1 // Copyright (c) 2009-2010 Satoshi Nakamoto
2 // Copyright (c) 2009-2012 The Bitcoin developers
3 // Distributed under the MIT/X11 software license, see the accompanying
4 // file COPYING or http://www.opensource.org/licenses/mit-license.php.
5 #ifndef BITCOIN_BIGNUM_H
6 #define BITCOIN_BIGNUM_H
10 #include <openssl/bn.h>
13 /** Errors thrown by the bignum class */
14 class bignum_error : public std::runtime_error
17 explicit bignum_error(const std::string& str) : std::runtime_error(str) {}
21 /** RAII encapsulated BN_CTX (OpenSSL bignum context) */
26 BN_CTX* operator=(BN_CTX* pnew) { return pctx = pnew; }
33 throw bignum_error("CAutoBN_CTX : BN_CTX_new() returned NULL");
42 operator BN_CTX*() { return pctx; }
43 BN_CTX& operator*() { return *pctx; }
44 BN_CTX** operator&() { return &pctx; }
45 bool operator!() { return (pctx == NULL); }
49 /** C++ wrapper for BIGNUM (OpenSSL bignum) */
60 CBigNum(const CBigNum& b)
63 if (!BN_copy(bn, b.bn))
66 throw bignum_error("CBigNum::CBigNum(const CBigNum&) : BN_copy failed");
70 CBigNum& operator=(const CBigNum& b)
73 if (!BN_copy(bn, b.bn))
74 throw bignum_error("CBigNum::operator= : BN_copy failed");
83 CBigNum(int8_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
84 CBigNum(int16_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
85 CBigNum(int32_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
86 CBigNum(int64_t n) { bn = BN_new(); if (n >= 0) setuint64(n); else setint64(n); }
88 CBigNum(uint8_t n) { bn = BN_new(); setuint32(n); }
89 CBigNum(uint16_t n) { bn = BN_new(); setuint32(n); }
90 CBigNum(uint32_t n) { bn = BN_new(); setuint32(n); }
91 CBigNum(uint64_t n) { bn = BN_new(); setuint64(n); }
93 explicit CBigNum(uint256 n) { bn = BN_new(); setuint256(n); }
94 explicit CBigNum(const std::vector<uint8_t>& vch)
100 /** Generates a cryptographically secure random number between zero and range exclusive
101 * i.e. 0 < returned number < range
102 * @param range The upper bound on the number.
105 static CBigNum randBignum(const CBigNum& range) {
107 if(!BN_rand_range(ret.bn, range.bn)){
108 throw bignum_error("CBigNum:rand element : BN_rand_range failed");
113 /** Generates a cryptographically secure random k-bit number
114 * @param k The bit length of the number.
117 static CBigNum RandKBitBigum(const uint32_t k){
119 if(!BN_rand(ret.bn, k, -1, 0)){
120 throw bignum_error("CBigNum:rand element : BN_rand failed");
125 /**Returns the size in bits of the underlying bignum.
