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FBB::BigInt

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FBB::BigInt: Arithmetic on Integers of Unlimited Size

NAME
FBB::BigInt - Arithmetic on Integers of Unlimited Size

SYNOPSIS

#include <bobcat/bigint> Linking option: -lssl -lbobcat

DESCRIPTION

This class is defined as a wrapper class around the openSSL BN series of functions, offering members to perform arithmetic on integral values of unlimited sizes. Members are offered to generate primes and to perform all kinds of common arithmetic operations on BigInt objects. Also, conversions to characters and standard numerical value types are offered. Below, the phrase the object may also refer to the object's value. The context in which this occurs will make clear that the object's value rather than the object as-is is referred to. Various constructors accept BIGNUM arguments. Type BIGNUM is the type containing an integer of unlimited precision as defined by OpenSSL. Signs of BigInt are handled in a special way. Whether a BigInt is negative or positive is determined by its sign-flag, and not by a sign bit as is the case with int typed values. Since BigInt values have unlimited precision shifting values to the left won't change their signs. Operators return either a reference to the current (modified) object or return a BigInt const object containing the computed value. The rule followed here was to implement the operators analogously to the way the operators work on int type values and variables. E.g., operator+() returns a BigInt const value whereas operator+=() returns a BigInt & reference. All members modifying their objects return a reference to the current (modified) object. All members not modifying the current object return a BigInt const object. If both members exists performing the same functionality the name of the member returning a BigInt const object ends in a c (const) (e.g., addMod and addModc. Almost all operators, members and constructors (except for the default constructor) throw Errno exceptions on failure.

