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(int8_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
96 CBigNum(int16_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
97 CBigNum(int32_t n) { bn = BN_new(); if (n >= 0) setuint32(n); else setint64(n); }
98 CBigNum(int64_t n) { bn = BN_new(); if (n >= 0) setuint64(n); else setint64(n); }
100 CBigNum(uint8_t n) { bn = BN_new(); setuint32(n); }
101 CBigNum(uint16_t n) { bn = BN_new(); setuint32(n); }
102 CBigNum(uint32_t n) { bn = BN_new(); setuint32(n); }
103 CBigNum(uint64_t n) { bn = BN_new(); setuint64(n); }
105 explicit CBigNum(uint256 n) { bn = BN_new(); setuint256(n); }
106 explicit CBigNum(const std::vector<uint8_t>& vch)
112 /** Generates a cryptographically secure random number between zero and range exclusive
113 * i.e. 0 < returned number < range
114 * @param range The upper bound on the number.
117 static CBigNum randBignum(const CBigNum& range) {
119 if(!BN_rand_range(ret.bn, range.bn)){
120 throw bignum_error("CBigNum:rand element : BN_rand_range failed");
125 /** Generates a cryptographically secure random k-bit number
126 * @param k The bit length of the number.
129 static CBigNum RandKBitBigum(const uint32_t k){
131 if(!BN_rand(ret.bn, k, -1, 0)){
132 throw bignum_error("CBigNum:rand element : BN_rand failed");
137 /**Returns the size in bits of the underlying bignum.
142 return BN_num_bits(bn);
146 void setuint32(uint32_t n)
148 if (!BN_set_word(bn, n))
149 throw bignum_error("CBigNum conversion from uint32_t : BN_set_word failed");
152 uint32_t getuint32() const
154 return BN_get_word(bn);
157 int32_t getint32() const
159 uint64_t n = BN_get_word(bn);
160 if (!BN_is_negative(bn))
161 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::max() : (int32_t)n);
163 return (n > (uint64_t)std::numeric_limits<int32_t>::max() ? std::numeric_limits<int32_t>::min() : -(int32_t)n);
166 void setint64(int64_t sn)
168 uint8_t pch[sizeof(sn) + 6];
169 uint8_t* p = pch + 4;
175 // 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
184 bool fLeadingZeroes = true;
185 for (int i = 0; i < 8; i++)
187 uint8_t c = (n >> 56) & 0xff;
194 *p++ = (fNegative ? 0x80 : 0);
197 fLeadingZeroes = false;
201 uint32_t nSize = (uint32_t) (p - (pch + 4));
202 pch[0] = (nSize >> 24) & 0xff;
203 pch[1] = (nSize >> 16) & 0xff;
204 pch[2] = (nSize >> 8) & 0xff;
205 pch[3] = (nSize) & 0xff;
206 BN_mpi2bn(pch, (int)(p - pch), bn);
211 size_t nSize = BN_bn2mpi(bn, NULL);
214 std::vector<uint8_t> vch(nSize);
215 BN_bn2mpi(bn, &vch[0]);
219 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
220 ((uint8_t*)&n)[i] = vch[j];
224 //supress msvc C4127: conditional expression is constant
225 inline bool check(bool value) {return value;}
227 void setuint64(uint64_t n)
229 // Use BN_set_word if word size is sufficient for uint64_t
230 if (check(sizeof(n) <= sizeof(BN_ULONG)))
232 if (!BN_set_word(bn, (BN_ULONG)n))
233 throw bignum_error("CBigNum conversion from uint64_t : BN_set_word failed");
237 uint8_t pch[sizeof(n) + 6];
238 uint8_t* p = pch + 4;
239 bool fLeadingZeroes = true;
240 for (int i = 0; i < 8; i++)
242 uint8_t c = (n >> 56) & 0xff;
250 fLeadingZeroes = false;
254 uint32_t nSize = (uint32_t) (p - (pch + 4));
255 pch[0] = (nSize >> 24) & 0xff;
256 pch[1] = (nSize >> 16) & 0xff;
257 pch[2] = (nSize >> 8) & 0xff;
258 pch[3] = (nSize) & 0xff;
259 BN_mpi2bn(pch, (int)(p - pch), bn);
262 void setuint160(uint160 n)
264 uint8_t pch[sizeof(n) + 6];
265 uint8_t* p = pch + 4;
266 bool fLeadingZeroes = true;
267 uint8_t* pbegin = (uint8_t*)&n;
268 uint8_t* psrc = pbegin + sizeof(n);
269 while (psrc != pbegin)
271 uint8_t c = *(--psrc);
278 fLeadingZeroes = false;
282 uint32_t nSize = (uint32_t) (p - (pch + 4));
283 pch[0] = (nSize >> 24) & 0xff;
284 pch[1] = (nSize >> 16) & 0xff;
285 pch[2] = (nSize >> 8) & 0xff;
286 pch[3] = (nSize >> 0) & 0xff;