130 return BN_num_bits(bn);
134 void setuint32(uint32_t n)
136 if (!BN_set_word(bn, n))
137 throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
140 uint32_t getuint32() const
142 return BN_get_word(bn);
145 int32_t getint32() const
147 uint64_t n = BN_get_word(bn);
148 if (!BN_is_negative(bn))
149 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
151 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
154 void setint64(int64_t sn)
156 uint8_t pch[sizeof(sn) + 6];
157 uint8_t* p = pch + 4;
163 // 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
172 bool fLeadingZeroes = true;
173 for (int i = 0; i < 8; i++)
175 uint8_t c = (n >> 56) & 0xff;
182 *p++ = (fNegative ? 0x80 : 0);
185 fLeadingZeroes = false;
189 uint32_t nSize = (uint32_t) (p - (pch + 4));
190 pch[0] = (nSize >> 24) & 0xff;
191 pch[1] = (nSize >> 16) & 0xff;
192 pch[2] = (nSize >> 8) & 0xff;
193 pch[3] = (nSize) & 0xff;
194 BN_mpi2bn(pch, (int)(p - pch), bn);
199 size_t nSize = BN_bn2mpi(bn, NULL);
202 std::vector<uint8_t> vch(nSize);
203 BN_bn2mpi(bn, &vch[0]);
207 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
208 ((uint8_t*)&n)[i] = vch[j];
212 //supress msvc C4127: conditional expression is constant
213 inline bool check(bool value) {return value;}
215 void setuint64(uint64_t n)
217 // Use BN_set_word if word size is sufficient for uint64_t
218 if (check(sizeof(n) <= sizeof(BN_ULONG)))
220 if (!BN_set_word(bn, (BN_ULONG)n))
221 throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed");
225 uint8_t pch[sizeof(n) + 6];
226 uint8_t* p = pch + 4;
227 bool fLeadingZeroes = true;
228 for (int i = 0; i < 8; i++)
230 uint8_t c = (n >> 56) & 0xff;
238 fLeadingZeroes = false;
242 uint32_t nSize = (uint32_t) (p - (pch + 4));
243 pch[0] = (nSize >> 24) & 0xff;
244 pch[1] = (nSize >> 16) & 0xff;
245 pch[2] = (nSize >> 8) & 0xff;
246 pch[3] = (nSize) & 0xff;
247 BN_mpi2bn(pch, (int)(p - pch), bn);
250 void setuint160(uint160 n)
252 uint8_t pch[sizeof(n) + 6];
253 uint8_t* p = pch + 4;
254 bool fLeadingZeroes = true;
255 uint8_t* pbegin = (uint8_t*)&n;
256 uint8_t* psrc = pbegin + sizeof(n);
257 while (psrc != pbegin)
259 uint8_t c = *(--psrc);
266 fLeadingZeroes = false;
270 uint32_t nSize = (uint32_t) (p - (pch + 4));
271 pch[0] = (nSize >> 24) & 0xff;
272 pch[1] = (nSize >> 16) & 0xff;
273 pch[2] = (nSize >> 8) & 0xff;
274 pch[3] = (nSize >> 0) & 0xff;
275 BN_mpi2bn(pch, (int) (p - pch), bn);
278 uint160 getuint160() const
280 unsigned int nSize = BN_bn2mpi(bn, NULL);
283 std::vector<uint8_t> vch(nSize);
284 BN_bn2mpi(bn, &vch[0]);
288 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
289 ((uint8_t*)&n)[i] = vch[j];
293 void setuint256(uint256 n)
295 uint8_t pch[sizeof(n) + 6];
296 uint8_t* p = pch + 4;
297 bool fLeadingZeroes = true;
298 uint8_t* pbegin = (uint8_t*)&n;
299 uint8_t* psrc = pbegin + sizeof(n);
300 while (psrc != pbegin)
302 uint8_t c = *(--psrc);
309 fLeadingZeroes = false;
313 uint32_t nSize = (uint32_t) (p - (pch + 4));
314 pch[0] = (nSize >> 24) & 0xff;
315 pch[1] = (nSize >> 16) & 0xff;
316 pch[2] = (nSize >> 8) & 0xff;
317 pch[3] = (nSize >> 0) & 0xff;
318 BN_mpi2bn(pch, (int) (p - pch), bn);
321 uint256 getuint256() const
323 unsigned int nSize = BN_bn2mpi(bn, NULL);
326 std::vector<uint8_t> vch(nSize);
327 BN_bn2mpi(bn, &vch[0]);
331 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
332 ((uint8_t*)&n)[i] = vch[j];
336 void setBytes(const std::vector<uint8_t>& vchBytes)
338 BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), bn);
341 std::vector<uint8_t> getBytes() const
343 int nBytes = BN_num_bytes(bn);
345 std::vector<uint8_t> vchBytes(nBytes);
347 int n = BN_bn2bin(bn, &vchBytes[0]);
349 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
355 void setvch(const std::vector<uint8_t>& vch)
357 std::vector<uint8_t> vch2(vch.size() + 4);
358 uint32_t nSize = (uint32_t) vch.size();
359 // BIGNUM's byte stream format expects 4 bytes of
360 // big endian size data info at the front
361 vch2[0] = (nSize >> 24) & 0xff;
362 vch2[1] = (nSize >> 16) & 0xff;