INHERITS FROM

-

ENUMERATIONS

Msb This (most significant bit) enumeration is used when generating a cryptographically strong random number. Its values are: o MSB_UNKNOWN: The most significant bit may be 0 or 1. o MSB_IS_ONE: The most significant bit is guaranteed to be 1. o TOP_TWO_BITS_ONE: The two most significant bits are guaranteed to be 1, resulting in a product of two values each containing nBits having 2 * nBits bits. Lsb This (least significant bit) enumeration is used when generating random numbers, ensuring that the resulting value is either odd or even. o EVEN: The random value will be an even value; o ODD: The random value will be an odd value.
CONSTRUCTORS
o BigInt(): The default constructor initializes a BigInt value to 0. o BigInt(BIGNUM const &value): This constructor initializes a BigInt from a BIGNUM. o BigInt(BIGNUM const *value): This constructor initializes a BigInt from a pointer to a const BIGNUM. o BigInt(Type value): This constructor is defined as a member template. Any type that can be converted using a static cast to an unsigned long can be used as argument to this constructor. Promotion is allowed, so in many situations where BigInts are expected a plain numerical value can be used as well. The standard copy constructor is available.
MEMBER FUNCTIONS
o BigInt &addMod(BigInt const &rhs, BigInt const &mod) : Rhs is added (modulo mod) to the current object. o BigInt const addModc(BigInt const &rhs, BigInt const &mod) : The sum (modulo mod) of the current object and rhs is returned. o BIGNUM const &bignum() const: A reference to the BIGNUM value maintained by the current BigInt object is returned. o char *bigEndian() const: The value represented by the current object is stored in a series of char typed values in big-endian order. If a value consists of 5 chars the eight most significant bits will be stored in the char having index value 0, the eight least significant bits will be stored in the char having index value 4. When needed simply swap char[i] with char[j] (i = 0 .. nBytes/2, j = nBytes-1 .. nBytes/2) to convert to little-endian order. The return value consists of a series of sizeInBytes() (see below) dynamically allocated char values. The caller of bigEndian owns the allocated memory and should eventually delete it again using delete[]. Note that the current object's sign cannot be inferred from the return value. o BigInt &clearBit(size_t index): The current object's bit at index position index is cleared. o BigInt const clearBit(size_t index) const: A copy of the current object having its bit at index position index cleared. o BigInt &div(BigInt *remainder, BigInt const &rhs): The current object is divided by rhs. The division's remainder is returned in *remainder. o BigInt const divc(BigInt *remainder, BigInt const &rhs) const: The quotient of the current object and rhs is returned. The division's remainder is returned in *remainder. o int compare(BigInt const &rsh) const: Using signed values, if the current object is smaller than rhs -1 is returned; if they are equal 0 is returned; if the current object is larger than ths 1 is returned (see also uCompare). o BigInt &exp(BigInt const &exponent): The current object is raised to the power exponent. o BigInt const expc(BigInt const &exponent) const: The current object raised to the power exponent is returned. o BigInt &expMod(BigInt const &exponent, BigInt const &mod): The current object is raised to the power exponent modulo mod. o BigInt const expModc(BigInt const &exponent, BigInt const &mod) const: The current object raised to the power exponent modulo mod is returned. o BigInt &gcd(BigInt const &rhs): The greatest common divisor (gcd) of the current object and rhs is assigned to the current object. To compute the least common multiple (lcm) the following relationship can be used: lcm(a, b) = a * b / a.gcd(b) o BigInt const gcdc(BigInt const &rhs) const: The greatest common divisor (gcd) of the current object and rhs is returned. To compute the least common multiple (lcm) the following relationship can be used: lcm(a, b) = a * b / a.gcd(b) o bool hasBit(size_t index): True is returned if the bit at index position index has been set, false otherwise. o BigInt &inverseMod(BigInt const &mod): The inverse of the current object modulo mod is assigned to the current object. This is the value ret for which the following expression holds true: (*this * ret) % mod = 1 o BigInt const inverseModc(BigInt const &mod) const: This inverse of the current object modulo mod is returned. o bool isNegative() const: Returns true if the current object contains a negative value. o bool isOdd() const: Returns true if the current object is an odd value. o bool isOne() const: Returns true if the current object equals one (1). o BigInt &isqrt(): The current object's integer square root value is assigned to the current object. The integer square root of a value x is the smallest integral value whose square does not exceed x. E.g., isqrt(17) == 4. o BigInt const