/* * RTSS (threshold secret sharing) * (C) 2009 Jack Lloyd * * Distributed under the terms of the Botan license */ #include #include #include #include #include #include #include namespace Botan { namespace { /** Table for GF(2^8) arithmetic (exponentials) */ const byte EXP[256] = { 0x01, 0x03, 0x05, 0x0F, 0x11, 0x33, 0x55, 0xFF, 0x1A, 0x2E, 0x72, 0x96, 0xA1, 0xF8, 0x13, 0x35, 0x5F, 0xE1, 0x38, 0x48, 0xD8, 0x73, 0x95, 0xA4, 0xF7, 0x02, 0x06, 0x0A, 0x1E, 0x22, 0x66, 0xAA, 0xE5, 0x34, 0x5C, 0xE4, 0x37, 0x59, 0xEB, 0x26, 0x6A, 0xBE, 0xD9, 0x70, 0x90, 0xAB, 0xE6, 0x31, 0x53, 0xF5, 0x04, 0x0C, 0x14, 0x3C, 0x44, 0xCC, 0x4F, 0xD1, 0x68, 0xB8, 0xD3, 0x6E, 0xB2, 0xCD, 0x4C, 0xD4, 0x67, 0xA9, 0xE0, 0x3B, 0x4D, 0xD7, 0x62, 0xA6, 0xF1, 0x08, 0x18, 0x28, 0x78, 0x88, 0x83, 0x9E, 0xB9, 0xD0, 0x6B, 0xBD, 0xDC, 0x7F, 0x81, 0x98, 0xB3, 0xCE, 0x49, 0xDB, 0x76, 0x9A, 0xB5, 0xC4, 0x57, 0xF9, 0x10, 0x30, 0x50, 0xF0, 0x0B, 0x1D, 0x27, 0x69, 0xBB, 0xD6, 0x61, 0xA3, 0xFE, 0x19, 0x2B, 0x7D, 0x87, 0x92, 0xAD, 0xEC, 0x2F, 0x71, 0x93, 0xAE, 0xE9, 0x20, 0x60, 0xA0, 0xFB, 0x16, 0x3A, 0x4E, 0xD2, 0x6D, 0xB7, 0xC2, 0x5D, 0xE7, 0x32, 0x56, 0xFA, 0x15, 0x3F, 0x41, 0xC3, 0x5E, 0xE2, 0x3D, 0x47, 0xC9, 0x40, 0xC0, 0x5B, 0xED, 0x2C, 0x74, 0x9C, 0xBF, 0xDA, 0x75, 0x9F, 0xBA, 0xD5, 0x64, 0xAC, 0xEF, 0x2A, 0x7E, 0x82, 0x9D, 0xBC, 0xDF, 0x7A, 0x8E, 0x89, 0x80, 0x9B, 0xB6, 0xC1, 0x58, 0xE8, 0x23, 0x65, 0xAF, 0xEA, 0x25, 0x6F, 0xB1, 0xC8, 0x43, 0xC5, 0x54, 0xFC, 0x1F, 0x21, 0x63, 0xA5, 0xF4, 0x07, 0x09, 0x1B, 0x2D, 0x77, 0x99, 0xB0, 0xCB, 0x46, 0xCA, 0x45, 0xCF, 0x4A, 0xDE, 0x79, 0x8B, 0x86, 0x91, 0xA8, 0xE3, 0x3E, 0x42, 0xC6, 0x51, 0xF3, 0x0E, 0x12, 0x36, 0x5A, 0xEE, 0x29, 0x7B, 0x8D, 0x8C, 0x8F, 0x8A, 0x85, 0x94, 0xA7, 0xF2, 0x0D, 0x17, 0x39, 0x4B, 0xDD, 0x7C, 0x84, 0x97, 0xA2, 0xFD, 0x1C, 0x24, 0x6C, 0xB4, 0xC7, 0x52, 0xF6, 0x01 }; /** Table for GF(2^8) arithmetic (logarithms) */ const byte LOG[] = { 0x90, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1A, 0xC6, 0x4B, 0xC7, 0x1B, 0x68, 0x33, 0xEE, 0xDF, 0x03, 0x64, 0x04, 0xE0, 0x0E, 0x34, 0x8D, 0x81, 0xEF, 0x4C, 0x71, 0x08, 0xC8, 0xF8, 0x69, 0x1C, 0xC1, 0x7D, 0xC2, 0x1D, 0xB5, 0xF9, 0xB9, 0x27, 0x6A, 0x4D, 0xE4, 0xA6, 0x72, 0x9A, 0xC9, 0x09, 0x78, 0x65, 0x2F, 0x8A, 0x05, 0x21, 0x0F, 0xE1, 0x24, 0x12, 0xF0, 0x82, 0x45, 0x35, 0x93, 0xDA, 0x8E, 0x96, 0x8F, 0xDB, 0xBD, 0x36, 0xD0, 0xCE, 0x94, 0x13, 0x5C, 0xD2, 0xF1, 0x40, 0x46, 0x83, 0x38, 0x66, 0xDD, 0xFD, 0x30, 0xBF, 0x06, 0x8B, 0x62, 0xB3, 0x25, 0xE2, 0x98, 0x22, 0x88, 0x91, 