363 vch2[2] = (nSize >> 8) & 0xff;
364 vch2[3] = (nSize >> 0) & 0xff;
365 // swap data to big endian
366 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
367 BN_mpi2bn(&vch2[0], (int) vch2.size(), bn);
370 std::vector<uint8_t> getvch() const
372 unsigned int nSize = BN_bn2mpi(bn, NULL);
374 return std::vector<uint8_t>();
375 std::vector<uint8_t> vch(nSize);
376 BN_bn2mpi(bn, &vch[0]);
377 vch.erase(vch.begin(), vch.begin() + 4);
378 reverse(vch.begin(), vch.end());
382 CBigNum& SetCompact(uint32_t nCompact)
384 uint32_t nSize = nCompact >> 24;
385 std::vector<uint8_t> vch(4 + nSize);
387 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
388 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
389 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
390 BN_mpi2bn(&vch[0], (int) vch.size(), bn);
394 uint32_t GetCompact() const
396 uint32_t nSize = BN_bn2mpi(bn, NULL);
397 std::vector<uint8_t> vch(nSize);
399 BN_bn2mpi(bn, &vch[0]);
400 uint32_t nCompact = nSize << 24;
401 if (nSize >= 1) nCompact |= (vch[4] << 16);
402 if (nSize >= 2) nCompact |= (vch[5] << 8);
403 if (nSize >= 3) nCompact |= (vch[6] << 0);
407 void SetHex(const std::string& str)
410 const char* psz = str.c_str();
411 while (isspace(*psz))
413 bool fNegative = false;
419 if (psz[0] == '0' && tolower(psz[1]) == 'x')
421 while (isspace(*psz))
424 // hex string to bignum
425 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 };
427 while (isxdigit(*psz))
430 int n = phexdigit[(uint8_t)*psz++];
437 std::string ToString(int nBase=10) const
440 CBigNum bnBase = nBase;
444 BN_set_negative(bn.bn, false);
447 if (BN_cmp(bn.bn, bn0.bn) == 0)
449 while (BN_cmp(bn.bn, bn0.bn) > 0)
451 if (!BN_div(dv.bn, rem.bn, bn.bn, bnBase.bn, pctx))
452 throw bignum_error("CBigNum::ToString() : BN_div failed");
454 uint32_t c = rem.getuint32();
455 str += "0123456789abcdef"[c];
457 if (BN_is_negative(bn.bn))
459 reverse(str.begin(), str.end());
463 std::string GetHex() const
468 BIGNUM* get() const {
472 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
474 return ::GetSerializeSize(getvch(), nType, nVersion);
477 template<typename Stream>
478 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
480 ::Serialize(s, getvch(), nType, nVersion);
483 template<typename Stream>
484 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
486 std::vector<uint8_t> vch;
487 ::Unserialize(s, vch, nType, nVersion);
492 * exponentiation with an int. this^e
493 * @param e the exponent as an int
496 CBigNum pow(const int e) const {
497 return this->pow(CBigNum(e));
501 * exponentiation this^e
502 * @param e the exponent
505 CBigNum pow(const CBigNum& e) const {
508 if (!BN_exp(ret.bn, bn, e.bn, pctx))
509 throw bignum_error("CBigNum::pow : BN_exp failed");
514 * modular multiplication: (this * b) mod m
518 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
521 if (!BN_mod_mul(ret.bn, bn, b.bn, m.bn, pctx))
522 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
528 * modular exponentiation: this^e mod n
532 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
537 CBigNum inv = this->inverse(m);
538 CBigNum posE = e * -1;
539 if (!BN_mod_exp(ret.bn, inv.bn, posE.bn, m.bn, pctx))
540 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
542 if (!BN_mod_exp(ret.bn, bn, e.bn, m.bn, pctx))
543 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
549 * Calculates the inverse of this element mod m.
550 * i.e. i such this*i = 1 mod m
552 * @return the inverse
554 CBigNum inverse(const CBigNum& m) const {
557 if (!BN_mod_inverse(ret.bn, bn, m.bn, pctx))
558 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
563 * Generates a random (safe) prime of numBits bits
564 * @param numBits the number of bits
565 * @param safe true for a safe prime
568 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
570 if(!BN_generate_prime_ex(ret.bn, numBits, (safe == true), NULL, NULL, NULL))
571 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
576 * Calculates the greatest common divisor (GCD) of two numbers.