287 BN_mpi2bn(pch, (int) (p - pch), bn);
290 uint160 getuint160() const
292 unsigned int nSize = BN_bn2mpi(bn, NULL);
295 std::vector<uint8_t> vch(nSize);
296 BN_bn2mpi(bn, &vch[0]);
300 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
301 ((uint8_t*)&n)[i] = vch[j];
305 void setuint256(uint256 n)
307 uint8_t pch[sizeof(n) + 6];
308 uint8_t* p = pch + 4;
309 bool fLeadingZeroes = true;
310 uint8_t* pbegin = (uint8_t*)&n;
311 uint8_t* psrc = pbegin + sizeof(n);
312 while (psrc != pbegin)
314 uint8_t c = *(--psrc);
321 fLeadingZeroes = false;
325 uint32_t nSize = (uint32_t) (p - (pch + 4));
326 pch[0] = (nSize >> 24) & 0xff;
327 pch[1] = (nSize >> 16) & 0xff;
328 pch[2] = (nSize >> 8) & 0xff;
329 pch[3] = (nSize >> 0) & 0xff;
330 BN_mpi2bn(pch, (int) (p - pch), bn);
333 uint256 getuint256() const
335 unsigned int nSize = BN_bn2mpi(bn, NULL);
338 std::vector<uint8_t> vch(nSize);
339 BN_bn2mpi(bn, &vch[0]);
343 for (size_t i = 0, j = vch.size()-1; i < sizeof(n) && j >= 4; i++, j--)
344 ((uint8_t*)&n)[i] = vch[j];
348 void setBytes(const std::vector<uint8_t>& vchBytes)
350 BN_bin2bn(&vchBytes[0], (int) vchBytes.size(), bn);
353 std::vector<uint8_t> getBytes() const
355 int nBytes = BN_num_bytes(bn);
357 std::vector<uint8_t> vchBytes(nBytes);
359 int n = BN_bn2bin(bn, &vchBytes[0]);
361 throw bignum_error("CBigNum::getBytes : BN_bn2bin failed");
367 void setvch(const std::vector<uint8_t>& vch)
369 std::vector<uint8_t> vch2(vch.size() + 4);
370 uint32_t nSize = (uint32_t) vch.size();
371 // BIGNUM's byte stream format expects 4 bytes of
372 // big endian size data info at the front
373 vch2[0] = (nSize >> 24) & 0xff;
374 vch2[1] = (nSize >> 16) & 0xff;
375 vch2[2] = (nSize >> 8) & 0xff;
376 vch2[3] = (nSize >> 0) & 0xff;
377 // swap data to big endian
378 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
379 BN_mpi2bn(&vch2[0], (int) vch2.size(), bn);
382 std::vector<uint8_t> getvch() const
384 unsigned int nSize = BN_bn2mpi(bn, NULL);
386 return std::vector<uint8_t>();
387 std::vector<uint8_t> vch(nSize);
388 BN_bn2mpi(bn, &vch[0]);
389 vch.erase(vch.begin(), vch.begin() + 4);
390 reverse(vch.begin(), vch.end());
394 CBigNum& SetCompact(uint32_t nCompact)
396 uint32_t nSize = nCompact >> 24;
397 std::vector<uint8_t> vch(4 + nSize);
399 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
400 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
401 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
402 BN_mpi2bn(&vch[0], (int) vch.size(), bn);
406 uint32_t GetCompact() const
408 uint32_t nSize = BN_bn2mpi(bn, NULL);
409 std::vector<uint8_t> vch(nSize);
411 BN_bn2mpi(bn, &vch[0]);
412 uint32_t nCompact = nSize << 24;
413 if (nSize >= 1) nCompact |= (vch[4] << 16);
414 if (nSize >= 2) nCompact |= (vch[5] << 8);
415 if (nSize >= 3) nCompact |= (vch[6] << 0);
419 void SetHex(const std::string& str)
422 const char* psz = str.c_str();
423 while (isspace(*psz))
425 bool fNegative = false;
431 if (psz[0] == '0' && tolower(psz[1]) == 'x')
433 while (isspace(*psz))
436 // hex string to bignum
437 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 };
439 while (isxdigit(*psz))
442 int n = phexdigit[(uint8_t)*psz++];
449 std::string ToString(int nBase=10) const
452 CBigNum bnBase = nBase;
456 BN_set_negative(bn.bn, false);
459 if (BN_cmp(bn.bn, bn0.bn) == 0)
461 while (BN_cmp(bn.bn, bn0.bn) > 0)
463 if (!BN_div(dv.bn, rem.bn, bn.bn, bnBase.bn, pctx))
464 throw bignum_error("CBigNum::ToString() : BN_div failed");
466 uint32_t c = rem.getuint32();
467 str += "0123456789abcdef"[c];
469 if (BN_is_negative(bn.bn))
471 reverse(str.begin(), str.end());
475 std::string GetHex() const
480 BIGNUM* get() const {
484 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
486 return ::GetSerializeSize(getvch(), nType, nVersion);
489 template<typename Stream>
490 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
