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>
12 #include "util.h" // for uint64
14 /** Errors thrown by the bignum class */
15 class bignum_error : public std::runtime_error
18 explicit bignum_error(const std::string& str) : std::runtime_error(str) {}
22 /** RAII encapsulated BN_CTX (OpenSSL bignum context) */
27 BN_CTX* operator=(BN_CTX* pnew) { return pctx = pnew; }
34 throw bignum_error("CAutoBN_CTX : BN_CTX_new() returned NULL");
43 operator BN_CTX*() { return pctx; }
44 BN_CTX& operator*() { return *pctx; }
45 BN_CTX** operator&() { return &pctx; }
46 bool operator!() { return (pctx == NULL); }
50 /** C++ wrapper for BIGNUM (OpenSSL bignum) */
51 class CBigNum : public BIGNUM
59 CBigNum(const CBigNum& b)
62 if (!BN_copy(this, &b))
65 throw bignum_error("CBigNum::CBigNum(const CBigNum&) : BN_copy failed");
69 CBigNum& operator=(const CBigNum& b)
71 if (!BN_copy(this, &b))
72 throw bignum_error("CBigNum::operator= : BN_copy failed");
81 //CBigNum(char n) is not portable. Use 'signed char' or 'unsigned char'.
82 CBigNum(signed char n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
83 CBigNum(short n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
84 CBigNum(int n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
85 CBigNum(long n) { BN_init(this); if (n >= 0) setulong(n); else setint64(n); }
86 CBigNum(int64 n) { BN_init(this); setint64(n); }
87 CBigNum(unsigned char n) { BN_init(this); setulong(n); }
88 CBigNum(unsigned short n) { BN_init(this); setulong(n); }
89 CBigNum(unsigned int n) { BN_init(this); setulong(n); }
90 CBigNum(unsigned long n) { BN_init(this); setulong(n); }
91 CBigNum(uint64 n) { BN_init(this); setuint64(n); }
92 explicit CBigNum(uint256 n) { BN_init(this); setuint256(n); }
94 explicit CBigNum(const std::vector<unsigned char>& 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, &range)){
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, 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(this);
134 void setulong(unsigned long n)
136 if (!BN_set_word(this, n))
137 throw bignum_error("CBigNum conversion from unsigned long : BN_set_word failed");
140 unsigned long getulong() const
142 return BN_get_word(this);
145 unsigned int getuint() const
147 return BN_get_word(this);
152 unsigned long n = BN_get_word(this);
153 if (!BN_is_negative(this))
154 return (n > (unsigned long)std::numeric_limits<int>::max() ? std::numeric_limits<int>::max() : n);
156 return (n > (unsigned long)std::numeric_limits<int>::max() ? std::numeric_limits<int>::min() : -(int)n);
159 void setint64(int64 sn)
161 unsigned char pch[sizeof(sn) + 6];
162 unsigned char* p = pch + 4;
168 // 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
177 bool fLeadingZeroes = true;
178 for (int i = 0; i < 8; i++)
180 unsigned char c = (n >> 56) & 0xff;
187 *p++ = (fNegative ? 0x80 : 0);
190 fLeadingZeroes = false;
194 unsigned int nSize = p - (pch + 4);
195 pch[0] = (nSize >> 24) & 0xff;
196 pch[1] = (nSize >> 16) & 0xff;
197 pch[2] = (nSize >> 8) & 0xff;
198 pch[3] = (nSize) & 0xff;
199 BN_mpi2bn(pch, p - pch, this);
204 unsigned int nSize = BN_bn2mpi(this, NULL);
207 std::vector<unsigned char> vch(nSize);
208 BN_bn2mpi(this, &vch[0]);
212 for (unsigned int i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
213 ((unsigned char*)&n)[i] = vch[j];
217 void setuint64(uint64 n)
219 unsigned char pch[sizeof(n) + 6];
220 unsigned char* p = pch + 4;
221 bool fLeadingZeroes = true;
222 for (int i = 0; i < 8; i++)
224 unsigned char c = (n >> 56) & 0xff;
232 fLeadingZeroes = false;
236 unsigned int nSize = p - (pch + 4);
237 pch[0] = (nSize >> 24) & 0xff;
238 pch[1] = (nSize >> 16) & 0xff;
239 pch[2] = (nSize >> 8) & 0xff;
240 pch[3] = (nSize) & 0xff;
241 BN_mpi2bn(pch, p - pch, this);
244 void setuint160(uint160 n)
246 unsigned char pch[sizeof(n) + 6];
247 unsigned char* p = pch + 4;
248 bool fLeadingZeroes = true;
249 unsigned char* pbegin = (unsigned char*)&n;
250 unsigned char* psrc = pbegin + sizeof(n);
251 while (psrc != pbegin)
253 unsigned char c = *(--psrc);
260 fLeadingZeroes = false;
264 unsigned int nSize = p - (pch + 4);
265 pch[0] = (nSize >> 24) & 0xff;
266 pch[1] = (nSize >> 16) & 0xff;
267 pch[2] = (nSize >> 8) & 0xff;
268 pch[3] = (nSize >> 0) & 0xff;
269 BN_mpi2bn(pch, p - pch, this);
272 uint160 getuint160() const
274 unsigned int nSize = BN_bn2mpi(this, NULL);
277 std::vector<unsigned char> vch(nSize);
278 BN_bn2mpi(this, &vch[0]);
282 for (unsigned int i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
283 ((unsigned char*)&n)[i] = vch[j];
287 void setuint256(uint256 n)
289 unsigned char pch[sizeof(n) + 6];
290 unsigned char* p = pch + 4;
291 bool fLeadingZeroes = true;