isqrtc() const: The integer square root of the current object is returned. o bool isZero() const: Returns true if the current object equals zero (0). o BigInt &lshift(): The current object's bits are shifted one bit to the left. The object's sign remains unaltered. o BigInt const lshiftc(): The current object's bits shifted one bit to the left are returned. The object's sign will be equal to the current object's sign. o BigInt &lshift(size_t nBits): The current object's bits are shifted nBits to the left. The object's sign remains unaltered. o BigInt const lshiftc(size_t nBits) const: The current object's bits shifted nBits bit to the left are returned. The object's sign will be equal to the current object's sign. o BigInt &maskBits(size_t lowerNBits): The current object's lowerNBits lower bits are kept, its higher order bits are cleared. The object's sign is not affected. o BigInt const maskBitsc(size_t lowerNBits) const: A copy of the current object is returned having all but its lowerNBits lower bits cleared. The sign of the returned object will be equal to the current object's sign. o BigInt &mulMod(BigInt const &rhs, BigInt const &mod): The current object is multiplied (modulo mod) by rhs. o BigInt const mulModc(BigInt const &rhs, BigInt const &mod) const: The current object multiplied (modulo mod) by rhs is returned. o BigInt &negate(): The current object's value is negated (i.e., the value changes its sign). o BigInt const negatec() const: The negated value of the current object is returned. o BigInt &rshift(): The current object's bits are shifted one bit to the right. The object's sign remains unaltered. o BigInt const rshiftc(): The current object's bits shifted one bit to the right are returned. The object's sign will be equal to the current object's sign. o BigInt &rshift(size_t nBits): The current object's bits are shifted nBits to the right. The object's sign remains unaltered. o BigInt const rshiftc(size_t nBits) const: The current object's bits shifted nBits bit to the right are returned. The object's sign will be equal to the current object's sign. o BigInt &setBit(size_t index): The bit at index position index is set. o BigInt const setBitc(size_t index) const: A copy of the current object is returned having its bit at index position index set. o BigInt &setBit(size_t index, bool value): The bit at index position index is set to value. o BigInt const setBitc(size_t index, bool value) const: A copy of the current object is returned having its bit at index position index set to value. o BigInt &setNegative(bool negative): The current object's sign will be set to negative if the function's argument is true, it will be set to positive if the function's argument is false. o BigInt const setNegativec(bool negative) const: A copy of the current object is return having a negative sign if the function's argument is true and a positive sign if the function's argument is false. o size_t size() const: The number of bytes required to store the current BIGNUM value is returned. o size_t sizeInBits() const: The number of bits required to represent the current BIGNUM value is returned. If you want to know the key size of RSA, DH or DSA keys functions like RSA_size(), DH_size(), or DSA_size() should be used. o BigInt &sqr(): The current object's value is squared. o BigInt const sqrc() const: The square of the current object is returned. o BigInt &sqrMod(BigInt const &mod) const: The current object's value is squared modulo mod. o BigInt const sqrModc(BigInt const &mod) const: The square (modulo mod) of the current object is returned. o BigInt &subMod(BigInt const &rhs, BigInt const &mod): Rhs is subtracted modulo mod from the current object. o BigInt const subModc(BigInt const &rhs, BigInt const &mod) const: The difference (modulo mod) of the current object and rhs is returned. o void swap(BigInt &other): The current object swaps its value with other. o BigInt &tildeBits(): All the bits in the bytes of the current object and the sign of the current object are toggled. So, after Bigint b(5); b.tildeBits(); b contains the value -250. Also see the discussion with operator~() below. o BigInt const tildeBitsc() const: A copy of the current object whose bits are toggled is returned. o BigInt &tildeInt(): The 'tilde' operation is performed on the current object using the standard int semantics. E.g., ~5 results in -6. Also see the discussion with operator~() below. o BigInt const tildeIntc() const: A copy of the current object is returned to which the 'tilde' operation has been performed using the standard int semantics. o unsigned long ulong() const: The absolute value stored in the current object is returned as an unsigned long. If it cannot be represented by an unsigned long it returns 0xffffffffL. o int uCompare(BigInt const &rsh) const: Using absolute values, if the current object is smaller than rhs -1 is returned; if they are equal 0 is returned; if the current object is larger than ths 1 is returned (see also uCompare).

