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 setuint256(uint256 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 uint256 getuint256() 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];
288 void setvch(const std::vector<unsigned char>& vch)
290 std::vector<unsigned char> vch2(vch.size() + 4);
291 unsigned int nSize = vch.size();
292 // BIGNUM's byte stream format expects 4 bytes of
293 // big endian size data info at the front
294 vch2[0] = (nSize >> 24) & 0xff;
295 vch2[1] = (nSize >> 16) & 0xff;
296 vch2[2] = (nSize >> 8) & 0xff;
297 vch2[3] = (nSize >> 0) & 0xff;
298 // swap data to big endian
299 reverse_copy(vch.begin(), vch.end(), vch2.begin() + 4);
300 BN_mpi2bn(&vch2[0], vch2.size(), this);
303 std::vector<unsigned char> getvch() const
305 unsigned int nSize = BN_bn2mpi(this, NULL);
307 return std::vector<unsigned char>();
308 std::vector<unsigned char> vch(nSize);
309 BN_bn2mpi(this, &vch[0]);
310 vch.erase(vch.begin(), vch.begin() + 4);
311 reverse(vch.begin(), vch.end());
315 CBigNum& SetCompact(unsigned int nCompact)
317 unsigned int nSize = nCompact >> 24;
318 std::vector<unsigned char> vch(4 + nSize);
320 if (nSize >= 1) vch[4] = (nCompact >> 16) & 0xff;
321 if (nSize >= 2) vch[5] = (nCompact >> 8) & 0xff;
322 if (nSize >= 3) vch[6] = (nCompact >> 0) & 0xff;
323 BN_mpi2bn(&vch[0], vch.size(), this);
327 unsigned int GetCompact() const
329 unsigned int nSize = BN_bn2mpi(this, NULL);
330 std::vector<unsigned char> vch(nSize);
332 BN_bn2mpi(this, &vch[0]);
333 unsigned int nCompact = nSize << 24;
334 if (nSize >= 1) nCompact |= (vch[4] << 16);
335 if (nSize >= 2) nCompact |= (vch[5] << 8);
336 if (nSize >= 3) nCompact |= (vch[6] << 0);
340 void SetHex(const std::string& str)
343 const char* psz = str.c_str();
344 while (isspace(*psz))
346 bool fNegative = false;
352 if (psz[0] == '0' && tolower(psz[1]) == 'x')
354 while (isspace(*psz))
357 // hex string to bignum
358 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 };
360 while (isxdigit(*psz))
363 int n = phexdigit[(unsigned char)*psz++];
370 std::string ToString(int nBase=10) const
373 CBigNum bnBase = nBase;
377 BN_set_negative(&bn, false);
380 if (BN_cmp(&bn, &bn0) == 0)
382 while (BN_cmp(&bn, &bn0) > 0)
384 if (!BN_div(&dv, &rem, &bn, &bnBase, pctx))
385 throw bignum_error("CBigNum::ToString() : BN_div failed");
387 unsigned int c = rem.getulong();
388 str += "0123456789abcdef"[c];
390 if (BN_is_negative(this))
392 reverse(str.begin(), str.end());
396 std::string GetHex() const
401 unsigned int GetSerializeSize(int nType=0, int nVersion=PROTOCOL_VERSION) const
403 return ::GetSerializeSize(getvch(), nType, nVersion);
406 template<typename Stream>
407 void Serialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION) const
409 ::Serialize(s, getvch(), nType, nVersion);
412 template<typename Stream>
413 void Unserialize(Stream& s, int nType=0, int nVersion=PROTOCOL_VERSION)
415 std::vector<unsigned char> vch;
416 ::Unserialize(s, vch, nType, nVersion);
421 * exponentiation with an int. this^e
422 * @param e the exponent as an int
425 CBigNum pow(const int e) const {
426 return this->pow(CBigNum(e));
430 * exponentiation this^e
431 * @param e the exponent
434 CBigNum pow(const CBigNum& e) const {
437 if (!BN_exp(&ret, this, &e, pctx))
438 throw bignum_error("CBigNum::pow : BN_exp failed");
443 * modular multiplication: (this * b) mod m
447 CBigNum mul_mod(const CBigNum& b, const CBigNum& m) const {
450 if (!BN_mod_mul(&ret, this, &b, &m, pctx))
451 throw bignum_error("CBigNum::mul_mod : BN_mod_mul failed");
457 * modular exponentiation: this^e mod n
461 CBigNum pow_mod(const CBigNum& e, const CBigNum& m) const {
466 CBigNum inv = this->inverse(m);
467 CBigNum posE = e * -1;
468 if (!BN_mod_exp(&ret, &inv, &posE, &m, pctx))
469 throw bignum_error("CBigNum::pow_mod: BN_mod_exp failed on negative exponent");
471 if (!BN_mod_exp(&ret, this, &e, &m, pctx))
472 throw bignum_error("CBigNum::pow_mod : BN_mod_exp failed");
478 * Calculates the inverse of this element mod m.