292 unsigned char* pbegin = (unsigned char*)&n;
293 unsigned char* psrc = pbegin + sizeof(n);
294 while (psrc != pbegin)
296 unsigned char c = *(--psrc);
303 fLeadingZeroes = false;
307 unsigned int nSize = p - (pch + 4);
308 pch[0] = (nSize >> 24) & 0xff;
309 pch[1] = (nSize >> 16) & 0xff;
310 pch[2] = (nSize >> 8) & 0xff;
311 pch[3] = (nSize >> 0) & 0xff;
312 BN_mpi2bn(pch, p - pch, this);
315 uint256 getuint256() const
317 unsigned int nSize = BN_bn2mpi(this, NULL);
320 std::vector<unsigned char> vch(nSize);
321 BN_bn2mpi(this, &vch[0]);
325 for (unsigned int i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
326 ((unsigned char*)&n)[i] = vch[j];
330 void setBytes(const std::vector<unsigned char>& vchBytes)
332 BN_bin2bn(&vchBytes[0], vchBytes.size(), this);
335 std::vector<unsigned char> getBytes() const
337 int nBytes = BN_num_bytes(this);
339 std::vector<unsigned char> vchBytes(nBytes);
341 int n = BN_bn2bin(this, &vchBytes[0]);
343 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
349 void setvch(const std::vector<unsigned char>& vch)
351 std::vector<unsigned char> vch2(vch.size() + 4);
352 unsigned int nSize = vch.size();
353 // BIGNUM's byte stream format expects 4 bytes of
354 // big endian size data info at the front
355 vch2[0] = (nSize >> 24) & 0xff;
356 vch2[1] = (nSize >> 16) & 0xff;
357 vch2[2] = (nSize >> 8) & 0xff;
358 vch2[3] = (nSize >> 0) & 0xff;
359 // swap data to big endian
360 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
361 BN_mpi2bn(&vch2[0], vch2.size(), this);
364 std::vector<unsigned char> getvch() const
366 unsigned int nSize = BN_bn2mpi(this, NULL);
368 return std::vector<unsigned char>();
369 std::vector<unsigned char> vch(nSize);
370 BN_bn2mpi(this, &vch[0]);
371 vch.erase(vch.begin(), vch.begin() + 4);
372 reverse(vch.begin(), vch.end());
376 CBigNum& SetCompact(unsigned int nCompact)
378 unsigned int nSize = nCompact >> 24;
379 std::vector<unsigned char> vch(4 + nSize);
381 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
382 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
383 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
384 BN_mpi2bn(&vch[0], vch.size(), this);
388 unsigned int GetCompact() const
390 unsigned int nSize = BN_bn2mpi(this, NULL);
391 std::vector<unsigned char> vch(nSize);
393 BN_bn2mpi(this, &vch[0]);
394 unsigned int nCompact = nSize << 24;
395 if (nSize >= 1) nCompact |= (vch[4] << 16);
396 if (nSize >= 2) nCompact |= (vch[5] << 8);
397 if (nSize >= 3) nCompact |= (vch[6] << 0);
401 void SetHex(const std::string& str)
404 const char* psz = str.c_str();
405 while (isspace(*psz))
407 bool fNegative = false;
413 if (psz[0] == '0' && tolower(psz[1]) == 'x')
415 while (isspace(*psz))
418 // hex string to bignum
419 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 };
421 while (isxdigit(*psz))
424 int n = phexdigit[(unsigned char)*psz++];
431 std::string ToString(int nBase=10) const
434 CBigNum bnBase = nBase;
438 BN_set_negative(&bn, false);
441 if (BN_cmp(&bn, &bn0) == 0)
443 while (BN_cmp(&bn, &bn0) > 0)
445 if (!BN_div(&dv, &rem, &bn, &bnBase, pctx))
446 throw bignum_error("CBigNum::ToString() : BN_div failed");
448 unsigned int c = rem.getulong();
449 str += "0123456789abcdef"[c];
451 if (BN_is_negative(this))
453 reverse(str.begin(), str.end());
457 std::string GetHex() const
462 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
464 return ::GetSerializeSize(getvch(), nType, nVersion);
467 template<typename Stream>
468 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
470 ::Serialize(s, getvch(), nType, nVersion);
473 template<typename Stream>
474 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
476 std::vector<unsigned char> vch;
477 ::Unserialize(s, vch, nType, nVersion);
482 * exponentiation with an int. this^e
483 * @param e the exponent as an int
486 CBigNum pow(const int e) const {
487 return this->pow(CBigNum(e));
491 * exponentiation this^e
492 * @param e the exponent
495 CBigNum pow(const CBigNum& e) const {
498 if (!BN_exp(&ret, this, &e, pctx))
499 throw bignum_error("CBigNum::pow : BN_exp failed");
504 * modular multiplication: (this * b) mod m
508 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
511 if (!BN_mod_mul(&ret, this, &b, &m, pctx))
512 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
518 * modular exponentiation: this^e mod n
522 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
527 CBigNum inv = this->inverse(m);
528 CBigNum posE = e * -1;
529 if (!BN_mod_exp(&ret, &inv, &posE, &m, pctx))
530 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
532 if (!BN_mod_exp(&ret, this, &e, &m, pctx))
533 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
539 * Calculates the inverse of this element mod m.
