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) */
50 class CBigNum : public BIGNUM
58 CBigNum(const CBigNum& b)
61 if (!BN_copy(this, &b))
64 throw bignum_error("CBigNum::CBigNum(const CBigNum&) : BN_copy failed");
68 CBigNum& operator=(const CBigNum& b)
70 if (!BN_copy(this, &b))
71 throw bignum_error("CBigNum::operator= : BN_copy failed");
80 CBigNum(int8_t n) { BN_init(this); if (n >= 0) setuint32(n); else setint64(n); }
81 CBigNum(int16_t n) { BN_init(this); if (n >= 0) setuint32(n); else setint64(n); }
82 CBigNum(int32_t n) { BN_init(this); if (n >= 0) setuint32(n); else setint64(n); }
83 CBigNum(int64_t n) { BN_init(this); if (n >= 0) setuint64(n); else setint64(n); }
85 CBigNum(uint8_t n) { BN_init(this); setuint32(n); }
86 CBigNum(uint16_t n) { BN_init(this); setuint32(n); }
87 CBigNum(uint32_t n) { BN_init(this); setuint32(n); }
88 CBigNum(uint64_t n) { BN_init(this); setuint64(n); }
90 explicit CBigNum(uint256 n) { BN_init(this); setuint256(n); }
91 explicit CBigNum(const std::vector<uint8_t>& vch)
97 /** Generates a cryptographically secure random number between zero and range exclusive
98 * i.e. 0 < returned number < range
99 * @param range The upper bound on the number.
102 static CBigNum randBignum(const CBigNum& range) {
104 if(!BN_rand_range(&ret, &range)){
105 throw bignum_error("CBigNum:rand element : BN_rand_range failed");
110 /** Generates a cryptographically secure random k-bit number
111 * @param k The bit length of the number.
114 static CBigNum RandKBitBigum(const uint32_t k){
116 if(!BN_rand(&ret, k, -1, 0)){
117 throw bignum_error("CBigNum:rand element : BN_rand failed");
122 /**Returns the size in bits of the underlying bignum.
127 return BN_num_bits(this);
131 void setuint32(uint32_t n)
133 if (!BN_set_word(this, n))
134 throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
137 uint32_t getuint32() const
139 return BN_get_word(this);
142 int32_t getint32() const
144 uint64_t n = BN_get_word(this);
145 if (!BN_is_negative(this))
146 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
148 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
151 void setint64(int64_t sn)
153 uint8_t pch[sizeof(sn) + 6];
154 uint8_t* p = pch + 4;
160 // 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
169 bool fLeadingZeroes = true;
170 for (int i = 0; i < 8; i++)
172 uint8_t c = (n >> 56) & 0xff;
179 *p++ = (fNegative ? 0x80 : 0);
182 fLeadingZeroes = false;
186 uint32_t nSize = (uint32_t) (p - (pch + 4));
187 pch[0] = (nSize >> 24) & 0xff;
188 pch[1] = (nSize >> 16) & 0xff;
189 pch[2] = (nSize >> 8) & 0xff;
190 pch[3] = (nSize) & 0xff;
191 BN_mpi2bn(pch, (int)(p - pch), this);
196 size_t nSize = BN_bn2mpi(this, NULL);
199 std::vector<uint8_t> vch(nSize);
200 BN_bn2mpi(this, &vch[0]);
204 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
205 ((uint8_t*)&n)[i] = vch[j];
209 //supress msvc C4127: conditional expression is constant
210 inline bool check(bool value) {return value;}
212 void setuint64(uint64_t n)
214 // Use BN_set_word if word size is sufficient for uint64_t
215 if (check(sizeof(n) <= sizeof(BN_ULONG)))
217 if (!BN_set_word(this, (BN_ULONG)n))
218 throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed");
222 uint8_t pch[sizeof(n) + 6];
223 uint8_t* p = pch + 4;
224 bool fLeadingZeroes = true;
225 for (int i = 0; i < 8; i++)
227 uint8_t c = (n >> 56) & 0xff;
235 fLeadingZeroes = false;
239 uint32_t nSize = (uint32_t) (p - (pch + 4));
240 pch[0] = (nSize >> 24) & 0xff;
241 pch[1] = (nSize >> 16) & 0xff;
242 pch[2] = (nSize >> 8) & 0xff;
243 pch[3] = (nSize) & 0xff;
244 BN_mpi2bn(pch, (int)(p - pch), this);
247 void setuint160(uint160 n)
249 uint8_t pch[sizeof(n) + 6];
250 uint8_t* p = pch + 4;
251 bool fLeadingZeroes = true;
252 uint8_t* pbegin = (uint8_t*)&n;
253 uint8_t* psrc = pbegin + sizeof(n);
254 while (psrc != pbegin)
256 uint8_t c = *(--psrc);
263 fLeadingZeroes = false;
267 uint32_t nSize = (uint32_t) (p - (pch + 4));
268 pch[0] = (nSize >> 24) & 0xff;
269 pch[1] = (nSize >> 16) & 0xff;
270 pch[2] = (nSize >> 8) & 0xff;
271 pch[3] = (nSize >> 0) & 0xff;
272 BN_mpi2bn(pch, (int) (p - pch), this);
275 uint160 getuint160() const
277 unsigned int nSize = BN_bn2mpi(this, NULL);
280 std::vector<uint8_t> vch(nSize);
281 BN_bn2mpi(this, &vch[0]);
285 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
286 ((uint8_t*)&n)[i] = vch[j];
290 void setuint256(uint256 n)
292 uint8_t pch[sizeof(n) + 6];
293 uint8_t* p = pch + 4;
294 bool fLeadingZeroes = true;
295 uint8_t* pbegin = (uint8_t*)&n;
296 uint8_t* psrc = pbegin + sizeof(n);
