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)
72 if (!BN_copy(bn, b.bn))
73 throw bignum_error("CBigNum::operator= : BN_copy failed");
82 CBigNum(int8_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
83 CBigNum(int16_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
84 CBigNum(int32_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
85 CBigNum(int64_t n) { bn = BN_new(); if (n >= 0) setuint64(n); else setint64(n); }
87 CBigNum(uint8_t n) { bn = BN_new(); setuint32(n); }
88 CBigNum(uint16_t n) { bn = BN_new(); setuint32(n); }
89 CBigNum(uint32_t n) { bn = BN_new(); setuint32(n); }
90 CBigNum(uint64_t n) { bn = BN_new(); setuint64(n); }
92 explicit CBigNum(uint256 n) { bn = BN_new(); setuint256(n); }
93 explicit CBigNum(const std::vector<uint8_t>& vch)
99 /** Generates a cryptographically secure random number between zero and range exclusive
100 * i.e. 0 < returned number < range
101 * @param range The upper bound on the number.
104 static CBigNum randBignum(const CBigNum& range) {
106 if(!BN_rand_range(ret.bn, range.bn)){
107 throw bignum_error("CBigNum:rand element : BN_rand_range failed");
112 /** Generates a cryptographically secure random k-bit number
113 * @param k The bit length of the number.
116 static CBigNum RandKBitBigum(const uint32_t k){
118 if(!BN_rand(ret.bn, k, -1, 0)){
119 throw bignum_error("CBigNum:rand element : BN_rand failed");
124 /**Returns the size in bits of the underlying bignum.
129 return BN_num_bits(bn);
133 void setuint32(uint32_t n)
135 if (!BN_set_word(bn, n))
136 throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
139 uint32_t getuint32() const
141 return BN_get_word(bn);
144 int32_t getint32() const
146 uint64_t n = BN_get_word(bn);
147 if (!BN_is_negative(bn))
148 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
150 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
153 void setint64(int64_t sn)
155 uint8_t pch[sizeof(sn) + 6];
156 uint8_t* p = pch + 4;
162 // 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
171 bool fLeadingZeroes = true;
172 for (int i = 0; i < 8; i++)
174 uint8_t c = (n >> 56) & 0xff;
181 *p++ = (fNegative ? 0x80 : 0);
184 fLeadingZeroes = false;
188 uint32_t nSize = (uint32_t) (p - (pch + 4));
189 pch[0] = (nSize >> 24) & 0xff;
190 pch[1] = (nSize >> 16) & 0xff;
191 pch[2] = (nSize >> 8) & 0xff;
192 pch[3] = (nSize) & 0xff;
193 BN_mpi2bn(pch, (int)(p - pch), bn);
198 size_t nSize = BN_bn2mpi(bn, NULL);
201 std::vector<uint8_t> vch(nSize);
202 BN_bn2mpi(bn, &vch[0]);
206 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
207 ((uint8_t*)&n)[i] = vch[j];
211 //supress msvc C4127: conditional expression is constant
212 inline bool check(bool value) {return value;}
214 void setuint64(uint64_t n)
216 // Use BN_set_word if word size is sufficient for uint64_t
217 if (check(sizeof(n) <= sizeof(BN_ULONG)))
219 if (!BN_set_word(bn, (BN_ULONG)n))
220 throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed");
224 uint8_t pch[sizeof(n) + 6];
225 uint8_t* p = pch + 4;
226 bool fLeadingZeroes = true;
227 for (int i = 0; i < 8; i++)
229 uint8_t c = (n >> 56) & 0xff;
237 fLeadingZeroes = false;
241 uint32_t nSize = (uint32_t) (p - (pch + 4));
242 pch[0] = (nSize >> 24) & 0xff;
243 pch[1] = (nSize >> 16) & 0xff;
244 pch[2] = (nSize >> 8) & 0xff;
245 pch[3] = (nSize) & 0xff;
246 BN_mpi2bn(pch, (int)(p - pch), bn);
249 void setuint160(uint160 n)
251 uint8_t pch[sizeof(n) + 6];
252 uint8_t* p = pch + 4;
253 bool fLeadingZeroes = true;
254 uint8_t* pbegin = (uint8_t*)&n;
255 uint8_t* psrc = pbegin + sizeof(n);
256 while (psrc != pbegin)
258 uint8_t c = *(--psrc);
265 fLeadingZeroes = false;
269 uint32_t nSize = (uint32_t) (p - (pch + 4));
270 pch[0] = (nSize >> 24) & 0xff;
271 pch[1] = (nSize >> 16) & 0xff;
272 pch[2] = (nSize >> 8) & 0xff;
273 pch[3] = (nSize >> 0) & 0xff;
274 BN_mpi2bn(pch, (int) (p - pch), bn);
277 uint160 getuint160() const
279 unsigned int nSize = BN_bn2mpi(bn, NULL);
282 std::vector<uint8_t> vch(nSize);
283 BN_bn2mpi(bn, &vch[0]);
287 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
288 ((uint8_t*)&n)[i] = vch[j];
292 void setuint256(uint256 n)
294 uint8_t pch[sizeof(n) + 6];
295 uint8_t* p = pch + 4;
296 bool fLeadingZeroes = true;
297 uint8_t* pbegin = (uint8_t*)&n;
298 uint8_t* psrc = pbegin + sizeof(n);
299 while (psrc != pbegin)
301 uint8_t c = *(--psrc);
308 fLeadingZeroes = false;
312 uint32_t nSize = (uint32_t) (p - (pch + 4));
313 pch[0] = (nSize >> 24) & 0xff;
