// Copyright (c) 2009-2010 Satoshi Nakamoto
-// Copyright (c) 2011 The Bitcoin developers
+// Copyright (c) 2009-2012 The Bitcoin developers
// Distributed under the MIT/X11 software license, see the accompanying
-// file license.txt or http://www.opensource.org/licenses/mit-license.php.
+// file COPYING or http://www.opensource.org/licenses/mit-license.php.
#ifndef BITCOIN_BIGNUM_H
#define BITCOIN_BIGNUM_H
#include <stdexcept>
#include <vector>
#include <openssl/bn.h>
-
#include "util.h"
+/** Errors thrown by the bignum class */
class bignum_error : public std::runtime_error
{
public:
};
-
+/** RAII encapsulated BN_CTX (OpenSSL bignum context) */
class CAutoBN_CTX
{
protected:
};
-
+/** C++ wrapper for BIGNUM (OpenSSL bignum) */
class CBigNum : public BIGNUM
{
public:
BN_clear_free(this);
}
- CBigNum(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(int64 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(uint64 n) { BN_init(this); setuint64(n); }
- explicit CBigNum(uint256 n) { BN_init(this); setuint256(n); }
+ 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); }
- explicit CBigNum(const std::vector<unsigned char>& vch)
+ 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<uint8_t>& vch)
{
BN_init(this);
setvch(vch);
}
- void setulong(unsigned long n)
- {
- if (!BN_set_word(this, n))
- throw bignum_error("CBigNum conversion from unsigned long : BN_set_word failed");
+ /** 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;
}
- unsigned long getulong() const
+ /**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)
{
- return BN_get_word(this);
+ if (!BN_set_word(this, n))
+ throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
}
- unsigned int getuint() const
+ uint32_t getuint32() const
{
return BN_get_word(this);
}
- int getint() const
+ int32_t getint32() const
{
- unsigned long n = BN_get_word(this);
+ uint64_t n = BN_get_word(this);
if (!BN_is_negative(this))
- return (n > std::numeric_limits<int>::max() ? std::numeric_limits<int>::max() : n);
+ return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
else
- return (n > std::numeric_limits<int>::max() ? std::numeric_limits<int>::min() : -(int)n);
+ return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
}
- void setint64(int64 n)
+ void setint64(int64_t sn)
{
- unsigned char pch[sizeof(n) + 6];
- unsigned char* p = pch + 4;
- bool fNegative = false;
- if (n < (int64)0)
+ uint8_t pch[sizeof(sn) + 6];
+ uint8_t* p = pch + 4;
+ bool fNegative;
+ uint64_t n;
+
+ if (sn < (int64_t)0)
{
- n = -n;
+ // 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;
+ uint8_t c = (n >> 56) & 0xff;
n <<= 8;
if (fLeadingZeroes)
{
}
*p++ = c;
}
- unsigned int nSize = p - (pch + 4);
+ 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, p - pch, this);
+ BN_mpi2bn(pch, (int)(p - pch), this);
+ }
+
+ uint64_t getuint64()
+ {
+ size_t nSize = BN_bn2mpi(this, NULL);
+ if (nSize < 4)
+ return 0;
+ std::vector<uint8_t> 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 n)
+ void setuint64(uint64_t n)
{
- unsigned char pch[sizeof(n) + 6];
- unsigned char* p = pch + 4;
+ // 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++)
{
- unsigned char c = (n >> 56) & 0xff;
+ uint8_t c = (n >> 56) & 0xff;
n <<= 8;
if (fLeadingZeroes)
{
}
*p++ = c;
}
- unsigned int nSize = p - (pch + 4);
+ 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, p - pch, this);
+ 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<uint8_t> 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)
{
- unsigned char pch[sizeof(n) + 6];
- unsigned char* p = pch + 4;
+ uint8_t pch[sizeof(n) + 6];
+ uint8_t* p = pch + 4;
bool fLeadingZeroes = true;
- unsigned char* pbegin = (unsigned char*)&n;