0x10, 0x7E, 0x6E, 0x48, 0xC3, 0xA3, 0xB6, 0x1E, 0x42, 0x3A, 0x6B, 0x28, 0x54, 0xFA, 0x85, 0x3D, 0xBA, 0x2B, 0x79, 0x0A, 0x15, 0x9B, 0x9F, 0x5E, 0xCA, 0x4E, 0xD4, 0xAC, 0xE5, 0xF3, 0x73, 0xA7, 0x57, 0xAF, 0x58, 0xA8, 0x50, 0xF4, 0xEA, 0xD6, 0x74, 0x4F, 0xAE, 0xE9, 0xD5, 0xE7, 0xE6, 0xAD, 0xE8, 0x2C, 0xD7, 0x75, 0x7A, 0xEB, 0x16, 0x0B, 0xF5, 0x59, 0xCB, 0x5F, 0xB0, 0x9C, 0xA9, 0x51, 0xA0, 0x7F, 0x0C, 0xF6, 0x6F, 0x17, 0xC4, 0x49, 0xEC, 0xD8, 0x43, 0x1F, 0x2D, 0xA4, 0x76, 0x7B, 0xB7, 0xCC, 0xBB, 0x3E, 0x5A, 0xFB, 0x60, 0xB1, 0x86, 0x3B, 0x52, 0xA1, 0x6C, 0xAA, 0x55, 0x29, 0x9D, 0x97, 0xB2, 0x87, 0x90, 0x61, 0xBE, 0xDC, 0xFC, 0xBC, 0x95, 0xCF, 0xCD, 0x37, 0x3F, 0x5B, 0xD1, 0x53, 0x39, 0x84, 0x3C, 0x41, 0xA2, 0x6D, 0x47, 0x14, 0x2A, 0x9E, 0x5D, 0x56, 0xF2, 0xD3, 0xAB, 0x44, 0x11, 0x92, 0xD9, 0x23, 0x20, 0x2E, 0x89, 0xB4, 0x7C, 0xB8, 0x26, 0x77, 0x99, 0xE3, 0xA5, 0x67, 0x4A, 0xED, 0xDE, 0xC5, 0x31, 0xFE, 0x18, 0x0D, 0x63, 0x8C, 0x80, 0xC0, 0xF7, 0x70, 0x07 }; byte gfp_mul(byte x, byte y) { if(x == 0 || y == 0) return 0; return EXP[(LOG[x] + LOG[y]) % 255]; } byte rtss_hash_id(const std::string& hash_name) { if(hash_name == "SHA-160") return 1; else if(hash_name == "SHA-256") return 2; else throw Invalid_Argument("RTSS only supports SHA-1 and SHA-256"); } HashFunction* get_rtss_hash_by_id(byte id) { if(id == 1) return new SHA_160; else if(id == 2) return new SHA_256; else throw Decoding_Error("Bad RTSS hash identifier"); } } RTSS_Share::RTSS_Share(const std::string& hex_input) { contents = hex_decode(hex_input); } byte RTSS_Share::share_id() const { if(!initialized()) throw Invalid_State("RTSS_Share::share_id not initialized"); return contents[20]; } std::string RTSS_Share::to_string() const { return hex_encode(&contents[0], contents.size()); } std::vector RTSS_Share::split(byte M, byte N, const byte S[], u16bit S_len, const byte identifier[16], RandomNumberGenerator& rng) { if(M == 0 || N == 0 || M > N) throw Encoding_Error("RTSS_Share::split: M == 0 or N == 0 or M > N"); SHA_256 hash; // always use SHA-256 when generating shares std::vector shares(N); // Create RTSS header in each share for(byte i = 0; i != N; ++i) { shares[i].contents += std::make_pair(identifier, 16); shares[i].contents += rtss_hash_id(hash.name()); shares[i].contents += M; shares[i].contents += get_byte(0, S_len); shares[i].contents += get_byte(1, S_len); } // Choose sequential values for X starting from 1 for(byte i = 0; i != N; ++i) shares[i].contents.push_back(i+1); // secret = S || H(S) SecureVector secret(S, S_len); secret += hash.process(S, S_len); for(size_t i = 0; i != secret.size(); ++i) { std::vector coefficients(M-1); rng.randomize(&coefficients[0], coefficients.size()); for(byte j = 0; j != N; ++j) { const byte X = j + 1; byte sum = secret[i]; byte X_i = X; for(size_t k = 0; k != coefficients.size(); ++k) { sum ^= gfp_mul(X_i, coefficients[k]); X_i = gfp_mul(X_i, X); } shares[j].contents.push_back(sum); } } return shares; } SecureVector RTSS_Share::reconstruct(const std::vector& shares) { const size_t RTSS_HEADER_SIZE = 20; for(size_t i = 0; i != shares.size(); ++i) { if(shares[i].size() != shares[0].size()) throw Decoding_Error("Different sized RTSS shares detected"); if(shares[i].share_id() == 0) throw Decoding_Error("Invalid (id = 0) RTSS share detected"); if(shares[i].size() < RTSS_HEADER_SIZE) throw Decoding_Error("Missing or malformed RTSS header"); if(!same_mem(&shares[0].contents[0], &shares[i].contents[0], RTSS_HEADER_SIZE)) throw Decoding_Error("Different RTSS headers detected"); } if(shares.size() < shares[0].contents[17]) throw Decoding_Error("Insufficient shares to do TSS reconstruction"); u16bit secret_len = make_u16bit(shares[0].contents[18], shares[0].contents[19]); byte hash_id = shares[0].contents[16]; std::unique_ptr hash(get_rtss_hash_by_id(hash_id)); if(shares[0].size() != secret_len + hash->output_length() + RTSS_HEADER_SIZE + 1) throw Decoding_Error("Bad RTSS length field in header"); std::vector V(shares.size()); SecureVector secret; for(size_t i = RTSS_HEADER_SIZE + 1; i != shares[0].size(); ++i) { for(size_t j = 0; j != V.size(); ++j) V[j] = shares[j].contents[i]; byte r = 0; for(size_t k = 0; k != shares.size(); ++k) { // L_i function: byte r2 = 1; for(size_t l = 0; l != shares.size(); ++l) { if(k == l) continue; byte share_k = shares[k].share_id(); byte share_l = shares[l].share_id(); if(share_k == share_l) throw Decoding_Error("Duplicate shares found in RTSS recovery"); byte div = EXP[(255 + LOG[share_l] - LOG[share_k ^ share_l]) % 255]; r2 = gfp_mul(r2, div); } r ^= gfp_mul(V[k], r2); } secret.push_back(r); } if(secret.size() != secret_len + hash->output_length()) throw Decoding_Error("Bad length in RTSS output"); hash->update(&secret[0], secret_len); SecureVector hash_check = hash->final(); if(!same_mem(&hash_check[0], &secret[secret_len], hash->output_length())) throw Decoding_Error("RTSS hash check failed"); return SecureVector(&secret[0], secret_len); } }