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)) {
75 throw bignum_error("CBigNum::operator= : BN_copy failed");
85 CBigNum(int8_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
86 CBigNum(int16_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
87 CBigNum(int32_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
88 CBigNum(int64_t n) { bn = BN_new(); if (n >= 0) setuint64(n); else setint64(n); }
90 CBigNum(uint8_t n) { bn = BN_new(); setuint32(n); }
91 CBigNum(uint16_t n) { bn = BN_new(); setuint32(n); }
92 CBigNum(uint32_t n) { bn = BN_new(); setuint32(n); }
93 CBigNum(uint64_t n) { bn = BN_new(); setuint64(n); }
95 explicit CBigNum(uint256 n) { bn = BN_new(); setuint256(n); }
96 explicit CBigNum(const std::vector<uint8_t>& vch)
102 /** Generates a cryptographically secure random number between zero and range exclusive
103 * i.e. 0 < returned number < range
104 * @param range The upper bound on the number.
107 static CBigNum randBignum(const CBigNum& range) {
109 if(!BN_rand_range(ret.bn, range.bn)){
110 throw bignum_error("CBigNum:rand element : BN_rand_range failed");
115 /** Generates a cryptographically secure random k-bit number
116 * @param k The bit length of the number.
119 static CBigNum RandKBitBigum(const uint32_t k){
121 if(!BN_rand(ret.bn, k, -1, 0)){
122 throw bignum_error("CBigNum:rand element : BN_rand failed");
127 /**Returns the size in bits of the underlying bignum.
132 return BN_num_bits(bn);
136 void setuint32(uint32_t n)
138 if (!BN_set_word(bn, n))
139 throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
142 uint32_t getuint32() const
144 return BN_get_word(bn);
147 int32_t getint32() const
149 uint64_t n = BN_get_word(bn);
150 if (!BN_is_negative(bn))
151 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
153 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
156 void setint64(int64_t sn)
158 uint8_t pch[sizeof(sn) + 6];
159 uint8_t* p = pch + 4;
165 // 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
174 bool fLeadingZeroes = true;
175 for (int i = 0; i < 8; i++)
177 uint8_t c = (n >> 56) & 0xff;
184 *p++ = (fNegative ? 0x80 : 0);
187 fLeadingZeroes = false;
191 uint32_t nSize = (uint32_t) (p - (pch + 4));
192 pch[0] = (nSize >> 24) & 0xff;
193 pch[1] = (nSize >> 16) & 0xff;
194 pch[2] = (nSize >> 8) & 0xff;
195 pch[3] = (nSize) & 0xff;
196 BN_mpi2bn(pch, (int)(p - pch), bn);
201 size_t nSize = BN_bn2mpi(bn, NULL);
204 std::vector<uint8_t> vch(nSize);
205 BN_bn2mpi(bn, &vch[0]);
209 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
210 ((uint8_t*)&n)[i] = vch[j];
214 //supress msvc C4127: conditional expression is constant
215 inline bool check(bool value) {return value;}
217 void setuint64(uint64_t n)
219 // Use BN_set_word if word size is sufficient for uint64_t
220 if (check(sizeof(n) <= sizeof(BN_ULONG)))
222 if (!BN_set_word(bn, (BN_ULONG)n))
223 throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed");
227 uint8_t pch[sizeof(n) + 6];
228 uint8_t* p = pch + 4;
229 bool fLeadingZeroes = true;
230 for (int i = 0; i < 8; i++)
232 uint8_t c = (n >> 56) & 0xff;
240 fLeadingZeroes = false;
244 uint32_t nSize = (uint32_t) (p - (pch + 4));
245 pch[0] = (nSize >> 24) & 0xff;
246 pch[1] = (nSize >> 16) & 0xff;
247 pch[2] = (nSize >> 8) & 0xff;
248 pch[3] = (nSize) & 0xff;
249 BN_mpi2bn(pch, (int)(p - pch), bn);
252 void setuint160(uint160 n)
254 uint8_t pch[sizeof(n) + 6];
255 uint8_t* p = pch + 4;
256 bool fLeadingZeroes = true;
257 uint8_t* pbegin = (uint8_t*)&n;
258 uint8_t* psrc = pbegin + sizeof(n);
259 while (psrc != pbegin)
261 uint8_t c = *(--psrc);
268 fLeadingZeroes = false;
272 uint32_t nSize = (uint32_t) (p - (pch + 4));
273 pch[0] = (nSize >> 24) & 0xff;
274 pch[1] = (nSize >> 16) & 0xff;
275 pch[2] = (nSize >> 8) & 0xff;
276 pch[3] = (nSize >> 0) & 0xff;
277 BN_mpi2bn(pch, (int) (p - pch), bn);
280 uint160 getuint160() const
282 unsigned int nSize = BN_bn2mpi(bn, NULL);
285 std::vector<uint8_t> vch(nSize);
286 BN_bn2mpi(bn, &vch[0]);
290 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
291 ((uint8_t*)&n)[i] = vch[j];
295 void setuint256(uint256 n)
297 uint8_t pch[sizeof(n) + 6];
298 uint8_t* p = pch + 4;
299 bool fLeadingZeroes = true;
300 uint8_t* pbegin = (uint8_t*)&n;
301 uint8_t* psrc = pbegin + sizeof(n);
302 while (psrc != pbegin)
304 uint8_t c = *(--psrc);
311 fLeadingZeroes = false;
315 uint32_t nSize = (uint32_t) (p - (pch + 4));
316 pch[0] = (nSize >> 24) & 0xff;
