p0 = a_lo * b_lo;
|
||||
uint64_t p1 = a_lo * b_hi;
|
||||
uint64_t p2 = a_hi * b_lo;
|
||||
uint64_t p3 = a_hi * b_hi;
|
||||
|
||||
uint64_t mid = p1 + (p0 >> 32);
|
||||
uint64_t mid_carry = 0;
|
||||
uint64_t mid2 = mid + p2;
|
||||
if (mid < p1) mid_carry++;
|
||||
if (mid2 < mid) mid_carry++;
|
||||
|
||||
u128 r;
|
||||
r.lo = (mid2 << 32) | (p0 & 0xFFFFFFFF);
|
||||
r.hi = p3 + (mid2 >> 32) + (mid_carry << 32);
|
||||
return r;
|
||||
}
|
||||
|
||||
// 128 / 64 -> quotient and remainder
|
||||
static inline uint64_t u128_div64(u128 num, uint64_t den, uint64_t* rem) {
|
||||
if (num.hi == 0) {
|
||||
*rem = num.lo % den;
|
||||
return num.lo / den;
|
||||
}
|
||||
|
||||
uint64_t q = 0;
|
||||
uint64_t r = 0;
|
||||
for (int i = 127; i >= 0; i--) {
|
||||
r = (r << 1);
|
||||
if (i >= 64) {
|
||||
r |= (num.hi >> (i - 64)) & 1;
|
||||
} else {
|
||||
r |= (num.lo >> i) & 1;
|
||||
}
|
||||
if (r >= den) {
|
||||
r -= den;
|
||||
if (i < 64) {
|
||||
q |= (1ULL << i);
|
||||
}
|
||||
}
|
||||
}
|
||||
*rem = r;
|
||||
return q;
|
||||
}
|
||||
|
||||
// Count leading zeros - portable
|
||||
static inline int clz64(uint64_t v) {
|
||||
if (v == 0) return 64;
|
||||
int n = 0;
|
||||
if ((v & 0xFFFFFFFF00000000ULL) == 0) {
|
||||
n += 32;
|
||||
v <<= 32;
|
||||
}
|
||||
if ((v & 0xFFFF000000000000ULL) == 0) {
|
||||
n += 16;
|
||||
v <<= 16;
|
||||
}
|
||||
if ((v & 0xFF00000000000000ULL) == 0) {
|
||||
n += 8;
|
||||
v <<= 8;
|
||||
}
|
||||
if ((v & 0xF000000000000000ULL) == 0) {
|
||||
n += 4;
|
||||
v <<= 4;
|
||||
}
|
||||
if ((v & 0xC000000000000000ULL) == 0) {
|
||||
n += 2;
|
||||
v <<= 2;
|
||||
}
|
||||
if ((v & 0x8000000000000000ULL) == 0) {
|
||||
n += 1;
|
||||
}
|
||||
return n;
|
||||
}
|
||||
|
||||
static inline int clz32(uint32_t v) {
|
||||
if (v == 0) return 32;
|
||||
int n = 0;
|
||||
if ((v & 0xFFFF0000U) == 0) {
|
||||
n += 16;
|
||||
v <<= 16;
|
||||
}
|
||||
if ((v & 0xFF000000U) == 0) {
|
||||
n += 8;
|
||||
v <<= 8;
|
||||
}
|
||||
if ((v & 0xF0000000U) == 0) {
|
||||
n += 4;
|
||||
v <<= 4;
|
||||
}
|
||||
if ((v & 0xC0000000U) == 0) {
|
||||
n += 2;
|
||||
v <<= 2;
|
||||
}
|
||||
if ((v & 0x80000000U) == 0) {
|
||||
n += 1;
|
||||
}
|
||||
return n;
|
||||
}
|
||||
|
||||
class BigNum {
|
||||
public:
|
||||
std::vector<uint64_t> limbs;
|
||||
|
||||
BigNum() = default;
|
||||
|
||||
void trim() {
|
||||
while (limbs.size() > 1 && limbs.back() == 0) {
|
||||
limbs.pop_back();
|
||||
}
|
||||
}
|
||||
|
||||
static BigNum from_bytes_be(const uint8_t* data, size_t len) {
|
||||
BigNum r;
|
||||
size_t n = (len + 7) / 8;
|
||||
r.limbs.resize(n, 0);
|
||||
for (size_t i = 0; i < len; i++) {
|
||||
size_t byte_pos = len - 1 - i;