297 while (psrc != pbegin)
299 uint8_t c = *(--psrc);
306 fLeadingZeroes = false;
310 uint32_t nSize = (uint32_t) (p - (pch + 4));
311 pch[0] = (nSize >> 24) & 0xff;
312 pch[1] = (nSize >> 16) & 0xff;
313 pch[2] = (nSize >> 8) & 0xff;
314 pch[3] = (nSize >> 0) & 0xff;
315 BN_mpi2bn(pch, (int) (p - pch), this);
318 uint256 getuint256() const
320 unsigned int nSize = BN_bn2mpi(this, NULL);
323 std::vector<uint8_t> vch(nSize);
324 BN_bn2mpi(this, &vch[0]);
328 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
329 ((uint8_t*)&n)[i] = vch[j];
333 void setBytes(const std::vector<uint8_t>& vchBytes)
335 BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), this);
338 std::vector<uint8_t> getBytes() const
340 int nBytes = BN_num_bytes(this);
342 std::vector<uint8_t> vchBytes(nBytes);
344 int n = BN_bn2bin(this, &vchBytes[0]);
346 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
352 void setvch(const std::vector<uint8_t>& vch)
354 std::vector<uint8_t> vch2(vch.size() + 4);
355 uint32_t nSize = (uint32_t) vch.size();
356 // BIGNUM's byte stream format expects 4 bytes of
357 // big endian size data info at the front
358 vch2[0] = (nSize >> 24) & 0xff;
359 vch2[1] = (nSize >> 16) & 0xff;
360 vch2[2] = (nSize >> 8) & 0xff;
361 vch2[3] = (nSize >> 0) & 0xff;
362 // swap data to big endian
363 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
364 BN_mpi2bn(&vch2[0], (int) vch2.size(), this);
367 std::vector<uint8_t> getvch() const
369 unsigned int nSize = BN_bn2mpi(this, NULL);
371 return std::vector<uint8_t>();
372 std::vector<uint8_t> vch(nSize);
373 BN_bn2mpi(this, &vch[0]);
374 vch.erase(vch.begin(), vch.begin() + 4);
375 reverse(vch.begin(), vch.end());
379 CBigNum& SetCompact(uint32_t nCompact)
381 uint32_t nSize = nCompact >> 24;
382 std::vector<uint8_t> vch(4 + nSize);
384 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
385 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
386 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
387 BN_mpi2bn(&vch[0], (int) vch.size(), this);
391 uint32_t GetCompact() const
393 uint32_t nSize = BN_bn2mpi(this, NULL);
394 std::vector<uint8_t> vch(nSize);
396 BN_bn2mpi(this, &vch[0]);
397 uint32_t nCompact = nSize << 24;
398 if (nSize >= 1) nCompact |= (vch[4] << 16);
399 if (nSize >= 2) nCompact |= (vch[5] << 8);
400 if (nSize >= 3) nCompact |= (vch[6] << 0);
404 void SetHex(const std::string& str)
407 const char* psz = str.c_str();
408 while (isspace(*psz))
410 bool fNegative = false;
416 if (psz[0] == '0' && tolower(psz[1]) == 'x')
418 while (isspace(*psz))
421 // hex string to bignum
422 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 };
424 while (isxdigit(*psz))
427 int n = phexdigit[(uint8_t)*psz++];
434 std::string ToString(int nBase=10) const
437 CBigNum bnBase = nBase;
441 BN_set_negative(&bn, false);
444 if (BN_cmp(&bn, &bn0) == 0)
446 while (BN_cmp(&bn, &bn0) > 0)
448 if (!BN_div(&dv, &rem, &bn, &bnBase, pctx))
449 throw bignum_error("CBigNum::ToString() : BN_div failed");
451 uint32_t c = rem.getuint32();
452 str += "0123456789abcdef"[c];
454 if (BN_is_negative(this))
456 reverse(str.begin(), str.end());
460 std::string GetHex() const
465 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
467 return ::GetSerializeSize(getvch(), nType, nVersion);
470 template<typename Stream>
471 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
473 ::Serialize(s, getvch(), nType, nVersion);
476 template<typename Stream>
477 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
479 std::vector<uint8_t> vch;
480 ::Unserialize(s, vch, nType, nVersion);
485 * exponentiation with an int. this^e
486 * @param e the exponent as an int
489 CBigNum pow(const int e) const {
490 return this->pow(CBigNum(e));
494 * exponentiation this^e
495 * @param e the exponent
498 CBigNum pow(const CBigNum& e) const {
501 if (!BN_exp(&ret, this, &e, pctx))
502 throw bignum_error("CBigNum::pow : BN_exp failed");
507 * modular multiplication: (this * b) mod m
511 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
514 if (!BN_mod_mul(&ret, this, &b, &m, pctx))
515 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
521 * modular exponentiation: this^e mod n
525 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
530 CBigNum inv = this->inverse(m);
531 CBigNum posE = e * -1;
532 if (!BN_mod_exp(&ret, &inv, &posE, &m, pctx))
533 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
535 if (!BN_mod_exp(&ret, this, &e, &m, pctx))
536 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
542 * Calculates the inverse of this element mod m.
