// Copyright (c) 2009-2010 Satoshi Nakamoto // Copyright (c) 2009-2012 The Bitcoin developers // Distributed under the MIT/X11 software license, see the accompanying // file COPYING or http://www.opensource.org/licenses/mit-license.php. #ifndef BITCOIN_BIGNUM_H #define BITCOIN_BIGNUM_H #include #include #include #include "util.h" /** Errors thrown by the bignum class */ class bignum_error : public std::runtime_error { public: explicit bignum_error(const std::string& str) : std::runtime_error(str) {} }; /** RAII encapsulated BN_CTX (OpenSSL bignum context) */ class CAutoBN_CTX { protected: BN_CTX* pctx; BN_CTX* operator=(BN_CTX* pnew) { return pctx = pnew; } public: CAutoBN_CTX() { pctx = BN_CTX_new(); if (pctx == NULL) throw bignum_error("CAutoBN_CTX : BN_CTX_new() returned NULL"); } ~CAutoBN_CTX() { if (pctx != NULL) BN_CTX_free(pctx); } operator BN_CTX*() { return pctx; } BN_CTX& operator*() { return *pctx; } BN_CTX** operator&() { return &pctx; } bool operator!() { return (pctx == NULL); } }; /** C++ wrapper for BIGNUM (OpenSSL bignum) */ class CBigNum : public BIGNUM { public: CBigNum() { BN_init(this); } CBigNum(const CBigNum& b) { BN_init(this); if (!BN_copy(this, &b)) { BN_clear_free(this); throw bignum_error("CBigNum::CBigNum(const CBigNum&) : BN_copy failed"); } } CBigNum& operator=(const CBigNum& b) { if (!BN_copy(this, &b)) throw bignum_error("CBigNum::operator= : BN_copy failed"); return (*this); } ~CBigNum() { BN_clear_free(this); } CBigNum(int8_t n) { BN_init(this); if (n >= 0) setuint32(n); else setint64(n); } CBigNum(int16_t n) { BN_init(this); if (n >= 0) setuint32(n); else setint64(n); } CBigNum(int32_t n) { BN_init(this); if (n >= 0) setuint32(n); else setint64(n); } CBigNum(int64_t n) { BN_init(this); if (n >= 0) setuint64(n); else setint64(n); } CBigNum(uint8_t n) { BN_init(this); setuint32(n); } CBigNum(uint16_t n) { BN_init(this); setuint32(n); } CBigNum(uint32_t n) { BN_init(this); setuint32(n); } CBigNum(uint64_t n) { BN_init(this); setuint64(n); } explicit CBigNum(uint256 n) { BN_init(this); setuint256(n); } explicit CBigNum(const std::vector& vch) { BN_init(this); setvch(vch); } /** Generates a cryptographically secure random number between zero and range exclusive * i.e. 0 < returned number < range * @param range The upper bound on the number. * @return */ static CBigNum randBignum(const CBigNum& range) { CBigNum ret; if(!BN_rand_range(&ret, &range)){ throw bignum_error("CBigNum:rand element : BN_rand_range failed"); } return ret; } /** Generates a cryptographically secure random k-bit number * @param k The bit length of the number. * @return */ static CBigNum RandKBitBigum(const uint32_t k){ CBigNum ret; if(!BN_rand(&ret, k, -1, 0)){ throw bignum_error("CBigNum:rand element : BN_rand failed"); } return ret; } /**Returns the size in bits of the underlying bignum. * * @return the size */ int bitSize() const{ return BN_num_bits(this); } void setuint32(uint32_t n) { if (!BN_set_word(this, n)) throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed"); } uint32_t getuint32() const { return BN_get_word(this); } int32_t getint32() const { uint64_t n = BN_get_word(this); if (!BN_is_negative(this)) return (n > (uint64_t)std::numeric_limits::max() ? std::numeric_limits::max() : (int32_t)n); else return (n > (uint64_t)std::numeric_limits::max() ? std::numeric_limits::min() : -(int32_t)n); } void setint64(int64_t sn) { uint8_t pch[sizeof(sn) + 6]; uint8_t* p = pch + 4; bool fNegative; uint64_t n; if (sn < (int64_t)0) { // Since the minimum signed integer cannot be represented as positive so long as its type is signed, and it's not well-defined what happens if you make it unsigned before negating it, we instead increment the negative integer by 1, convert it, then increment the (now positive) unsigned integer by 1 to compensate n = -(sn + 1); ++n; fNegative = true; } else { n = sn; fNegative = false; } bool fLeadingZeroes = true; for (int i = 0; i < 8; i++) { uint8_t c = (n >> 56) & 0xff; n <<= 8; if (fLeadingZeroes) { if (c == 0) continue; if (c & 0x80) *p++ = (fNegative ? 