577 * @param m the second element
580 CBigNum gcd( const CBigNum& b) const{
583 if (!BN_gcd(ret.bn, bn, b.bn, pctx))
584 throw bignum_error("CBigNum::gcd*= :BN_gcd");
589 * Miller-Rabin primality test on this element
590 * @param checks: optional, the number of Miller-Rabin tests to run
591 * default causes error rate of 2^-80.
592 * @return true if prime
594 bool isPrime(const int checks=BN_prime_checks) const {
596 int ret = BN_is_prime(bn, checks, NULL, pctx, NULL);
598 throw bignum_error("CBigNum::isPrime :BN_is_prime");
604 return BN_is_one(bn);
608 bool operator!() const
610 return BN_is_zero(bn);
613 CBigNum& operator+=(const CBigNum& b)
615 if (!BN_add(bn, bn, b.bn))
616 throw bignum_error("CBigNum::operator+= : BN_add failed");
620 CBigNum& operator-=(const CBigNum& b)
626 CBigNum& operator*=(const CBigNum& b)
629 if (!BN_mul(bn, bn, b.bn, pctx))
630 throw bignum_error("CBigNum::operator*= : BN_mul failed");
634 CBigNum& operator/=(const CBigNum& b)
640 CBigNum& operator%=(const CBigNum& b)
646 CBigNum& operator<<=(unsigned int shift)
648 if (!BN_lshift(bn, bn, shift))
649 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
653 CBigNum& operator>>=(unsigned int shift)
655 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
656 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
659 if (BN_cmp(a.bn, bn) > 0)
665 if (!BN_rshift(bn, bn, shift))
666 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
671 CBigNum& operator++()
674 if (!BN_add(bn, bn, BN_value_one()))
675 throw bignum_error("CBigNum::operator++ : BN_add failed");
679 const CBigNum operator++(int)
682 const CBigNum ret = *this;
687 CBigNum& operator--()
691 if (!BN_sub(r.bn, bn, BN_value_one()))
692 throw bignum_error("CBigNum::operator-- : BN_sub failed");
697 const CBigNum operator--(int)
700 const CBigNum ret = *this;
705 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
706 friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
707 friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b);
708 friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b);
709 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
710 friend inline const CBigNum operator+(const CBigNum& a, const CBigNum& b);
711 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
712 friend inline const CBigNum operator*(const CBigNum& a);
714 friend inline const CBigNum operator-(const CBigNum& a);
715 friend inline const CBigNum operator<<(const CBigNum& a, unsigned int shift);
717 friend inline bool operator==(const CBigNum& a, const CBigNum& b);
718 friend inline bool operator!=(const CBigNum& a, const CBigNum& b);
719 friend inline bool operator<=(const CBigNum& a, const CBigNum& b);
720 friend inline bool operator>=(const CBigNum& a, const CBigNum& b);
721 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
722 friend inline bool operator>(const CBigNum& a, const CBigNum& b);
723 friend inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b);
728 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
731 if (!BN_add(r.bn, a.bn, b.bn))
732 throw bignum_error("CBigNum::operator+ : BN_add failed");
736 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
739 if (!BN_sub(r.bn, a.bn, b.bn))
740 throw bignum_error("CBigNum::operator- : BN_sub failed");
744 inline const CBigNum operator-(const CBigNum& a)
747 BN_set_negative(r.bn, !BN_is_negative(r.bn));
751 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
755 if (!BN_mul(r.bn, a.bn, b.bn, pctx))
756 throw bignum_error("CBigNum::operator* : BN_mul failed");
760 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
764 if (!BN_div(r.bn, NULL, a.bn, b.bn, pctx))
765 throw bignum_error("CBigNum::operator/ : BN_div failed");
769 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
773 if (!BN_nnmod(r.bn, a.bn, b.bn, pctx))
774 throw bignum_error("CBigNum::operator% : BN_div failed");
778 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
781 if (!BN_lshift(r.bn, a.bn, shift))
782 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
786 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
793 inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) == 0); }
794 inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) != 0); }
795 inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) <= 0); }
796 inline bool operator>=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) >= 0); }
797 inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) < 0); }
798 inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) > 0); }
800 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
802 typedef CBigNum Bignum;