314 pch[1] = (nSize >> 16) & 0xff;
315 pch[2] = (nSize >> 8) & 0xff;
316 pch[3] = (nSize >> 0) & 0xff;
317 BN_mpi2bn(pch, (int) (p - pch), bn);
320 uint256 getuint256() const
322 unsigned int nSize = BN_bn2mpi(bn, NULL);
325 std::vector<uint8_t> vch(nSize);
326 BN_bn2mpi(bn, &vch[0]);
330 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
331 ((uint8_t*)&n)[i] = vch[j];
335 void setBytes(const std::vector<uint8_t>& vchBytes)
337 BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), bn);
340 std::vector<uint8_t> getBytes() const
342 int nBytes = BN_num_bytes(bn);
344 std::vector<uint8_t> vchBytes(nBytes);
346 int n = BN_bn2bin(bn, &vchBytes[0]);
348 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
354 void setvch(const std::vector<uint8_t>& vch)
356 std::vector<uint8_t> vch2(vch.size() + 4);
357 uint32_t nSize = (uint32_t) vch.size();
358 // BIGNUM's byte stream format expects 4 bytes of
359 // big endian size data info at the front
360 vch2[0] = (nSize >> 24) & 0xff;
361 vch2[1] = (nSize >> 16) & 0xff;
362 vch2[2] = (nSize >> 8) & 0xff;
363 vch2[3] = (nSize >> 0) & 0xff;
364 // swap data to big endian
365 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
366 BN_mpi2bn(&vch2[0], (int) vch2.size(), bn);
369 std::vector<uint8_t> getvch() const
371 unsigned int nSize = BN_bn2mpi(bn, NULL);
373 return std::vector<uint8_t>();
374 std::vector<uint8_t> vch(nSize);
375 BN_bn2mpi(bn, &vch[0]);
376 vch.erase(vch.begin(), vch.begin() + 4);
377 reverse(vch.begin(), vch.end());
381 CBigNum& SetCompact(uint32_t nCompact)
383 uint32_t nSize = nCompact >> 24;
384 std::vector<uint8_t> vch(4 + nSize);
386 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
387 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
388 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
389 BN_mpi2bn(&vch[0], (int) vch.size(), bn);
393 uint32_t GetCompact() const
395 uint32_t nSize = BN_bn2mpi(bn, NULL);
396 std::vector<uint8_t> vch(nSize);
398 BN_bn2mpi(bn, &vch[0]);
399 uint32_t nCompact = nSize << 24;
400 if (nSize >= 1) nCompact |= (vch[4] << 16);
401 if (nSize >= 2) nCompact |= (vch[5] << 8);
402 if (nSize >= 3) nCompact |= (vch[6] << 0);
406 void SetHex(const std::string& str)
409 const char* psz = str.c_str();
410 while (isspace(*psz))
412 bool fNegative = false;
418 if (psz[0] == '0' && tolower(psz[1]) == 'x')
420 while (isspace(*psz))
423 // hex string to bignum
424 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 };
426 while (isxdigit(*psz))
429 int n = phexdigit[(uint8_t)*psz++];
436 std::string ToString(int nBase=10) const
439 CBigNum bnBase = nBase;
443 BN_set_negative(bn.bn, false);
446 if (BN_cmp(bn.bn, bn0.bn) == 0)
448 while (BN_cmp(bn.bn, bn0.bn) > 0)
450 if (!BN_div(dv.bn, rem.bn, bn.bn, bnBase.bn, pctx))
451 throw bignum_error("CBigNum::ToString() : BN_div failed");
453 uint32_t c = rem.getuint32();
454 str += "0123456789abcdef"[c];
456 if (BN_is_negative(bn.bn))
458 reverse(str.begin(), str.end());
462 std::string GetHex() const
467 BIGNUM* get() const {
471 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
473 return ::GetSerializeSize(getvch(), nType, nVersion);
476 template<typename Stream>
477 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
479 ::Serialize(s, getvch(), nType, nVersion);
482 template<typename Stream>
483 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
485 std::vector<uint8_t> vch;
486 ::Unserialize(s, vch, nType, nVersion);
491 * exponentiation with an int. this^e
492 * @param e the exponent as an int
495 CBigNum pow(const int e) const {
496 return this->pow(CBigNum(e));
500 * exponentiation this^e
501 * @param e the exponent
504 CBigNum pow(const CBigNum& e) const {
507 if (!BN_exp(ret.bn, bn, e.bn, pctx))
508 throw bignum_error("CBigNum::pow : BN_exp failed");
513 * modular multiplication: (this * b) mod m
517 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
520 if (!BN_mod_mul(ret.bn, bn, b.bn, m.bn, pctx))
521 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
527 * modular exponentiation: this^e mod n
531 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
536 CBigNum inv = this->inverse(m);
537 CBigNum posE = e * -1;
538 if (!BN_mod_exp(ret.bn, inv.bn, posE.bn, m.bn, pctx))
539 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
541 if (!BN_mod_exp(ret.bn, bn, e.bn, m.bn, pctx))
542 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
548 * Calculates the inverse of this element mod m.