0x80 : 0); else if (fNegative) c |= 0x80; fLeadingZeroes = false; } *p++ = c; } uint32_t nSize = (uint32_t) (p - (pch + 4)); pch[0] = (nSize >> 24) & 0xff; pch[1] = (nSize >> 16) & 0xff; pch[2] = (nSize >> 8) & 0xff; pch[3] = (nSize) & 0xff; BN_mpi2bn(pch, (int)(p - pch), this); } uint64_t getuint64() { size_t nSize = BN_bn2mpi(this, NULL); if (nSize < 4) return 0; std::vector vch(nSize); BN_bn2mpi(this, &vch[0]); if (vch.size() > 4) vch[4] &= 0x7f; uint64_t n = 0; for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--) ((uint8_t*)&n)[i] = vch[j]; return n; } void setuint64(uint64_t n) { // Use BN_set_word if word size is sufficient for uint64_t if (sizeof(n) <= sizeof(BN_ULONG)) { if (!BN_set_word(this, (BN_ULONG)n)) throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed"); return; } uint8_t pch[sizeof(n) + 6]; uint8_t* p = pch + 4; bool fLeadingZeroes = true; for (int i = 0; i < 8; i++) { uint8_t c = (n >> 56) & 0xff; n <<= 8; if (fLeadingZeroes) { if (c == 0) continue; if (c & 0x80) *p++ = 0; fLeadingZeroes = false; } *p++ = c; } uint32_t nSize = (uint32_t) (p - (pch + 4)); pch[0] = (nSize >> 24) & 0xff; pch[1] = (nSize >> 16) & 0xff; pch[2] = (nSize >> 8) & 0xff; pch[3] = (nSize) & 0xff; BN_mpi2bn(pch, (int)(p - pch), this); } void setuint160(uint160 n) { uint8_t pch[sizeof(n) + 6]; uint8_t* p = pch + 4; bool fLeadingZeroes = true; uint8_t* pbegin = (uint8_t*)&n; uint8_t* psrc = pbegin + sizeof(n); while (psrc != pbegin) { uint8_t c = *(--psrc); if (fLeadingZeroes) { if (c == 0) continue; if (c & 0x80) *p++ = 0; fLeadingZeroes = false; } *p++ = c; } uint32_t nSize = (uint32_t) (p - (pch + 4)); pch[0] = (nSize >> 24) & 0xff; pch[1] = (nSize >> 16) & 0xff; pch[2] = (nSize >> 8) & 0xff; pch[3] = (nSize >> 0) & 0xff; BN_mpi2bn(pch, (int) (p - pch), this); } uint160 getuint160() const { unsigned int nSize = BN_bn2mpi(this, NULL); if (nSize < 4) return 0; std::vector vch(nSize); BN_bn2mpi(this, &vch[0]); if (vch.size() > 4) vch[4] &= 0x7f; uint160 n = 0; for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--) ((uint8_t*)&n)[i] = vch[j]; return n; } void setuint256(uint256 n) { uint8_t pch[sizeof(n) + 6]; uint8_t* p = pch + 4; bool fLeadingZeroes = true; uint8_t* pbegin = (uint8_t*)&n; uint8_t* psrc = pbegin + sizeof(n); while (psrc != pbegin) { uint8_t c = *(--psrc); if (fLeadingZeroes) { if (c == 0) continue; if (c & 0x80) *p++ = 0; fLeadingZeroes = false; } *p++ = c; } uint32_t nSize = (uint32_t) (p - (pch + 4)); pch[0] = (nSize >> 24) & 0xff; pch[1] = (nSize >> 16) & 0xff; pch[2] = (nSize >> 8) & 0xff; pch[3] = (nSize >> 0) & 0xff; BN_mpi2bn(pch, (int) (p - pch), this); } uint256 getuint256() const { unsigned int nSize = BN_bn2mpi(this, NULL); if (nSize < 4) return 0; std::vector vch(nSize); BN_bn2mpi(this, &vch[0]); if (vch.size() > 4) vch[4] &= 0x7f; uint256 n = 0; for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--) ((uint8_t*)&n)[i] = vch[j]; return n; } void setBytes(const std::vector& vchBytes) { BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), this); } std::vector getBytes() const { int nBytes = BN_num_bytes(this); std::vector vchBytes(nBytes); int n = BN_bn2bin(this, &vchBytes[0]); if (n != nBytes) { throw bignum_error("CBigNum::getBytes : BN_bn2bin failed"); } return vchBytes; } void setvch(const std::vector& vch) { std::vector vch2(vch.size() + 4); uint32_t nSize = (uint32_t) vch.size(); // BIGNUM's byte stream format expects 4 bytes of // big endian size data info at the front vch2[0] = (nSize >> 24) & 0xff; vch2[1] = (nSize >> 16) & 0xff; vch2[2] = (nSize >> 8) & 0xff; vch2[3] = (nSize >> 0) & 0xff; // swap data to big endian reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4); BN_mpi2bn(&vch2[0], (int) vch2.size(), this); } std::vector getvch() const { unsigned int nSize = BN_bn2mpi(this, NULL); if (nSize <= 4) return std::vector(); std::vector vch(nSize); BN_bn2mpi(this, &vch[0]); vch.erase(vch.begin(), vch.begin() + 4); reverse(vch.begin(), vch.end()); return vch; } CBigNum& SetCompact(uint32_t nCompact) { uint32_t nSize = nCompact >> 24; std::vector vch(4 + nSize); vch[3] = nSize; if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff; if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff; if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff; BN_mpi2bn(&vch[0], (int) vch.size(), this); return *this; } uint32_t GetCompact() const { uint32_t nSize = BN_bn2mpi(this, NULL); std::vector vch(nSize); nSize -= 4; BN_bn2mpi(this, &vch[0]); uint32_t nCompact = nSize << 24; if (nSize >= 1) nCompact |= (vch[4] << 16); if (nSize >= 2) nCompact |= (vch[5] << 8); if (nSize >= 3) nCompact |= (vch[6] << 0); return nCompact; } void SetHex(const std::string& str) { // skip 0x const char* psz = str.c_str(); while (isspace(*psz)) psz++; bool fNegative = false; if (*psz == '-') { fNegative = true; psz++; } if (psz[0] == '0' && tolower(psz[1]) == 'x') psz += 2; while (isspace(*psz)) psz++; // hex string to bignum static const signed char phexdigit[256] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,1,2,3,4,5,6,7,8,9,0,0,0,0,0,0, 0,0xa,0xb,0xc,0xd,0xe,0xf,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0xa,0xb,0xc,0xd,0xe,0xf,0,0,0,0,0,0,0,0,0 }; *this = 0; while (isxdigit(*psz)) { *this <<= 4; int n = phexdigit[(uint8_t)*psz++]; *this += n; } if (fNegative) *this = 0 - *this; } std::string ToString(int nBase=10) const { CAutoBN_CTX pctx; CBigNum bnBase = nBase; CBigNum bn0 = 0; std::string str; CBigNum bn = *this; BN_set_negative(&bn, false); CBigNum dv; CBigNum rem; if (BN_cmp(&bn, &bn0) == 0) return "0"; while (BN_cmp(&bn, &bn0) > 0) { if (!BN_div(&dv, &rem, &bn, &bnBase, pctx)) throw bignum_error("CBigNum::ToString() : BN_div failed"); bn = dv; uint32_t c = rem.getuint32(); str += "0123456789abcdef"[c]; } if (BN_is_negative(this)) str += "-"; reverse(str.begin(), str.end()); return str; } std::string GetHex() const { return ToString(16); } unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const { return ::GetSerializeSize(getvch(), nType, nVersion); } template void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const { ::Serialize(s, getvch(), nType, nVersion); } template void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) { std::vector vch; ::Unserialize(s, vch, nType, nVersion); setvch(vch); } /** * exponentiation with an int. this^e * @param e the exponent as an int * @return */ CBigNum pow(const int e) const { return this->pow(CBigNum(e)); } /** * exponentiation this^e * @param e the exponent * @return */ CBigNum pow(const CBigNum& e) const { CAutoBN_CTX pctx; CBigNum ret; if (!BN_exp(&ret, this, &e, pctx)) throw bignum_error("CBigNum::pow : BN_exp failed"); return ret; } /** * modular multiplication: (this * b) mod m * @param b operand * @param m modulus */ CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const { CAutoBN_CTX pctx; CBigNum ret; if (!BN_mod_mul(&ret, this, &b, &m, pctx)) throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed"); return ret; } /** * modular exponentiation: this^e mod n * @param e exponent * @param m modulus */ CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const { CAutoBN_CTX pctx; CBigNum ret; if( e < 0){ // g^-x = (g^-1)^x CBigNum inv = this->inverse(m); CBigNum posE = e * -1; if (!BN_mod_exp(&ret, &inv, &posE, &m, pctx)) throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent"); }else if (!BN_mod_exp(&ret, this, &e, &m, pctx)) throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed"); return ret; } /** * Calculates the inverse of this element mod m. * i.e. i such this*i = 1 mod m * @param m the modu * @return the inverse */ CBigNum inverse(const CBigNum& m) const { CAutoBN_CTX pctx; CBigNum ret; if (!BN_mod_inverse(&ret, this, &m, pctx)) throw bignum_error("CBigNum::inverse*= :BN_mod_inverse"); return ret; } /** * Generates a random (safe) prime of numBits bits * @param numBits the number of bits * @param safe true for a safe prime * @return the prime */ static CBigNum generatePrime(const unsigned int numBits, bool safe = false) { CBigNum ret; if(!BN_generate_prime_ex(&ret, numBits, (safe == true), NULL, NULL, NULL)) throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex"); return ret; } /** * Calculates the greatest common divisor (GCD) of two numbers. * @param m the second element * @return the GCD */ CBigNum gcd( const CBigNum& b) const{ CAutoBN_CTX pctx; CBigNum ret; if (!BN_gcd(&ret, this, &b, pctx)) throw bignum_error("CBigNum::gcd*= :BN_gcd"); return ret; } /** * Miller-Rabin primality test on this element * @param checks: optional, the number of Miller-Rabin tests to run * default causes error rate of 2^-80. * @return true if prime */ bool isPrime(const int checks=BN_prime_checks) const { CAutoBN_CTX pctx; int ret = BN_is_prime(this, checks, NULL, pctx, NULL); if(ret < 0){ throw bignum_error("CBigNum::isPrime :BN_is_prime"); } return ret != 0; } bool isOne() const { return BN_is_one(this); } bool operator!