src/bignum.h
// 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 "serialize.h"
#include "uint256.h"
#include "version.h"
#include <openssl/bn.h>
#include <stdexcept>
#include <vector>
#include <stdint.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(char n) is not portable. Use 'signed char' or 'unsigned char'.
CBigNum(signed char n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
CBigNum(short n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
CBigNum(int n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
CBigNum(long n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
CBigNum(long long n) { BN_init(this); setint64(n); }
CBigNum(unsigned char n) { BN_init(this); setulong(n); }
CBigNum(unsigned short n) { BN_init(this); setulong(n); }
CBigNum(unsigned int n) { BN_init(this); setulong(n); }
CBigNum(unsigned long n) { BN_init(this); setulong(n); }
CBigNum(unsigned long long n) { BN_init(this); setuint64(n); }
explicit CBigNum(uint256 n) { BN_init(this); setuint256(n); }
explicit CBigNum(const std::vector<unsigned char>& 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 setulong(unsigned long n)
{
if (!BN_set_word(this, n))
throw bignum_error("CBigNum conversion from unsigned long : BN_set_word failed");
}
unsigned long getulong() const
{
return BN_get_word(this);
}
unsigned int getuint() const
{
return BN_get_word(this);
}
int getint() const
{
unsigned long n = BN_get_word(this);
if (!BN_is_negative(this))
return (n > (unsigned long)std::numeric_limits<int>::max() ? std::numeric_limits<int>::max() : n);
else
return (n > (unsigned long)std::numeric_limits<int>::max() ? std::numeric_limits<int>::min() : -(int)n);
}
void setint64(int64_t sn)
{
unsigned char pch[sizeof(sn) + 6];
unsigned char* 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++)
{
unsigned char 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;
}
unsigned int nSize = 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, p - pch, this);
}
uint64_t getuint64()
{
unsigned int nSize = BN_bn2mpi(this, NULL);
if (nSize < 4)
return 0;
std::vector<unsigned char> vch(nSize);
BN_bn2mpi(this, &vch[0]);
if (vch.size() > 4)
vch[4] &= 0x7f;
uint64_t n = 0;
for (unsigned int i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
((unsigned char*)&n)[i] = vch[j];
return n;
}
void setuint64(uint64_t n)
{
unsigned char pch[sizeof(n) + 6];
unsigned char* p = pch + 4;
bool fLeadingZeroes = true;
for (int i = 0; i < 8; i++)
{
unsigned char c = (n >> 56) & 0xff;
n <<= 8;
if (fLeadingZeroes)
{
if (c == 0)
continue;
if (c & 0x80)
*p++ = 0;
fLeadingZeroes = false;
}
*p++ = c;
}
unsigned int nSize = 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, p - pch, this);
}
void setuint256(uint256 n)
{
unsigned char pch[sizeof(n) + 6];
unsigned char* p = pch + 4;
bool fLeadingZeroes = true;
unsigned char* pbegin = (unsigned char*)&n;
unsigned char* psrc = pbegin + sizeof(n);
while (psrc != pbegin)
{
unsigned char c = *(--psrc);
if (fLeadingZeroes)
{
if (c == 0)
continue;
if (c & 0x80)
*p++ = 0;
fLeadingZeroes = false;
}
*p++ = c;
}
unsigned int nSize = 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, p - pch, this);
}
uint256 getuint256() const
{
unsigned int nSize = BN_bn2mpi(this, NULL);
if (nSize < 4)
return 0;
std::vector<unsigned char> vch(nSize);
BN_bn2mpi(this, &vch[0]);
if (vch.size() > 4)
vch[4] &= 0x7f;
uint256 n = 0;
for (unsigned int i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
((unsigned char*)&n)[i] = vch[j];
return n;
}
void setvch(const std::vector<unsigned char>& vch)
{
std::vector<unsigned char> vch2(vch.size() + 4);
unsigned int nSize = 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], vch2.size(), this);
}
std::vector<unsigned char> getvch() const
{
unsigned int nSize = BN_bn2mpi(this, NULL);
if (nSize <= 4)
return std::vector<unsigned char>();
std::vector<unsigned char> vch(nSize);
BN_bn2mpi(this, &vch[0]);
vch.erase(vch.begin(), vch.begin() + 4);
reverse(vch.begin(), vch.end());
return vch;
}
CBigNum& SetCompact(unsigned int nCompact)
{
unsigned int nSize = nCompact >> 24;
std::vector<unsigned char> 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], vch.size(), this);
return *this;
}
unsigned int GetCompact() const
{
unsigned int nSize = BN_bn2mpi(this, NULL);
std::vector<unsigned char> vch(nSize);
nSize -= 4;
BN_bn2mpi(this, &vch[0]);
unsigned int 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[(unsigned char)*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;
unsigned int c = rem.getulong();
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<typename Stream>
void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
{
::Serialize(s, getvch(), nType, nVersion);
}
template<typename Stream>
void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
{
std::vector<unsigned char> 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;
}
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