479 * i.e. i such this*i = 1 mod m
481 * @return the inverse
483 CBigNum inverse(const CBigNum& m) const {
486 if (!BN_mod_inverse(&ret, this, &m, pctx))
487 throw bignum_error("CBigNum::inverse*= :BN_mod_inverse");
492 * Generates a random (safe) prime of numBits bits
493 * @param numBits the number of bits
494 * @param safe true for a safe prime
497 static CBigNum generatePrime(const unsigned int numBits, bool safe = false) {
499 if(!BN_generate_prime_ex(&ret, numBits, (safe == true), NULL, NULL, NULL))
500 throw bignum_error("CBigNum::generatePrime*= :BN_generate_prime_ex");
505 * Calculates the greatest common divisor (GCD) of two numbers.
506 * @param m the second element
509 CBigNum gcd( const CBigNum& b) const{
512 if (!BN_gcd(&ret, this, &b, pctx))
513 throw bignum_error("CBigNum::gcd*= :BN_gcd");
518 * Miller-Rabin primality test on this element
519 * @param checks: optional, the number of Miller-Rabin tests to run
520 * default causes error rate of 2^-80.
521 * @return true if prime
523 bool isPrime(const int checks=BN_prime_checks) const {
525 int ret = BN_is_prime(this, checks, NULL, pctx, NULL);
527 throw bignum_error("CBigNum::isPrime :BN_is_prime");
533 return BN_is_one(this);
537 bool operator!() const
539 return BN_is_zero(this);
542 CBigNum& operator+=(const CBigNum& b)
544 if (!BN_add(this, this, &b))
545 throw bignum_error("CBigNum::operator+= : BN_add failed");
549 CBigNum& operator-=(const CBigNum& b)
555 CBigNum& operator*=(const CBigNum& b)
558 if (!BN_mul(this, this, &b, pctx))
559 throw bignum_error("CBigNum::operator*= : BN_mul failed");
563 CBigNum& operator/=(const CBigNum& b)
569 CBigNum& operator%=(const CBigNum& b)
575 CBigNum& operator<<=(unsigned int shift)
577 if (!BN_lshift(this, this, shift))
578 throw bignum_error("CBigNum:operator<<= : BN_lshift failed");
582 CBigNum& operator>>=(unsigned int shift)
584 // Note: BN_rshift segfaults on 64-bit if 2^shift is greater than the number
585 // if built on ubuntu 9.04 or 9.10, probably depends on version of OpenSSL
588 if (BN_cmp(&a, this) > 0)
594 if (!BN_rshift(this, this, shift))
595 throw bignum_error("CBigNum:operator>>= : BN_rshift failed");
600 CBigNum& operator++()
603 if (!BN_add(this, this, BN_value_one()))
604 throw bignum_error("CBigNum::operator++ : BN_add failed");
608 const CBigNum operator++(int)
611 const CBigNum ret = *this;
616 CBigNum& operator--()
620 if (!BN_sub(&r, this, BN_value_one()))
621 throw bignum_error("CBigNum::operator-- : BN_sub failed");
626 const CBigNum operator--(int)
629 const CBigNum ret = *this;
635 friend inline const CBigNum operator-(const CBigNum& a, const CBigNum& b);
636 friend inline const CBigNum operator/(const CBigNum& a, const CBigNum& b);
637 friend inline const CBigNum operator%(const CBigNum& a, const CBigNum& b);
638 friend inline const CBigNum operator*(const CBigNum& a, const CBigNum& b);
639 friend inline bool operator<(const CBigNum& a, const CBigNum& b);
644 inline const CBigNum operator+(const CBigNum& a, const CBigNum& b)
647 if (!BN_add(&r, &a, &b))
648 throw bignum_error("CBigNum::operator+ : BN_add failed");
652 inline const CBigNum operator-(const CBigNum& a, const CBigNum& b)
655 if (!BN_sub(&r, &a, &b))
656 throw bignum_error("CBigNum::operator- : BN_sub failed");
660 inline const CBigNum operator-(const CBigNum& a)
663 BN_set_negative(&r, !BN_is_negative(&r));
667 inline const CBigNum operator*(const CBigNum& a, const CBigNum& b)
671 if (!BN_mul(&r, &a, &b, pctx))
672 throw bignum_error("CBigNum::operator* : BN_mul failed");
676 inline const CBigNum operator/(const CBigNum& a, const CBigNum& b)
680 if (!BN_div(&r, NULL, &a, &b, pctx))
681 throw bignum_error("CBigNum::operator/ : BN_div failed");
685 inline const CBigNum operator%(const CBigNum& a, const CBigNum& b)
689 if (!BN_nnmod(&r, &a, &b, pctx))
690 throw bignum_error("CBigNum::operator% : BN_div failed");
694 inline const CBigNum operator<<(const CBigNum& a, unsigned int shift)
697 if (!BN_lshift(&r, &a, shift))
698 throw bignum_error("CBigNum:operator<< : BN_lshift failed");
702 inline const CBigNum operator>>(const CBigNum& a, unsigned int shift)
709 inline bool operator==(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) == 0); }
710 inline bool operator!=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) != 0); }
711 inline bool operator<=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) <= 0); }
712 inline bool operator>=(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) >= 0); }
713 inline bool operator<(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) < 0); }
714 inline bool operator>(const CBigNum& a, const CBigNum& b) { return (BN_cmp(&a, &b) > 0); }
716 inline std::ostream& operator<<(std::ostream &strm, const CBigNum &b) { return strm << b.ToString(10); }
718 typedef CBigNum Bignum;