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/*
* BigInt
* (C) 1999-2008 Jack Lloyd
* 2007 FlexSecure
*
* Distributed under the terms of the Botan license
*/
#ifndef BOTAN_BIGINT_H__
#define BOTAN_BIGINT_H__
#include <botan/rng.h>
#include <botan/secmem.h>
#include <botan/mp_types.h>
#include <iosfwd>
namespace Botan {
/**
* Arbitrary precision integer
*/
class BOTAN_DLL BigInt
{
public:
/**
* Base enumerator for encoding and decoding
*/
enum Base { Octal = 8, Decimal = 10, Hexadecimal = 16, Binary = 256 };
/**
* Sign symbol definitions for positive and negative numbers
*/
enum Sign { Negative = 0, Positive = 1 };
/**
* Number types (currently only power-of-2 supported)
*/
enum NumberType { Power2 };
/**
* DivideByZero Exception
*/
struct BOTAN_DLL DivideByZero : public Exception
{ DivideByZero() : Exception("BigInt divide by zero") {} };
/**
* += operator
* @param y the BigInt to add to this
*/
BigInt& operator+=(const BigInt& y);
/**
* -= operator
* @param y the BigInt to subtract from this
*/
BigInt& operator-=(const BigInt& y);
/**
* *= operator
* @param y the BigInt to multiply with this
*/
BigInt& operator*=(const BigInt& y);
/**
* /= operator
* @param y the BigInt to divide this by
*/
BigInt& operator/=(const BigInt& y);
/**
* Modulo operator
* @param y the modulus to reduce this by
*/
BigInt& operator%=(const BigInt& y);
/**
* Modulo operator
* @param y the modulus (word) to reduce this by
*/
word operator%=(word y);
/**
* Left shift operator
* @param shift the number of bits to shift this left by
*/
BigInt& operator<<=(u32bit shift);
/**
* Right shift operator
* @param shift the number of bits to shift this right by
*/
BigInt& operator>>=(u32bit shift);
/**
* Increment operator
*/
BigInt& operator++() { return (*this += 1); }
/**
* Decrement operator
*/
BigInt& operator--() { return (*this -= 1); }
/**
* Postfix increment operator
*/
BigInt operator++(int) { BigInt x = (*this); ++(*this); return x; }
/**
* Postfix decrement operator
*/
BigInt operator--(int) { BigInt x = (*this); --(*this); return x; }
/**
* Unary negation operator
* @return negative this
*/
BigInt operator-() const;
/**
* ! operator
* @return true iff this is zero, otherwise false
*/
bool operator !() const { return (!is_nonzero()); }
/**
* [] operator (array access)
* @param i a word index
* @return the word at index i
*/
word& operator[](u32bit i) { return reg[i]; }
/**
* [] operator (array access)
* @param i a word index
* @return the word at index i
*/
word operator[](u32bit i) const { return reg[i]; }
/**
* Zeroize the BigInt
*/
void clear() { get_reg().clear(); }
/**
* Compare this to another BigInt
* @param n the BigInt value to compare with
* @param check_signs include sign in comparison?
* @result if (this<n) return -1, if (this>n) return 1, if both
* values are identical return 0 [like Perl's <=> operator]
*/
s32bit cmp(const BigInt& n, bool check_signs = true) const;
/**
* Test if the integer has an even value
* @result true if the integer is even, false otherwise
*/
bool is_even() const { return (get_bit(0) == 0); }
/**
* Test if the integer has an odd value
* @result true if the integer is odd, false otherwise
*/
bool is_odd() const { return (get_bit(0) == 1); }
/**
* Test if the integer is not zero
* @result true if the integer is non-zero, false otherwise
*/
bool is_nonzero() const { return (!is_zero()); }
/**
* Test if the integer is zero
* @result true if the integer is zero, false otherwise
*/
bool is_zero() const
{
const u32bit sw = sig_words();
for(u32bit i = 0; i != sw; ++i)
if(reg[i])
return false;
return true;
}
/**
* Set bit at specified position
* @param n bit position to set
*/
void set_bit(u32bit n);
/**
* Clear bit at specified position
* @param n bit position to clear
*/
void clear_bit(u32bit n);
/**
* Clear all but the lowest n bits
* @param n amount of bits to keep
*/
void mask_bits(u32bit n);
/**
* Return bit value at specified position
* @param n the bit offset to test
* @result true, if the bit at position n is set, false otherwise
*/
bool get_bit(u32bit n) const;
/**
* Return (a maximum of) 32 bits of the complete value
* @param offset the offset to start extracting
* @param length amount of bits to extract (starting at offset)
* @result the integer extracted from the register starting at
* offset with specified length
*/
u32bit get_substring(u32bit offset, u32bit length) const;
/**
* @param n the offset to get a byte from
* @result byte at offset n
*/
byte byte_at(u32bit n) const;
/**
* Return the word at a specified position of the internal register
* @param n position in the register
* @return value at position n
*/
word word_at(u32bit n) const
{ return ((n < size()) ? reg[n] : 0); }
/**
* Return the integer as an unsigned 32bit-integer-value. If the
* value is negative OR too big to be stored in a u32bit, this
* function will throw an exception.