|
||||
r.limbs[byte_pos / 8] |= static_cast<uint64_t>(data[i])
|
||||
<< (8 * (byte_pos % 8));
|
||||
}
|
||||
r.trim();
|
||||
return r;
|
||||
}
|
||||
|
||||
void to_bytes_be(uint8_t* out, size_t len) const {
|
||||
std::memset(out, 0, len);
|
||||
for (size_t i = 0; i < len; i++) {
|
||||
size_t byte_pos = len - 1 - i;
|
||||
size_t li = byte_pos / 8;
|
||||
if (li < limbs.size()) {
|
||||
out[i] = static_cast<uint8_t>(limbs[li] >> (8 * (byte_pos % 8)));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
static int compare(const BigNum& a, const BigNum& b) {
|
||||
size_t an = a.limbs.size(), bn = b.limbs.size();
|
||||
size_t n = std::max(an, bn);
|
||||
for (size_t i = n; i > 0; i--) {
|
||||
uint64_t al = (i - 1 < an) ? a.limbs[i - 1] : 0;
|
||||
uint64_t bl = (i - 1 < bn) ? b.limbs[i - 1] : 0;
|
||||
if (al < bl) return -1;
|
||||
if (al > bl) return 1;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
static BigNum sub(const BigNum& a, const BigNum& b) {
|
||||
BigNum r;
|
||||
size_t n = a.limbs.size();
|
||||
r.limbs.resize(n, 0);
|
||||
uint64_t borrow = 0;
|
||||
for (size_t i = 0; i < n; i++) {
|
||||
uint64_t bl = (i < b.limbs.size()) ? b.limbs[i] : 0;
|
||||
u128 diff = u128_sub(u128_sub(u128_from(a.limbs[i]), bl), borrow);
|
||||
r.limbs[i] = diff.lo;
|
||||
borrow = (diff.hi >> 63) ? 1 : 0;
|
||||
}
|
||||
r.trim();
|
||||
return r;
|
||||
}
|
||||
|
||||
static BigNum mul(const BigNum& a, const BigNum& b) {
|
||||
size_t an = a.limbs.size(), bn = b.limbs.size();
|
||||
BigNum r;
|
||||
r.limbs.resize(an + bn, 0);
|
||||
for (size_t i = 0; i < an; i++) {
|
||||
uint64_t carry = 0;
|
||||
for (size_t j = 0; j < bn; j++) {
|
||||
u128 prod = u128_mul64(a.limbs[i], b.limbs[j]);
|
||||
prod = u128_add(prod, r.limbs[i + j]);
|
||||
prod = u128_add(prod, carry);
|
||||
r.limbs[i + j] = prod.lo;
|
||||
carry = prod.hi;
|
||||
}
|
||||
r.limbs[i + bn] += carry;
|
||||
}
|
||||
r.trim();
|
||||
return r;
|
||||
}
|
||||
|
||||
static BigNum mod(const BigNum& a, const BigNum& m) {
|
||||
if (compare(a, m) < 0) return a;
|
||||
|
||||
size_t n = m.limbs.size();
|
||||
size_t total = a.limbs.size();
|
||||
|
||||
if (n == 0 || (n == 1 && m.limbs[0] == 0)) {
|
||||
return BigNum();
|
||||
}
|
||||
|
||||
if (n == 1) {
|
||||
uint64_t d = m.limbs[0];
|
||||
uint64_t rem = 0;
|
||||
for (size_t i = total; i > 0; i--) {
|
||||
u128 cur = u128_or64(u128_shl(u128_from(rem), 64), a.limbs[i - 1]);
|
||||
u128_div64(cur, d, &rem);
|
||||
}
|
||||
BigNum r;
|
||||
r.limbs = {rem};
|
||||
r.trim();
|
||||
return r;
|
||||
}
|
||||
|
||||
int shift = 0;
|
||||
uint64_t top = m.limbs[n - 1];
|
||||
if (top != 0) {
|
||||
shift = clz64(top);
|
||||
}
|
