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)
62 BIGNUM *dup = BN_dup(b.bn);
65 throw bignum_error("CBigNum::CBigNum(const CBigNum&) : BN_dup failed");
70 CBigNum& operator=(const CBigNum& b)
72 BIGNUM *dup = BN_dup(b.bn);
75 throw bignum_error("CBigNum::operator= : BN_dup failed");
81 CBigNum(const BIGNUM *bnp) {
82 BIGNUM *dup = BN_dup(bnp);
85 throw bignum_error("CBigNum::CBigNum(const BIGNUM*) : BN_dup failed");
95 CBigNum(bool n) { bn = BN_new(); setuint32(n); }
97 CBigNum(int8_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
98 CBigNum(int16_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
99 CBigNum(int32_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
100 CBigNum(int64_t n) { bn = BN_new(); if (n >= 0) setuint64(n); else setint64(n); }
102 CBigNum(uint8_t n) { bn = BN_new(); setuint32(n); }
103 CBigNum(uint16_t n) { bn = BN_new(); setuint32(n); }
104 CBigNum(uint32_t n) { bn = BN_new(); setuint32(n); }
105 CBigNum(uint64_t n) { bn = BN_new(); setuint64(n); }
107 explicit CBigNum(uint256 n) { bn = BN_new(); setuint256(n); }
108 explicit CBigNum(const std::vector<uint8_t>& vch)
114 /** Generates a cryptographically secure random number between zero and range exclusive
115 * i.e. 0 < returned number < range
116 * @param range The upper bound on the number.
119 static CBigNum randBignum(const CBigNum& range) {
121 if(!BN_rand_range(ret.bn, range.bn)){
122 throw bignum_error("CBigNum:rand element : BN_rand_range failed");
127 /** Generates a cryptographically secure random k-bit number
128 * @param k The bit length of the number.
131 static CBigNum RandKBitBigum(const uint32_t k){
133 if(!BN_rand(ret.bn, k, -1, 0)){
134 throw bignum_error("CBigNum:rand element : BN_rand failed");
139 /**Returns the size in bits of the underlying bignum.
144 return BN_num_bits(bn);
148 void setuint32(uint32_t n)
150 if (!BN_set_word(bn, n))
151 throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
154 uint32_t getuint32() const
156 return BN_get_word(bn);
159 int32_t getint32() const
161 uint64_t n = BN_get_word(bn);
162 if (!BN_is_negative(bn))
163 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
165 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
168 void setint64(int64_t sn)
170 uint8_t pch[sizeof(sn) + 6];
171 uint8_t* p = pch + 4;
177 // 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
186 bool fLeadingZeroes = true;
187 for (int i = 0; i < 8; i++)
189 uint8_t c = (n >> 56) & 0xff;
196 *p++ = (fNegative ? 0x80 : 0);
199 fLeadingZeroes = false;
203 uint32_t nSize = (uint32_t) (p - (pch + 4));
204 pch[0] = (nSize >> 24) & 0xff;
205 pch[1] = (nSize >> 16) & 0xff;
206 pch[2] = (nSize >> 8) & 0xff;
207 pch[3] = (nSize) & 0xff;
208 BN_mpi2bn(pch, (int)(p - pch), bn);
213 size_t nSize = BN_bn2mpi(bn, NULL);
216 std::vector<uint8_t> vch(nSize);
217 BN_bn2mpi(bn, &vch[0]);
221 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
222 ((uint8_t*)&n)[i] = vch[j];
226 //supress msvc C4127: conditional expression is constant
227 inline bool check(bool value) {return value;}
229 void setuint64(uint64_t n)
231 // Use BN_set_word if word size is sufficient for uint64_t
232 if (check(sizeof(n) <= sizeof(BN_ULONG)))
234 if (!BN_set_word(bn, (BN_ULONG)n))
235 throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed");