492 ::Serialize(s, getvch(), nType, nVersion);
495 template<typename Stream>
496 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
498 std::vector<uint8_t> vch;
499 ::Unserialize(s, vch, nType, nVersion);
504 * exponentiation with an int. this^e
505 * @param e the exponent as an int
508 CBigNum pow(const int e) const {
509 return this->pow(CBigNum(e));
513 * exponentiation this^e
514 * @param e the exponent
517 CBigNum pow(const CBigNum& e) const {
520 if (!BN_exp(ret.bn, bn, e.bn, pctx))
521 throw bignum_error("CBigNum::pow : BN_exp failed");
526 * modular multiplication: (this * b) mod m
530 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
533 if (!BN_mod_mul(ret.bn, bn, b.bn, m.bn, pctx))
534 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
540 * modular exponentiation: this^e mod n
544 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
549 CBigNum inv = this->inverse(m);
550 CBigNum posE = e * -1;
551 if (!BN_mod_exp(ret.bn, inv.bn, posE.bn, m.bn, pctx))
552 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
554 if (!BN_mod_exp(ret.bn, bn, e.bn, m.bn, pctx))
555 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
561 * Calculates the inverse of this element mod m.
562 * i.e. i such this*i = 1 mod m
564 * @return the inverse
566 CBigNum inverse(const CBigNum& m) const {
569 if (!BN_mod_inverse(ret.bn, bn, m.bn, pctx))
570 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
575 * Generates a random (safe) prime of numBits bits
576 * @param numBits the number of bits
577 * @param safe true for a safe prime
580 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
582 if(!BN_generate_prime_ex(ret.bn, numBits, (safe == true), NULL, NULL, NULL))
583 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
588 * Calculates the greatest common divisor (GCD) of two numbers.
589 * @param m the second element
592 CBigNum gcd( const CBigNum& b) const{
595 if (!BN_gcd(ret.bn, bn, b.bn, pctx))
596 throw bignum_error("CBigNum::gcd*= :BN_gcd");
601 * Miller-Rabin primality test on this element
602 * @param checks: optional, the number of Miller-Rabin tests to run
603 * default causes error rate of 2^-80.
604 * @return true if prime
606 bool isPrime(const int checks=BN_prime_checks) const {
608 int ret = BN_is_prime_ex(bn, checks, pctx, NULL);
610 throw bignum_error("CBigNum::isPrime :BN_is_prime");
616 return BN_is_one(bn);
620 bool operator!() const
622 return BN_is_zero(bn);
625 CBigNum& operator+=(const CBigNum& b)
627 if (!BN_add(bn, bn, b.bn))
628 throw bignum_error("CBigNum::operator+= : BN_add failed");
632 CBigNum& operator-=(const CBigNum& b)
638 CBigNum& operator*=(const CBigNum& b)
641 if (!BN_mul(bn, bn, b.bn, pctx))
642 throw bignum_error("CBigNum::operator*= : BN_mul failed");
646 CBigNum& operator/=(const CBigNum& b)
652 CBigNum& operator%=(const CBigNum& b)
658 CBigNum& operator<<=(unsigned int shift)
660 if (!BN_lshift(bn, bn, shift))
661 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
665 CBigNum& operator>>=(unsigned int shift)
667 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
668 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
671 if (BN_cmp(a.bn, bn) > 0)
677 if (!BN_rshift(bn, bn, shift))
678 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
683 CBigNum& operator++()
686 if (!BN_add(bn, bn, BN_value_one()))
687 throw bignum_error("CBigNum::operator++ : BN_add failed");
691 const CBigNum operator++(int)
694 const CBigNum ret = *this;
699 CBigNum& operator--()
703 if (!BN_sub(r.bn, bn, BN_value_one()))
704 throw bignum_error("CBigNum::operator-- : BN_sub failed");
709 const CBigNum operator--(int)
712 const CBigNum ret = *this;
717 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
718 friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
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 bool 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;