||||
|
||||
BigNum u, v;
|
||||
u.limbs.resize(total + 1, 0);
|
||||
if (shift > 0) {
|
||||
uint64_t carry = 0;
|
||||
for (size_t i = 0; i < total; i++) {
|
||||
u128 val = u128_or64(u128_shl(u128_from(a.limbs[i]), shift), carry);
|
||||
u.limbs[i] = val.lo;
|
||||
carry = val.hi;
|
||||
}
|
||||
u.limbs[total] = carry;
|
||||
} else {
|
||||
for (size_t i = 0; i < total; i++) u.limbs[i] = a.limbs[i];
|
||||
u.limbs[total] = 0;
|
||||
}
|
||||
|
||||
v.limbs.resize(n, 0);
|
||||
if (shift > 0) {
|
||||
uint64_t carry = 0;
|
||||
for (size_t i = 0; i < n; i++) {
|
||||
u128 val = u128_or64(u128_shl(u128_from(m.limbs[i]), shift), carry);
|
||||
v.limbs[i] = val.lo;
|
||||
carry = val.hi;
|
||||
}
|
||||
} else {
|
||||
v.limbs = m.limbs;
|
||||
}
|
||||
|
||||
uint64_t vn_1 = v.limbs[n - 1];
|
||||
uint64_t vn_2 = (n >= 2) ? v.limbs[n - 2] : 0;
|
||||
|
||||
for (size_t j = total; j >= n; j--) {
|
||||
u128 num_top =
|
||||
u128_or64(u128_shl(u128_from(u.limbs[j]), 64), u.limbs[j - 1]);
|
||||
uint64_t rhat_val;
|
||||
uint64_t qhat_val = u128_div64(num_top, vn_1, &rhat_val);
|
||||
|
||||
while (true) {
|
||||
u128 qv2 = u128_mul64(qhat_val, vn_2);
|
||||
u128 rhs = u128_or64(u128_shl(u128_from(rhat_val), 64), u.limbs[j - 2]);
|
||||
bool gt = (qv2.hi > rhs.hi) || (qv2.hi == rhs.hi && qv2.lo > rhs.lo);
|
||||
if (!gt) break;
|
||||
qhat_val--;
|
||||
uint64_t old_rhat = rhat_val;
|
||||
rhat_val += vn_1;
|
||||
if (rhat_val < old_rhat) break;
|
||||
}
|
||||
|
||||
uint64_t carry = 0;
|
||||
for (size_t i = 0; i < n; i++) {
|
||||
u128 prod = u128_mul64(qhat_val, v.limbs[i]);
|
||||
prod = u128_add(prod, carry);
|
||||
uint64_t prod_lo = prod.lo;
|
||||
carry = prod.hi;
|
||||
uint64_t u_val = u.limbs[j - n + i];
|
||||
u.limbs[j - n + i] = u_val - prod_lo;
|
||||
if (u_val < prod_lo) carry++;
|
||||
}
|
||||
int64_t final_diff =
|
||||
static_cast<int64_t>(u.limbs[j]) - static_cast<int64_t>(carry);
|
||||
u.limbs[j] = static_cast<uint64_t>(final_diff);
|
||||
|
||||
if (final_diff < 0) {
|
||||
uint64_t c = 0;
|
||||
for (size_t i = 0; i < n; i++) {
|
||||
u128 sum = u128_add(u128_from(u.limbs[j - n + i]), v.limbs[i]);
|
||||
sum = u128_add(sum, c);
|
||||
u.limbs[j - n + i] = sum.lo;
|
||||
c = sum.hi;
|
||||
}
|
||||
u.limbs[j] += c;
|
||||
}
|
||||
}
|
||||
|
||||
BigNum r;
|
||||
r.limbs.resize(n, 0);
|
||||
if (shift > 0) {
|
||||
uint64_t carry = 0;
|
||||
for (size_t i = n; i > 0; i--) {
|
||||
u128 val = u128_or64(u128_shl(u128_from(carry), 64), u.limbs[i - 1]);
|
||||
r.limbs[i - 1] = u128_shr(val, shift).lo;
|
||||
carry = u.limbs[i - 1] & ((1ULL << shift) - 1);
|
||||
}
|
||||
} else {
|
||||
for (size_t i = 0; i < n; i++) r.limbs[i] = u.limbs[i];