239 uint8_t pch[sizeof(n) + 6];
240 uint8_t* p = pch + 4;
241 bool fLeadingZeroes = true;
242 for (int i = 0; i < 8; i++)
244 uint8_t c = (n >> 56) & 0xff;
252 fLeadingZeroes = false;
256 uint32_t nSize = (uint32_t) (p - (pch + 4));
257 pch[0] = (nSize >> 24) & 0xff;
258 pch[1] = (nSize >> 16) & 0xff;
259 pch[2] = (nSize >> 8) & 0xff;
260 pch[3] = (nSize) & 0xff;
261 BN_mpi2bn(pch, (int)(p - pch), bn);
264 void setuint160(uint160 n)
266 uint8_t pch[sizeof(n) + 6];
267 uint8_t* p = pch + 4;
268 bool fLeadingZeroes = true;
269 uint8_t* pbegin = (uint8_t*)&n;
270 uint8_t* psrc = pbegin + sizeof(n);
271 while (psrc != pbegin)
273 uint8_t c = *(--psrc);
280 fLeadingZeroes = false;
284 uint32_t nSize = (uint32_t) (p - (pch + 4));
285 pch[0] = (nSize >> 24) & 0xff;
286 pch[1] = (nSize >> 16) & 0xff;
287 pch[2] = (nSize >> 8) & 0xff;
288 pch[3] = (nSize >> 0) & 0xff;
289 BN_mpi2bn(pch, (int) (p - pch), bn);
292 uint160 getuint160() const
294 unsigned int nSize = BN_bn2mpi(bn, NULL);
297 std::vector<uint8_t> vch(nSize);
298 BN_bn2mpi(bn, &vch[0]);
302 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
303 ((uint8_t*)&n)[i] = vch[j];
307 void setuint256(uint256 n)
309 uint8_t pch[sizeof(n) + 6];
310 uint8_t* p = pch + 4;
311 bool fLeadingZeroes = true;
312 uint8_t* pbegin = (uint8_t*)&n;
313 uint8_t* psrc = pbegin + sizeof(n);
314 while (psrc != pbegin)
316 uint8_t c = *(--psrc);
323 fLeadingZeroes = false;
327 uint32_t nSize = (uint32_t) (p - (pch + 4));
328 pch[0] = (nSize >> 24) & 0xff;
329 pch[1] = (nSize >> 16) & 0xff;
330 pch[2] = (nSize >> 8) & 0xff;
331 pch[3] = (nSize >> 0) & 0xff;
332 BN_mpi2bn(pch, (int) (p - pch), bn);
335 uint256 getuint256() const
337 unsigned int nSize = BN_bn2mpi(bn, NULL);
340 std::vector<uint8_t> vch(nSize);
341 BN_bn2mpi(bn, &vch[0]);
345 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
346 ((uint8_t*)&n)[i] = vch[j];
350 void setBytes(const std::vector<uint8_t>& vchBytes)
352 BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), bn);
355 std::vector<uint8_t> getBytes() const
357 int nBytes = BN_num_bytes(bn);
359 std::vector<uint8_t> vchBytes(nBytes);
361 int n = BN_bn2bin(bn, &vchBytes[0]);
363 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
369 void setvch(const std::vector<uint8_t>& vch)
371 std::vector<uint8_t> vch2(vch.size() + 4);
372 uint32_t nSize = (uint32_t) vch.size();
373 // BIGNUM's byte stream format expects 4 bytes of
374 // big endian size data info at the front
375 vch2[0] = (nSize >> 24) & 0xff;
376 vch2[1] = (nSize >> 16) & 0xff;
377 vch2[2] = (nSize >> 8) & 0xff;
378 vch2[3] = (nSize >> 0) & 0xff;
379 // swap data to big endian
380 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
381 BN_mpi2bn(&vch2[0], (int) vch2.size(), bn);
384 std::vector<uint8_t> getvch() const
386 unsigned int nSize = BN_bn2mpi(bn, NULL);
388 return std::vector<uint8_t>();
389 std::vector<uint8_t> vch(nSize);
390 BN_bn2mpi(bn, &vch[0]);
391 vch.erase(vch.begin(), vch.begin() + 4);
392 reverse(vch.begin(), vch.end());
396 CBigNum& SetCompact(uint32_t nCompact)
398 uint32_t nSize = nCompact >> 24;
399 std::vector<uint8_t> vch(4 + nSize);
401 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
402 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