543 * i.e. i such this*i = 1 mod m
545 * @return the inverse
547 CBigNum inverse(const CBigNum& m) const {
550 if (!BN_mod_inverse(&ret, this, &m, pctx))
551 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
556 * Generates a random (safe) prime of numBits bits
557 * @param numBits the number of bits
558 * @param safe true for a safe prime
561 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
563 if(!BN_generate_prime_ex(&ret, numBits, (safe == true), NULL, NULL, NULL))
564 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
569 * Calculates the greatest common divisor (GCD) of two numbers.
570 * @param m the second element
573 CBigNum gcd( const CBigNum& b) const{
576 if (!BN_gcd(&ret, this, &b, pctx))
577 throw bignum_error("CBigNum::gcd*= :BN_gcd");
582 * Miller-Rabin primality test on this element
583 * @param checks: optional, the number of Miller-Rabin tests to run
584 * default causes error rate of 2^-80.
585 * @return true if prime
587 bool isPrime(const int checks=BN_prime_checks) const {
589 int ret = BN_is_prime(this, checks, NULL, pctx, NULL);
591 throw bignum_error("CBigNum::isPrime :BN_is_prime");
597 return BN_is_one(this);
601 bool operator!() const
603 return BN_is_zero(this);
606 CBigNum& operator+=(const CBigNum& b)
608 if (!BN_add(this, this, &b))
609 throw bignum_error("CBigNum::operator+= : BN_add failed");
613 CBigNum& operator-=(const CBigNum& b)
619 CBigNum& operator*=(const CBigNum& b)
622 if (!BN_mul(this, this, &b, pctx))
623 throw bignum_error("CBigNum::operator*= : BN_mul failed");
627 CBigNum& operator/=(const CBigNum& b)
633 CBigNum& operator%=(const CBigNum& b)
639 CBigNum& operator<<=(unsigned int shift)
641 if (!BN_lshift(this, this, shift))
642 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
646 CBigNum& operator>>=(unsigned int shift)
648 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
649 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
652 if (BN_cmp(&a, this) > 0)
658 if (!BN_rshift(this, this, shift))
659 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
664 CBigNum& operator++()
667 if (!BN_add(this, this, BN_value_one()))
668 throw bignum_error("CBigNum::operator++ : BN_add failed");
672 const CBigNum operator++(int)
675 const CBigNum ret = *this;
680 CBigNum& operator--()
684 if (!BN_sub(&r, this, BN_value_one()))
685 throw bignum_error("CBigNum::operator-- : BN_sub failed");
690 const CBigNum operator--(int)
693 const CBigNum ret = *this;
699 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
700 friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
701 friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b);
702 friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b);
703 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
708 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
711 if (!BN_add(&r, &a, &b))
712 throw bignum_error("CBigNum::operator+ : BN_add failed");
716 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
719 if (!BN_sub(&r, &a, &b))
720 throw bignum_error("CBigNum::operator- : BN_sub failed");
724 inline const CBigNum operator-(const CBigNum& a)
727 BN_set_negative(&r, !BN_is_negative(&r));
731 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
735 if (!BN_mul(&r, &a, &b, pctx))
736 throw bignum_error("CBigNum::operator* : BN_mul failed");
740 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
744 if (!BN_div(&r, NULL, &a, &b, pctx))
745 throw bignum_error("CBigNum::operator/ : BN_div failed");
749 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
753 if (!BN_nnmod(&r, &a, &b, pctx))
754 throw bignum_error("CBigNum::operator% : BN_div failed");
758 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
761 if (!BN_lshift(&r, &a, shift))
762 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
766 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
773 inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) == 0); }
774 inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) != 0); }
775 inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) <= 0); }
776 inline bool operator>=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) >= 0); }
777 inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) < 0); }
778 inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) > 0); }
780 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
782 typedef CBigNum Bignum;