|
||||
}
|
||||
|
||||
r.trim();
|
||||
return r;
|
||||
}
|
||||
|
||||
static BigNum modexp(const BigNum& base, uint32_t exp,
|
||||
const BigNum& mod_val) {
|
||||
BigNum result;
|
||||
result.limbs = {1};
|
||||
|
||||
if (exp == 0) {
|
||||
return mod(result, mod_val);
|
||||
}
|
||||
|
||||
int highest_bit = 31 - clz32(exp);
|
||||
BigNum b = mod(base, mod_val);
|
||||
|
||||
for (int i = highest_bit; i >= 0; i--) {
|
||||
result = mod(mul(result, result), mod_val);
|
||||
if ((exp >> i) & 1) {
|
||||
result = mod(mul(result, b), mod_val);
|
||||
}
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace bignum
|
||||
} // namespace xecrypt
|
||||
|
||||
// Performs RSA public-key encryption/decryption matching
|
||||
// XeCryptBnQwNeRsaPubCrypt. All buffers use the Xbox 360 layout: big-endian
|
||||
// uint64 limbs in little-endian limb order.
|
||||
//
|
||||
// qw_a: input data (num_qwords * 8 bytes)
|
||||
// qw_b: output buffer (num_qwords * 8 bytes)
|
||||
// modulus: RSA modulus following the XECRYPT_RSA header (num_qwords * 8 bytes)
|
||||
// num_qwords: number of 64-bit limbs
|
||||
// exponent: public exponent
|
||||
//
|
||||
// Returns 1 on success, 0 on failure.
|
||||
inline uint32_t XeCryptBnQwNeRsaPubCrypt(const uint8_t* qw_a, uint8_t* qw_b,
|
||||
const uint8_t* modulus,
|
||||
uint32_t num_qwords,
|
||||
uint32_t exponent) {
|
||||
// Reject keys below 512 bits (8 qwords) to match original BCrypt behavior.
|
||||
if (num_qwords < 8) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
uint32_t modulus_size = num_qwords * 8;
|
||||
|
||||
auto input_be = std::vector<uint8_t>(modulus_size);
|
||||
auto mod_be = std::vector<uint8_t>(modulus_size);
|
||||
|
||||
// Reverse qword order to produce big-endian byte arrays
|
||||
for (uint32_t i = 0; i < num_qwords; i++) {
|
||||
std::memcpy(&input_be[i * 8], &qw_a[(num_qwords - 1 - i) * 8], 8);
|
||||
std::memcpy(&mod_be[i * 8], &modulus[(num_qwords - 1 - i) * 8], 8);
|
||||
}
|
||||
|
||||
auto base =
|
||||
xecrypt::bignum::BigNum::from_bytes_be(input_be.data(), modulus_size);
|
||||
auto mod =
|
||||
xecrypt::bignum::BigNum::from_bytes_be(mod_be.data(), modulus_size);
|
||||
|
||||
auto result = xecrypt::bignum::BigNum::modexp(base, exponent, mod);
|
||||
|
||||
auto result_be = std::vector<uint8_t>(modulus_size);
|
||||
result.to_bytes_be(result_be.data(), modulus_size);
|
||||
|
||||
// Convert back to Xbox format: reverse qword order
|
||||
for (uint32_t i = 0; i < num_qwords; i++) {
|
||||
std::memcpy(&qw_b[i * 8], &result_be[(num_qwords - 1 - i) * 8], 8);
|
||||
}
|
||||
|
||||
return 1;
|
||||
}
|
||||
|
||||
#endif // XECRYPT_RSA_H_
|
||||
Reference in New Issue
Block a user