OVERLOADED OPERATORS

Except for some operators all operators perform their intuitive operations. Where that isn't completely true an explanatory remark is provided. E.g., operator*() multiplies two BigInts, possibly promoting one of the operands; operator*=() multiplies the lhs by the rhs BigInt, possibly promoting the rhs operand. Here are the available operators: Unary operators: o BigInt &operator++(): o BigInt const operator++(int): o BigInt &operator--(): o BigInt const operator--(int): o BigInt const operator-(): o int operator[](size_t idx) const: With BigInt const objects it returns the bit-value of the object's idxth bit as the value 0 or 1. o BigInt::Bit operator[](size_t idx): With non-const BigInt objects it returns a reference to the bit-value of the object's idxth bit. When used as lvalue assigning a 0 or non-zero value to the operator's return value will either clear or set the bit. Likewise, the following arithmetic assignment operators may be used: binary or (|=), binary and (&=) or binary xor (^=). When used as rvalue the value of the object's idxth bit is returned as a bool value. When inseerted into a std::ostream the bit's value is displayed as 0 or 1. o BigInt const operator~(): This operator is not implemented as it cannot be implemented so that it matches the actions of this operator when applied to int type values. When used on int values this operator toggles all the int's bits. E.g., ~5 represents -6, and ~-6 again equals five. The -6 is the result of the sign bit of int values. The obvious implementation of BigInt::operator~() is to toggle all the value's bits and to toggle its sign bit. For 5 this would result in -250: 5, being 101 (binary), fits in one byte, so ~5 becomes 11111010 (binary), which is 250. Its sign must be reversed as well, so it becomes -250. This clearly differs from the value represented by the int constant ~5: when constructing BigInt(~5), the value -6 is obtained. It is possible to change the implementation. E.g., after Bigint b(5); b = ~b; ~b could be implemented so that it results in the value -6. But this too leads to unexpected results. While 5 & ~5 == 0, this would no longer hold true for BigInt objects: Assuming b contains 5 then b & ~b would expand to (binary) 101 & (negative)110 which equals (binary) 100. Since either implementation produces unexpected results BigInt::operator~() was not implemented. Instead two members are offered: tildeBits(), toggling all the bits of all the BigInt bytes and toggling its sign (so Bigint b(5); b.tildeBits(); changes b's value into -250), and tildeInt() changing the object's value into the value that would have been obtained if a BigInt was a mere int (so Bigint b(5); b.tildeInt(); changes b's value into -6). Binary operators: o BigInt const operator*(BigInt const &lhs, BigInt const &rhs): o BigInt const operator/(BigInt const &lhs, BigInt const &rhs): This operator returns the quotient of the lhs object divided by the rhs object. The remainder is lost (The member div performs the division and makes the remainder available as well). o BigInt const operator%(BigInt const &lhs, BigInt const &rhs): o BigInt const operator+(BigInt const &lhs, BigInt const &rhs): o BigInt const operator-(BigInt const &lhs, BigInt const &rhs): o BigInt const operator<<(BigInt const &lhs, size_t nBits): See also the lshift members. If lhs is positive, o BigInt const operator>>=(BigInt const &lhs, size_t nBits): See also the rshift members. o BigInt const operator&(BigInt const &lhs, BigInt const &rhs): This operator returns a BigInt value consisting of the bit_and-ed bits and sign flags of lhs and rhs operands. Consequently, if one operand is positive, the resulting value will be positive. o BigInt const operator|(BigInt const &lhs, BigInt const &rhs): This operator returns a BigInt value consisting of the bit_or-ed bits and sign flags of lhs and rhs operands. Consequently, if either operand is negative, the result will be negative. o BigInt const operator^(BigInt const &lhs, BigInt const &rhs): This operator returns a BigInt value consisting of the bit_xor-ed bits and sign flags of lhs and rhs operands. Consequently, if exactly one operand is negative, the result will be negative. (Arithmetic) assignment operator(s): o BigInt &operator=(BigInt const &rhs): o BigInt &operator*=(BigInt const &rhs): o BigInt &operator/=(BigInt const &rhs): This operator assigns the result of the (integer) division of the current BigInt object by ths to the current object. The remainder is lost. The member div divides and makes the remainder available as well. o BigInt &operator%=(BigInt const &rhs): o BigInt &operator+=(BigInt const &rhs): o BigInt &operator-=(BigInt const &rhs): o BigInt &operator<<=(size_t nBits): See also the lshift members. o BigInt &operator>>=(size_t nBits): See also the rshift members. o BigInt &operator&(BigInt const &rhs): This operator bit_ands the bits and sign flags of the current object and the rhs operand. o BigInt &operator|(BigInt const &rhs): This operator bit_ors the bits and sign flags of the current object and the rhs operand. o BigInt &operator^(BigInt const &rhs): This operator bit_xors the bits and sign flags of the current object and the rhs operand.