540 * i.e. i such this*i = 1 mod m
542 * @return the inverse
544 CBigNum inverse(const CBigNum& m) const {
547 if (!BN_mod_inverse(&ret, this, &m, pctx))
548 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
553 * Generates a random (safe) prime of numBits bits
554 * @param numBits the number of bits
555 * @param safe true for a safe prime
558 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
560 if(!BN_generate_prime_ex(&ret, numBits, (safe == true), NULL, NULL, NULL))
561 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
566 * Calculates the greatest common divisor (GCD) of two numbers.
567 * @param m the second element
570 CBigNum gcd( const CBigNum& b) const{
573 if (!BN_gcd(&ret, this, &b, pctx))
574 throw bignum_error("CBigNum::gcd*= :BN_gcd");
579 * Miller-Rabin primality test on this element
580 * @param checks: optional, the number of Miller-Rabin tests to run
581 * default causes error rate of 2^-80.
582 * @return true if prime
584 bool isPrime(const int checks=BN_prime_checks) const {
586 int ret = BN_is_prime(this, checks, NULL, pctx, NULL);
588 throw bignum_error("CBigNum::isPrime :BN_is_prime");
594 return BN_is_one(this);
598 bool operator!() const
600 return BN_is_zero(this);
603 CBigNum& operator+=(const CBigNum& b)
605 if (!BN_add(this, this, &b))
606 throw bignum_error("CBigNum::operator+= : BN_add failed");
610 CBigNum& operator-=(const CBigNum& b)
616 CBigNum& operator*=(const CBigNum& b)
619 if (!BN_mul(this, this, &b, pctx))
620 throw bignum_error("CBigNum::operator*= : BN_mul failed");
624 CBigNum& operator/=(const CBigNum& b)
630 CBigNum& operator%=(const CBigNum& b)
636 CBigNum& operator<<=(unsigned int shift)
638 if (!BN_lshift(this, this, shift))
639 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
643 CBigNum& operator>>=(unsigned int shift)
645 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
646 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
649 if (BN_cmp(&a, this) > 0)
655 if (!BN_rshift(this, this, shift))
656 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
661 CBigNum& operator++()
664 if (!BN_add(this, this, BN_value_one()))
665 throw bignum_error("CBigNum::operator++ : BN_add failed");
669 const CBigNum operator++(int)
672 const CBigNum ret = *this;
677 CBigNum& operator--()
681 if (!BN_sub(&r, this, BN_value_one()))
682 throw bignum_error("CBigNum::operator-- : BN_sub failed");
687 const CBigNum operator--(int)
690 const CBigNum ret = *this;
696 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
697 friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
698 friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b);
699 friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b);
700 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
705 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
708 if (!BN_add(&r, &a, &b))
709 throw bignum_error("CBigNum::operator+ : BN_add failed");
713 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
716 if (!BN_sub(&r, &a, &b))
717 throw bignum_error("CBigNum::operator- : BN_sub failed");
721 inline const CBigNum operator-(const CBigNum& a)
724 BN_set_negative(&r, !BN_is_negative(&r));
728 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
732 if (!BN_mul(&r, &a, &b, pctx))
733 throw bignum_error("CBigNum::operator* : BN_mul failed");
737 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
741 if (!BN_div(&r, NULL, &a, &b, pctx))
742 throw bignum_error("CBigNum::operator/ : BN_div failed");
746 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
750 if (!BN_nnmod(&r, &a, &b, pctx))
751 throw bignum_error("CBigNum::operator% : BN_div failed");
755 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
758 if (!BN_lshift(&r, &a, shift))
759 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
763 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
770 inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) == 0); }
771 inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) != 0); }
772 inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) <= 0); }
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); }
777 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
779 typedef CBigNum Bignum;