- unsigned char* psrc = pbegin + sizeof(n);
+ uint8_t* pbegin = (uint8_t*)&n;
+ uint8_t* psrc = pbegin + sizeof(n);
while (psrc != pbegin)
{
- unsigned char c = *(--psrc);
+ uint8_t c = *(--psrc);
if (fLeadingZeroes)
{
if (c == 0)
}
*p++ = c;
}
- unsigned int nSize = p - (pch + 4);
+ 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, p - pch, this);
+ BN_mpi2bn(pch, (int) (p - pch), this);
}
- uint256 getuint256()
+ uint256 getuint256() const
{
unsigned int nSize = BN_bn2mpi(this, NULL);
if (nSize < 4)
return 0;
- std::vector<unsigned char> vch(nSize);
+ std::vector<uint8_t> vch(nSize);
BN_bn2mpi(this, &vch[0]);
if (vch.size() > 4)
vch[4] &= 0x7f;
uint256 n = 0;
- for (int i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
- ((unsigned char*)&n)[i] = vch[j];
+ 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 setvch(const std::vector<unsigned char>& vch)
+ void setBytes(const std::vector<uint8_t>& vchBytes)
+ {
+ BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), this);
+ }
+
+ std::vector<uint8_t> getBytes() const
+ {
+ int nBytes = BN_num_bytes(this);
+
+ std::vector<uint8_t> 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<uint8_t>& vch)
{
- std::vector<unsigned char> vch2(vch.size() + 4);
- unsigned int nSize = vch.size();
+ std::vector<uint8_t> 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[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);
+ BN_mpi2bn(&vch2[0], (int) vch2.size(), this);
}
- std::vector<unsigned char> getvch() const
+ std::vector<uint8_t> getvch() const
{
unsigned int nSize = BN_bn2mpi(this, NULL);
- if (nSize < 4)
- return std::vector<unsigned char>();
- std::vector<unsigned char> vch(nSize);
+ if (nSize <= 4)
+ return std::vector<uint8_t>();
+ std::vector<uint8_t> 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)
+ CBigNum& SetCompact(uint32_t nCompact)
{
- unsigned int nSize = nCompact >> 24;
- std::vector<unsigned char> vch(4 + nSize);
+ uint32_t nSize = nCompact >> 24;
+ std::vector<uint8_t> 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);
+ BN_mpi2bn(&vch[0], (int) vch.size(), this);
return *this;
}
- unsigned int GetCompact() const
+ uint32_t GetCompact() const
{
- unsigned int nSize = BN_bn2mpi(this, NULL);
- std::vector<unsigned char> vch(nSize);
+ uint32_t nSize = BN_bn2mpi(this, NULL);
+ std::vector<uint8_t> vch(nSize);
nSize -= 4;
BN_bn2mpi(this, &vch[0]);
- unsigned int nCompact = nSize << 24;
+ 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);
psz++;
// hex string to bignum
- static 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 };
+ 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[*psz++];
+ int n = phexdigit[(uint8_t)*psz++];
*this += n;
}
if (fNegative)
if (!BN_div(&dv, &rem, &bn, &bnBase, pctx))
throw bignum_error("CBigNum::ToString() : BN_div failed");
bn = dv;
- unsigned int c = rem.getulong();
+ uint32_t c = rem.getuint32();
str += "0123456789abcdef"[c];
}
if (BN_is_negative(this))
template<typename Stream>
void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
{
- std::vector<unsigned char> vch;
+ std::vector<uint8_t> 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
{
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
+ // 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)
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);
};
{
CAutoBN_CTX pctx;
CBigNum r;
- if (!BN_mod(&r, &a, &b, pctx))
+ if (!BN_nnmod(&r, &a, &b, pctx))
throw bignum_error("CBigNum::operator% : BN_div failed");
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 std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
+
+typedef CBigNum Bignum;
+
#endif
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