317 pch[1] = (nSize >> 16) & 0xff;
318 pch[2] = (nSize >> 8) & 0xff;
319 pch[3] = (nSize >> 0) & 0xff;
320 BN_mpi2bn(pch, (int) (p - pch), bn);
323 uint256 getuint256() const
325 unsigned int nSize = BN_bn2mpi(bn, NULL);
328 std::vector<uint8_t> vch(nSize);
329 BN_bn2mpi(bn, &vch[0]);
333 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
334 ((uint8_t*)&n)[i] = vch[j];
338 void setBytes(const std::vector<uint8_t>& vchBytes)
340 BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), bn);
343 std::vector<uint8_t> getBytes() const
345 int nBytes = BN_num_bytes(bn);
347 std::vector<uint8_t> vchBytes(nBytes);
349 int n = BN_bn2bin(bn, &vchBytes[0]);
351 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
357 void setvch(const std::vector<uint8_t>& vch)
359 std::vector<uint8_t> vch2(vch.size() + 4);
360 uint32_t nSize = (uint32_t) vch.size();
361 // BIGNUM's byte stream format expects 4 bytes of
362 // big endian size data info at the front
363 vch2[0] = (nSize >> 24) & 0xff;
364 vch2[1] = (nSize >> 16) & 0xff;
365 vch2[2] = (nSize >> 8) & 0xff;
366 vch2[3] = (nSize >> 0) & 0xff;
367 // swap data to big endian
368 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
369 BN_mpi2bn(&vch2[0], (int) vch2.size(), bn);
372 std::vector<uint8_t> getvch() const
374 unsigned int nSize = BN_bn2mpi(bn, NULL);
376 return std::vector<uint8_t>();
377 std::vector<uint8_t> vch(nSize);
378 BN_bn2mpi(bn, &vch[0]);
379 vch.erase(vch.begin(), vch.begin() + 4);
380 reverse(vch.begin(), vch.end());
384 CBigNum& SetCompact(uint32_t nCompact)
386 uint32_t nSize = nCompact >> 24;
387 std::vector<uint8_t> vch(4 + nSize);
389 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
390 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
391 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
392 BN_mpi2bn(&vch[0], (int) vch.size(), bn);
396 uint32_t GetCompact() const
398 uint32_t nSize = BN_bn2mpi(bn, NULL);
399 std::vector<uint8_t> vch(nSize);
401 BN_bn2mpi(bn, &vch[0]);
402 uint32_t nCompact = nSize << 24;
403 if (nSize >= 1) nCompact |= (vch[4] << 16);
404 if (nSize >= 2) nCompact |= (vch[5] << 8);
405 if (nSize >= 3) nCompact |= (vch[6] << 0);
409 void SetHex(const std::string& str)
412 const char* psz = str.c_str();
413 while (isspace(*psz))
415 bool fNegative = false;
421 if (psz[0] == '0' && tolower(psz[1]) == 'x')
423 while (isspace(*psz))
426 // hex string to bignum
427 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 };
429 while (isxdigit(*psz))
432 int n = phexdigit[(uint8_t)*psz++];
439 std::string ToString(int nBase=10) const
442 CBigNum bnBase = nBase;
446 BN_set_negative(bn.bn, false);
449 if (BN_cmp(bn.bn, bn0.bn) == 0)
451 while (BN_cmp(bn.bn, bn0.bn) > 0)
453 if (!BN_div(dv.bn, rem.bn, bn.bn, bnBase.bn, pctx))
454 throw bignum_error("CBigNum::ToString() : BN_div failed");
456 uint32_t c = rem.getuint32();
457 str += "0123456789abcdef"[c];
459 if (BN_is_negative(bn.bn))
461 reverse(str.begin(), str.end());
465 std::string GetHex() const
470 BIGNUM* get() const {
474 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
476 return ::GetSerializeSize(getvch(), nType, nVersion);
479 template<typename Stream>
480 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
482 ::Serialize(s, getvch(), nType, nVersion);
485 template<typename Stream>
486 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
488 std::vector<uint8_t> vch;
489 ::Unserialize(s, vch, nType, nVersion);
494 * exponentiation with an int. this^e
495 * @param e the exponent as an int
498 CBigNum pow(const int e) const {
499 return this->pow(CBigNum(e));
503 * exponentiation this^e
504 * @param e the exponent
507 CBigNum pow(const CBigNum& e) const {
510 if (!BN_exp(ret.bn, bn, e.bn, pctx))
511 throw bignum_error("CBigNum::pow : BN_exp failed");
516 * modular multiplication: (this * b) mod m
520 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
523 if (!BN_mod_mul(ret.bn, bn, b.bn, m.bn, pctx))
524 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
530 * modular exponentiation: this^e mod n
534 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
539 CBigNum inv = this->inverse(m);
540 CBigNum posE = e * -1;
541 if (!BN_mod_exp(ret.bn, inv.bn, posE.bn, m.bn, pctx))
542 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
544 if (!BN_mod_exp(ret.bn, bn, e.bn, m.bn, pctx))
545 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
551 * Calculates the inverse of this element mod m.