STATIC MEMBERS

All members returning a BigInt computed from a set of arguments and not requiring an existing BigInt object are defined as static members. o BigInt const fromText(std::string text, int mode = 0): This member converts a textual representation of a number to a BigInt value. Conversion continues until the end of text or until a character outside of an expected range is encountered. The expected range may be preset by specifying mode as ios::dec, ios::oct, or ios::hex or (the default) the expected range is determined by fromText itself by inspecting the characters in text. By default if text contains hexadecimal characters then fromText assumes that the number is represented as a hexadecimal value (e.g., "abc" is converted to the (decimal) value 2748); if text starts with 0 and contains only characters in the range 0 until (including) 7 then fromText assumes the number is represented as an octal value (e.g., "01234" is converted to the (decimal) value 668). Otherwise a decimal value is assumed. If the text does not represent a valid numerical value (of the given extraction mode) then a FBB::Errno exception is thrown (fromText: text does not represent a BigInt value). o BigInt const rand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb = ODD): This member returns a cryptographically strong pseudo-random number of size bits. The most significant bit(s) can be controlled by msb (by default MSB_IS_ONE), the least significant bit can be controlled by lsb (by default ODD). Before calling this member the random number generator must have been seeded. o BigInt const randRange(BigInt const &max): This member returns a cryptographically strong pseudo-random number in the range 0 <= number < max. Before calling this member the random number generator must have been seeded. o BigInt const setBigEndian(std::string const &bytes): The bytes.length() bytes of bytes are used to compute a BigInt object which is returned by this function. The characters in bytes are interpreted as a series of bytes in big-endian order. See also the member function bigEndian() above. The returned BigInt has a positive value. o BigInt const prime(size_t nBits, BigInt const *mod = 0, BigInt const *rem = 0, PrimeType primeType = ANY): This member returns a prime number of bBits bits. If both mod and rem are non-zero, the condition prime % mod == rem. (E.g., use prime % mod == 1 in order to suit a given generator). The parameter primeType can be ANY, (prime - 1) / 2 may or may not be a prime. If it is SAFE then (prime - 1) / 2 will be a (so-called safe) prime. o BigInt const pseudoRand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb = ODD): This member returns a potentially predictable pseudo-random number of size bits. The most significant bit(s) can be controlled by msb (by default MSB_IS_ONE), the least significant bit can be controlled by lsb (by default ODD). It can be used for non-cryptographic purposes and for certain purposes in cryptographic protocols, but usually not for key generation. o BigInt const pseudoRandRange(BigInt const &max): This member returns a potentially predictable pseudo-random number in the range 0 <= number < max.

FREE FUNCTIONS IN THE FBB NAMESPACE

o std::ostream &operator<<(ostream &out, BigInt const &value): Inserts value into the provided ostream. If the hex manipulator has been inserted into the stream before inserting the BigInt value the value will be displayed as a hexadecimal value (without a leading 0x); if the oct manipulator has been inserted the value will be represented as an octal value (starting with a 0). The value will be displayed as a decimal value if the dec manipulator is active. If the BigInt value is negative its value will be preceded by a minus character. o std::istream &operator>>(istream &in, BigInt &value): Extracts value from the provided istream. Depending on the currently set extraction mode (dec, oct, or hex) the matching set of characters will be extracted from in and converted to a number which is stored in value. Extraction stops at EOF or at the first character outside of the range of characters matching the extraction mode. if no numerical characters were extracted the stream's failbit is set. The extracted value may be preceded by a minus character, resulting in an extracted negative value.

EXAMPLE

#include <iostream> #include <bobcat/bigint> using namespace std; using namespace FBB; int main(int argc, char **argv) { BigInt value(BigInt::prime(100)); BigInt mod(BigInt::rand(50)); BigInt inverse(value.inverseModc(mod)); cout << '(' << value << " * " << inverse << ") % " << mod << " = " << ( value * inverse ) % mod << endl; }
FILES
bobcat/bigint - defines the class interface
SEE ALSO
bobcat(7), RAND_seed(3)

BUGS

None Reported.

DISTRIBUTION FILES

o bobcat_2.18.00-x.dsc: detached signature; o bobcat_2.18.00-x.tar.gz: source archive; o bobcat_2.18.00-x_i386.changes: change log; o libbobcat1_2.18.00-x_*.deb: debian package holding the libraries; o libbobcat1-dev_2.18.00-x_*.deb: debian package holding the libraries, headers and manual pages; o //sourceforge.net/projects/bobcat: public archive location;

BOBCAT

Bobcat is an acronym of 'Brokken's Own Base Classes And Templates'.

COPYRIGHT

This is free software, distributed under the terms of the GNU General Public License (GPL).
AUTHOR
Frank B. Brokken (f.b.brokken@rug.nl). FBB::BIGINT(3)
 
 
 

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