() const { return BN_is_zero(this); } CBigNum& operator+=(const CBigNum& b) { if (!BN_add(this, this, &b)) throw bignum_error("CBigNum::operator+= : BN_add failed"); return *this; } CBigNum& operator-=(const CBigNum& b) { *this = *this - b; return *this; } CBigNum& operator*=(const CBigNum& b) { CAutoBN_CTX pctx; if (!BN_mul(this, this, &b, pctx)) throw bignum_error("CBigNum::operator*= : BN_mul failed"); return *this; } CBigNum& operator/=(const CBigNum& b) { *this = *this / b; return *this; } CBigNum& operator%=(const CBigNum& b) { *this = *this % b; return *this; } CBigNum& operator<<=(unsigned int shift) { if (!BN_lshift(this, this, shift)) throw bignum_error("CBigNum:operator<<= : BN_lshift failed"); return *this; } CBigNum& operator>>=(unsigned int shift) { // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL CBigNum a = 1; a <<= shift; if (BN_cmp(&a, this) > 0) { *this = 0; return *this; } if (!BN_rshift(this, this, shift)) throw bignum_error("CBigNum:operator>>= : BN_rshift failed"); return *this; } CBigNum& operator++() { // prefix operator if (!BN_add(this, this, BN_value_one())) throw bignum_error("CBigNum::operator++ : BN_add failed"); return *this; } const CBigNum operator++(int) { // postfix operator const CBigNum ret = *this; ++(*this); return ret; } CBigNum& operator--() { // prefix operator CBigNum r; if (!BN_sub(&r, this, BN_value_one())) throw bignum_error("CBigNum::operator-- : BN_sub failed"); *this = r; return *this; } const CBigNum operator--(int) { // postfix operator const CBigNum ret = *this; --(*this); return ret; } friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b); friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b); friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b); friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b); friend inline bool operator<(const CBigNum& a, const CBigNum& b); }; inline const CBigNum operator+(const CBigNum& a, const CBigNum& b) { CBigNum r; if (!BN_add(&r, &a, &b)) throw bignum_error("CBigNum::operator+ : BN_add failed"); return r; } inline const CBigNum operator-(const CBigNum& a, const CBigNum& b) { CBigNum r; if (!BN_sub(&r, &a, &b)) throw bignum_error("CBigNum::operator- : BN_sub failed"); return r; } inline const CBigNum operator-(const CBigNum& a) { CBigNum r(a); BN_set_negative(&r, !BN_is_negative(&r)); return r; } inline const CBigNum operator*(const CBigNum& a, const CBigNum& b) { CAutoBN_CTX pctx; CBigNum r; if (!BN_mul(&r, &a, &b, pctx)) throw bignum_error("CBigNum::operator* : BN_mul failed"); return r; } inline const CBigNum operator/(const CBigNum& a, const CBigNum& b) { CAutoBN_CTX pctx; CBigNum r; if (!BN_div(&r, NULL, &a, &b, pctx)) throw bignum_error("CBigNum::operator/ : BN_div failed"); return r; } inline const CBigNum operator%(const CBigNum& a, const CBigNum& b) { CAutoBN_CTX pctx; CBigNum r; if (!BN_nnmod(&r, &a, &b, pctx)) throw bignum_error("CBigNum::operator% : BN_div failed"); return r; } inline const CBigNum operator<<(const CBigNum& a, unsigned int shift) { CBigNum r; if (!BN_lshift(&r, &a, shift)) throw bignum_error("CBigNum:operator<< : BN_lshift failed"); return r; } inline const CBigNum operator>>(const CBigNum& a, unsigned int shift) { CBigNum r = a; r >>= shift; return r; } inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) == 0); } inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) != 0); } inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) <= 0); } inline bool operator>=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) >= 0); } inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) < 0); } inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) > 0); } inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); } typedef CBigNum Bignum; #endif