*
* @result unsigned 32 bit representation of this
*/
u32bit to_u32bit() const;
/**
* Tests if the sign of the integer is negative
* @result true, iff the integer has a negative sign
*/
bool is_negative() const { return (sign() == Negative); }
/**
* Tests if the sign of the integer is positive
* @result true, iff the integer has a positive sign
*/
bool is_positive() const { return (sign() == Positive); }
/**
* Return the sign of the integer
* @result the sign of the integer
*/
Sign sign() const { return (signedness); }
/**
* @result the opposite sign of the represented integer value
*/
Sign reverse_sign() const;
/**
* Flip the sign of this BigInt
*/
void flip_sign();
/**
* Set sign of the integer
* @param sign new Sign to set
*/
void set_sign(Sign sign);
/**
* @result absolute (positive) value of this
*/
BigInt abs() const;
/**
* Give size of internal register
* @result size of internal register in words
*/
u32bit size() const { return get_reg().size(); }
/**
* Return how many words we need to hold this value
* @result significant words of the represented integer value
*/
u32bit sig_words() const
{
const word* x = reg.begin();
u32bit sig = reg.size();
while(sig && (x[sig-1] == 0))
sig--;
return sig;
}
/**
* Give byte length of the integer
* @result byte length of the represented integer value
*/
u32bit bytes() const;
/**
* Get the bit length of the integer
* @result bit length of the represented integer value
*/
u32bit bits() const;
/**
* Return a pointer to the big integer word register
* @result a pointer to the start of the internal register of
* the integer value
*/
const word* data() const { return reg.begin(); }
/**
* return a reference to the internal register containing the value
* @result a reference to the word-array (SecureVector<word>)
* with the internal register value (containing the integer
* value)
*/
SecureVector<word>& get_reg() { return reg; }
/**
* return a const reference to the internal register containing the value
* @result a const reference to the word-array (SecureVector<word>)
* with the internal register value (containing the integer value)
*/
const SecureVector<word>& get_reg() const { return reg; }
/**
* Increase internal register buffer by n words
* @param n increase by n words
*/
void grow_reg(u32bit n);
void grow_to(u32bit n);
/**
* Fill BigInt with a random number with size of bitsize
* @param rng the random number generator to use
* @param bitsize number of bits the created random value should have
*/
void randomize(RandomNumberGenerator& rng, u32bit bitsize = 0);
/**
* Store BigInt-value in a given byte array
* @param buf destination byte array for the integer value
*/
void binary_encode(byte buf[]) const;
/**
* Read integer value from a byte array with given size
* @param buf byte array buffer containing the integer
* @param length size of buf
*/
void binary_decode(const byte buf[], u32bit length);
/**
* Read integer value from a byte array (MemoryRegion<byte>)
* @param buf the array to load from
*/
void binary_decode(const MemoryRegion<byte>& buf);
/**
* @param base the base to measure the size for
* @return size of this integer in base base
*/
u32bit encoded_size(Base base = Binary) const;
/**
* @param rng a random number generator
* @param min the minimum value
* @param max the maximum value
* @return random integer between min and max
*/
static BigInt random_integer(RandomNumberGenerator& rng,
const BigInt& min,
const BigInt& max);
/**
* Encode the integer value from a BigInt to a SecureVector of bytes
* @param n the BigInt to use as integer source
* @param base number-base of resulting byte array representation
* @result SecureVector of bytes containing the integer with given base
*/
static SecureVector<byte> encode(const BigInt& n, Base base = Binary);
/**
* Encode the integer value from a BigInt to a byte array
* @param buf destination byte array for the encoded integer
* value with given base
* @param n the BigInt to use as integer source