403 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
404 BN_mpi2bn(&vch[0], (int) vch.size(), bn);
408 uint32_t GetCompact() const
410 uint32_t nSize = BN_bn2mpi(bn, NULL);
411 std::vector<uint8_t> vch(nSize);
413 BN_bn2mpi(bn, &vch[0]);
414 uint32_t nCompact = nSize << 24;
415 if (nSize >= 1) nCompact |= (vch[4] << 16);
416 if (nSize >= 2) nCompact |= (vch[5] << 8);
417 if (nSize >= 3) nCompact |= (vch[6] << 0);
421 void SetHex(const std::string& str)
424 const char* psz = str.c_str();
425 while (isspace(*psz))
427 bool fNegative = false;
433 if (psz[0] == '0' && tolower(psz[1]) == 'x')
435 while (isspace(*psz))
438 // hex string to bignum
439 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 };
441 while (isxdigit(*psz))
444 int n = phexdigit[(uint8_t)*psz++];
451 std::string ToString(int nBase=10) const
454 CBigNum bnBase = nBase;
458 BN_set_negative(bn.bn, false);
461 if (BN_cmp(bn.bn, bn0.bn) == 0)
463 while (BN_cmp(bn.bn, bn0.bn) > 0)
465 if (!BN_div(dv.bn, rem.bn, bn.bn, bnBase.bn, pctx))
466 throw bignum_error("CBigNum::ToString() : BN_div failed");
468 uint32_t c = rem.getuint32();
469 str += "0123456789abcdef"[c];
471 if (BN_is_negative(bn.bn))
473 reverse(str.begin(), str.end());
477 std::string GetHex() const
482 BIGNUM* get() const {
486 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
488 return ::GetSerializeSize(getvch(), nType, nVersion);
491 template<typename Stream>
492 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
494 ::Serialize(s, getvch(), nType, nVersion);
497 template<typename Stream>
498 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
500 std::vector<uint8_t> vch;
501 ::Unserialize(s, vch, nType, nVersion);
506 * exponentiation with an int. this^e
507 * @param e the exponent as an int
510 CBigNum pow(const int e) const {
511 return this->pow(CBigNum(e));
515 * exponentiation this^e
516 * @param e the exponent
519 CBigNum pow(const CBigNum& e) const {
522 if (!BN_exp(ret.bn, bn, e.bn, pctx))
523 throw bignum_error("CBigNum::pow : BN_exp failed");
528 * modular multiplication: (this * b) mod m
532 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
535 if (!BN_mod_mul(ret.bn, bn, b.bn, m.bn, pctx))
536 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
542 * modular exponentiation: this^e mod n
546 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
551 CBigNum inv = this->inverse(m);
552 CBigNum posE = e * -1;
553 if (!BN_mod_exp(ret.bn, inv.bn, posE.bn, m.bn, pctx))
554 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
556 if (!BN_mod_exp(ret.bn, bn, e.bn, m.bn, pctx))
557 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
563 * Calculates the inverse of this element mod m.
564 * i.e. i such this*i = 1 mod m
566 * @return the inverse
568 CBigNum inverse(const CBigNum& m) const {
571 if (!BN_mod_inverse(ret.bn, bn, m.bn, pctx))
572 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
577 * Generates a random (safe) prime of numBits bits
578 * @param numBits the number of bits
579 * @param safe true for a safe prime
582 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
584 if(!BN_generate_prime_ex(ret.bn, numBits, (safe == true), NULL, NULL, NULL))
585 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
590 * Calculates the greatest common divisor (GCD) of two numbers.