552 * i.e. i such this*i = 1 mod m
554 * @return the inverse
556 CBigNum inverse(const CBigNum& m) const {
559 if (!BN_mod_inverse(ret.bn, bn, m.bn, pctx))
560 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
565 * Generates a random (safe) prime of numBits bits
566 * @param numBits the number of bits
567 * @param safe true for a safe prime
570 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
572 if(!BN_generate_prime_ex(ret.bn, numBits, (safe == true), NULL, NULL, NULL))
573 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
578 * Calculates the greatest common divisor (GCD) of two numbers.
579 * @param m the second element
582 CBigNum gcd( const CBigNum& b) const{
585 if (!BN_gcd(ret.bn, bn, b.bn, pctx))
586 throw bignum_error("CBigNum::gcd*= :BN_gcd");
591 * Miller-Rabin primality test on this element
592 * @param checks: optional, the number of Miller-Rabin tests to run
593 * default causes error rate of 2^-80.
594 * @return true if prime
596 bool isPrime(const int checks=BN_prime_checks) const {
598 int ret = BN_is_prime(bn, checks, NULL, pctx, NULL);
600 throw bignum_error("CBigNum::isPrime :BN_is_prime");
606 return BN_is_one(bn);
610 bool operator!() const
612 return BN_is_zero(bn);
615 CBigNum& operator+=(const CBigNum& b)
617 if (!BN_add(bn, bn, b.bn))
618 throw bignum_error("CBigNum::operator+= : BN_add failed");
622 CBigNum& operator-=(const CBigNum& b)
628 CBigNum& operator*=(const CBigNum& b)
631 if (!BN_mul(bn, bn, b.bn, pctx))
632 throw bignum_error("CBigNum::operator*= : BN_mul failed");
636 CBigNum& operator/=(const CBigNum& b)
642 CBigNum& operator%=(const CBigNum& b)
648 CBigNum& operator<<=(unsigned int shift)
650 if (!BN_lshift(bn, bn, shift))
651 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
655 CBigNum& operator>>=(unsigned int shift)
657 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
658 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
661 if (BN_cmp(a.bn, bn) > 0)
667 if (!BN_rshift(bn, bn, shift))
668 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
673 CBigNum& operator++()
676 if (!BN_add(bn, bn, BN_value_one()))
677 throw bignum_error("CBigNum::operator++ : BN_add failed");
681 const CBigNum operator++(int)
684 const CBigNum ret = *this;
689 CBigNum& operator--()
693 if (!BN_sub(r.bn, bn, BN_value_one()))
694 throw bignum_error("CBigNum::operator-- : BN_sub failed");
699 const CBigNum operator--(int)
702 const CBigNum ret = *this;
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 const CBigNum operator%(const CBigNum& a, const CBigNum& b);
710 friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b);
711 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
712 friend inline const CBigNum operator+(const CBigNum& a, const CBigNum& b);
713 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
714 friend inline const CBigNum operator*(const CBigNum& a);
716 friend inline const CBigNum operator-(const CBigNum& a);
717 friend inline const CBigNum operator<<(const CBigNum& a, unsigned int shift);
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 bool operator<(const CBigNum& a, const CBigNum& b);
724 friend inline bool operator>(const CBigNum& a, const CBigNum& b);
725 friend inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b);
730 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
733 if (!BN_add(r.bn, a.bn, b.bn))
734 throw bignum_error("CBigNum::operator+ : BN_add failed");
738 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
741 if (!BN_sub(r.bn, a.bn, b.bn))
742 throw bignum_error("CBigNum::operator- : BN_sub failed");
746 inline const CBigNum operator-(const CBigNum& a)
749 BN_set_negative(r.bn, !BN_is_negative(r.bn));
753 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
757 if (!BN_mul(r.bn, a.bn, b.bn, pctx))
758 throw bignum_error("CBigNum::operator* : BN_mul failed");
762 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
766 if (!BN_div(r.bn, NULL, a.bn, b.bn, pctx))
767 throw bignum_error("CBigNum::operator/ : BN_div failed");
771 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
775 if (!BN_nnmod(r.bn, a.bn, b.bn, pctx))
776 throw bignum_error("CBigNum::operator% : BN_div failed");
780 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
783 if (!BN_lshift(r.bn, a.bn, shift))
784 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
788 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
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); }
799 inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) < 0); }
800 inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(a.bn, b.bn) > 0); }
802 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
804 typedef CBigNum Bignum;