* @param base number-base of resulting byte array representation
*/
static void encode(byte buf[], const BigInt& n, Base base = Binary);
/**
* Create a BigInt from an integer in a byte array
* @param buf the binary value to load
* @param length size of buf
* @param base number-base of the integer in buf
* @result BigInt representing the integer in the byte array
*/
static BigInt decode(const byte buf[], u32bit length,
Base base = Binary);
/**
* Create a BigInt from an integer in a byte array
* @param buf the binary value to load
* @param base number-base of the integer in buf
* @result BigInt representing the integer in the byte array
*/
static BigInt decode(const MemoryRegion<byte>& buf,
Base base = Binary);
/**
* Encode a BigInt to a byte array according to IEEE 1363
* @param n the BigInt to encode
* @param bytes the length of the resulting SecureVector<byte>
* @result a SecureVector<byte> containing the encoded BigInt
*/
static SecureVector<byte> encode_1363(const BigInt& n, u32bit bytes);
/**
* Swap this value with another
* @param other BigInt to swap values with
*/
void swap(BigInt& other);
/**
* Create empty BigInt
*/
BigInt() { signedness = Positive; }
/**
* Create BigInt from 64 bit integer
* @param n initial value of this BigInt
*/
BigInt(u64bit n);
/**
* Copy Constructor
* @param other the BigInt to copy
*/
BigInt(const BigInt& other);
/**
* Create BigInt from a string. If the string starts with 0x the
* rest of the string will be interpreted as hexadecimal digits.
* If the string starts with 0 and the second character is NOT an
* 'x' the string will be interpreted as octal digits. If the
* string starts with non-zero digit, it will be interpreted as a
* decimal number.
*
* @param str the string to parse for an integer value
*/
BigInt(const std::string& str);
/**
* Create a BigInt from an integer in a byte array
* @param buf the byte array holding the value
* @param length size of buf
* @param base is the number base of the integer in buf
*/
BigInt(const byte buf[], u32bit length, Base base = Binary);
/**
* Create a random BigInt of the specified size
* @param rng random number generator
* @param bits size in bits
*/
BigInt(RandomNumberGenerator& rng, u32bit bits);
/**
* Create BigInt of specified size, all zeros
* @param sign the sign
* @param n size of the internal register in words
*/
BigInt(Sign sign, u32bit n);
/**
* Create a number of the specified type and size
* @param type the type of number to create. For Power2,
* will create the integer 2^n
* @param n a size/length parameter, interpretation depends upon
* the value of type
*/
BigInt(NumberType type, u32bit n);
private:
SecureVector<word> reg;
Sign signedness;
};
/*
* Arithmetic Operators
*/
BigInt BOTAN_DLL operator+(const BigInt& x, const BigInt& y);
BigInt BOTAN_DLL operator-(const BigInt& x, const BigInt& y);
BigInt BOTAN_DLL operator*(const BigInt& x, const BigInt& y);
BigInt BOTAN_DLL operator/(const BigInt& x, const BigInt& d);
BigInt BOTAN_DLL operator%(const BigInt& x, const BigInt& m);
word BOTAN_DLL operator%(const BigInt& x, word m);
BigInt BOTAN_DLL operator<<(const BigInt& x, u32bit n);
BigInt BOTAN_DLL operator>>(const BigInt& x, u32bit n);
/*
* Comparison Operators
*/
inline bool operator==(const BigInt& a, const BigInt& b)
{ return (a.cmp(b) == 0); }
inline bool operator!=(const BigInt& a, const BigInt& b)
{ return (a.cmp(b) != 0); }
inline bool operator<=(const BigInt& a, const BigInt& b)
{ return (a.cmp(b) <= 0); }
inline bool operator>=(const BigInt& a, const BigInt& b)
{ return (a.cmp(b) >= 0); }
inline bool operator<(const BigInt& a, const BigInt& b)
{ return (a.cmp(b) < 0); }
inline bool operator>(const BigInt& a, const BigInt& b)
{ return (a.cmp(b) > 0); }
/*
* I/O Operators
*/
BOTAN_DLL std::ostream& operator<<(std::ostream&, const BigInt&);
BOTAN_DLL std::istream& operator>>(std::istream&, BigInt&);
}
namespace std {
inline void swap(Botan::BigInt& a, Botan::BigInt& b) { a.swap(b); }
}
#endif
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