549 * i.e. i such this*i = 1 mod m
551 * @return the inverse
553 CBigNum inverse(const CBigNum& m) const {
556 if (!BN_mod_inverse(ret.bn, bn, m.bn, pctx))
557 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
562 * Generates a random (safe) prime of numBits bits
563 * @param numBits the number of bits
564 * @param safe true for a safe prime
567 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
569 if(!BN_generate_prime_ex(ret.bn, numBits, (safe == true), NULL, NULL, NULL))
570 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
575 * Calculates the greatest common divisor (GCD) of two numbers.
576 * @param m the second element
579 CBigNum gcd( const CBigNum& b) const{
582 if (!BN_gcd(ret.bn, bn, b.bn, pctx))
583 throw bignum_error("CBigNum::gcd*= :BN_gcd");
588 * Miller-Rabin primality test on this element
589 * @param checks: optional, the number of Miller-Rabin tests to run
590 * default causes error rate of 2^-80.
591 * @return true if prime
593 bool isPrime(const int checks=BN_prime_checks) const {
595 int ret = BN_is_prime(bn, checks, NULL, pctx, NULL);
597 throw bignum_error("CBigNum::isPrime :BN_is_prime");
603 return BN_is_one(bn);
607 bool operator!() const
609 return BN_is_zero(bn);
612 CBigNum& operator+=(const CBigNum& b)
614 if (!BN_add(bn, bn, b.bn))
615 throw bignum_error("CBigNum::operator+= : BN_add failed");
619 CBigNum& operator-=(const CBigNum& b)
625 CBigNum& operator*=(const CBigNum& b)
628 if (!BN_mul(bn, bn, b.bn, pctx))
629 throw bignum_error("CBigNum::operator*= : BN_mul failed");
633 CBigNum& operator/=(const CBigNum& b)
639 CBigNum& operator%=(const CBigNum& b)
645 CBigNum& operator<<=(unsigned int shift)
647 if (!BN_lshift(bn, bn, shift))
648 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
652 CBigNum& operator>>=(unsigned int shift)
654 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
655 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
658 if (BN_cmp(a.bn, bn) > 0)
664 if (!BN_rshift(bn, bn, shift))
665 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
670 CBigNum& operator++()
673 if (!BN_add(bn, bn, BN_value_one()))
674 throw bignum_error("CBigNum::operator++ : BN_add failed");
678 const CBigNum operator++(int)
681 const CBigNum ret = *this;
686 CBigNum& operator--()
690 if (!BN_sub(r.bn, bn, BN_value_one()))
691 throw bignum_error("CBigNum::operator-- : BN_sub failed");
696 const CBigNum operator--(int)
699 const CBigNum ret = *this;
704 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
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 bool operator<(const CBigNum& a, const CBigNum& b);
709 friend inline const CBigNum 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);
713 friend inline const CBigNum operator-(const CBigNum& a);
714 friend inline const CBigNum operator<<(const CBigNum& a, unsigned int shift);
716 friend inline bool operator==(const CBigNum& a, const CBigNum& b);
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 std::ostream& operator<<(std::ostream &strm, const CBigNum &b);
727 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
730 if (!BN_add(r.bn, a.bn, b.bn))
731 throw bignum_error("CBigNum::operator+ : BN_add failed");
735 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
738 if (!BN_sub(r.bn, a.bn, b.bn))
739 throw bignum_error("CBigNum::operator- : BN_sub failed");
743 inline const CBigNum operator-(const CBigNum& a)
746 BN_set_negative(r.bn, !BN_is_negative(r.bn));
750 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
754 if (!BN_mul(r.bn, a.bn, b.bn, pctx))
755 throw bignum_error("CBigNum::operator* : BN_mul failed");
759 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
763 if (!BN_div(r.bn, NULL, a.bn, b.bn, pctx))
764 throw bignum_error("CBigNum::operator/ : BN_div failed");
768 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
772 if (!BN_nnmod(r.bn, a.bn, b.bn, pctx))
773 throw bignum_error("CBigNum::operator% : BN_div failed");
777 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
780 if (!BN_lshift(r.bn, a.bn, shift))
781 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
785 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
792 inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) == 0); }
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); }
799 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
801 typedef CBigNum Bignum;