591 * @param m the second element
594 CBigNum gcd( const CBigNum& b) const{
597 if (!BN_gcd(ret.bn, bn, b.bn, pctx))
598 throw bignum_error("CBigNum::gcd*= :BN_gcd");
603 * Miller-Rabin primality test on this element
604 * @param checks: optional, the number of Miller-Rabin tests to run
605 * default causes error rate of 2^-80.
606 * @return true if prime
608 bool isPrime(const int checks=BN_prime_checks) const {
610 int ret = BN_is_prime_ex(bn, checks, pctx, NULL);
612 throw bignum_error("CBigNum::isPrime :BN_is_prime");
618 return BN_is_one(bn);
622 bool operator!() const
624 return BN_is_zero(bn);
627 CBigNum& operator+=(const CBigNum& b)
629 if (!BN_add(bn, bn, b.bn))
630 throw bignum_error("CBigNum::operator+= : BN_add failed");
634 CBigNum& operator-=(const CBigNum& b)
640 CBigNum& operator*=(const CBigNum& b)
643 if (!BN_mul(bn, bn, b.bn, pctx))
644 throw bignum_error("CBigNum::operator*= : BN_mul failed");
648 CBigNum& operator/=(const CBigNum& b)
654 CBigNum& operator%=(const CBigNum& b)
660 CBigNum& operator<<=(unsigned int shift)
662 if (!BN_lshift(bn, bn, shift))
663 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
667 CBigNum& operator>>=(unsigned int shift)
669 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
670 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
673 if (BN_cmp(a.bn, bn) > 0)
679 if (!BN_rshift(bn, bn, shift))
680 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
685 CBigNum& operator++()
688 if (!BN_add(bn, bn, BN_value_one()))
689 throw bignum_error("CBigNum::operator++ : BN_add failed");
693 const CBigNum operator++(int)
696 const CBigNum ret = *this;
701 CBigNum& operator--()
705 if (!BN_sub(r.bn, bn, BN_value_one()))
706 throw bignum_error("CBigNum::operator-- : BN_sub failed");
711 const CBigNum operator--(int)
714 const CBigNum ret = *this;
719 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
720 friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
721 friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b);
722 friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b);
723 friend inline const CBigNum operator+(const CBigNum& a, const CBigNum& b);
724 friend inline const CBigNum operator*(const CBigNum& a);
726 friend inline const CBigNum operator-(const CBigNum& a);
727 friend inline const CBigNum operator<<(const CBigNum& a, unsigned int shift);
729 friend inline bool operator==(const CBigNum& a, const CBigNum& b);
730 friend inline bool operator!=(const CBigNum& a, const CBigNum& b);
731 friend inline bool operator<=(const CBigNum& a, const CBigNum& b);
732 friend inline bool operator>=(const CBigNum& a, const CBigNum& b);
733 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
734 friend inline bool operator>(const CBigNum& a, const CBigNum& b);
735 friend inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b);
740 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
743 if (!BN_add(r.bn, a.bn, b.bn))
744 throw bignum_error("CBigNum::operator+ : BN_add failed");
748 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
751 if (!BN_sub(r.bn, a.bn, b.bn))
752 throw bignum_error("CBigNum::operator- : BN_sub failed");
756 inline const CBigNum operator-(const CBigNum& a)
759 BN_set_negative(r.bn, !BN_is_negative(r.bn));
763 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
767 if (!BN_mul(r.bn, a.bn, b.bn, pctx))
768 throw bignum_error("CBigNum::operator* : BN_mul failed");
772 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
776 if (!BN_div(r.bn, NULL, a.bn, b.bn, pctx))
777 throw bignum_error("CBigNum::operator/ : BN_div failed");
781 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
785 if (!BN_nnmod(r.bn, a.bn, b.bn, pctx))
786 throw bignum_error("CBigNum::operator% : BN_div failed");
790 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
793 if (!BN_lshift(r.bn, a.bn, shift))
794 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
798 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
805 inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) == 0); }
806 inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) != 0); }
807 inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) <= 0); }
808 inline bool operator>=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) >= 0); }
809 inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) < 0); }
810 inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) > 0); }
812 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
814 typedef CBigNum Bignum;