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<h1 id="title">FBB::BigInt</h1>
<h2 id="author">libbobcat-dev_4.04.00-x.tar.gz</h2>
<h2 id="date">2005-2016</h2>
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<h1 id="title">FBB::BigInt(3bobcat)</h1>
<h2 id="author">libbobcat-dev_4.04.00-x.tar.gz Big Integers</h2>
<h2 id="date">2005-2016</h2>
<p>
<h2 >NAME</h2>FBB::BigInt - Arithmetic on Integers of Unlimited Size
<p>
<h2 >SYNOPSIS</h2>
<strong >#include <bobcat/bigint></strong><br/>
Linking option: <em >-lbobcat -lcrypto</em>
<p>
<h2 >DESCRIPTION</h2>
<p>
This class is defined as a wrapper class around the <em >openSSL</em> <em >BN</em> 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 <em >BigInt</em> objects. Also, conversions
to characters and standard numerical value types are offered.
<p>
Below, the phrase <em >the object</em> 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.
<p>
Various constructors accept <em >BIGNUM</em> arguments. Type <em >BIGNUM</em> is the type
containing an integer of unlimited precision as defined by OpenSSL.
<p>
Signs of <em >BigInt</em> are handled in a special way. Whether a <em >BigInt</em> is
negative or positive is determined by its sign-flag, and not by a sign bit as
is the case with <em >int</em> typed values. Since <em >BigInt</em> values have unlimited
precision shifting values to the left won't change their signs.
<p>
Operators return either a reference to the current (modified) object or return
a <em >BigInt</em> object containing the computed value. The rule followed here was
to implement the operators analogously to the way the operators work on
<em >int</em> type values and variables. E.g., <em >operator+()</em> returns a <em >BigInt</em>
value whereas <em >operator+=()</em> returns a <em >BigInt &</em> reference.
<p>
All members modifying their objects return a reference to the current
(modified) object. All members not modifying the current object return a
<em >BigInt</em> object. If both members exists performing the same
functionality the name of the member returning a <em >BigInt</em> object ends
in a <em >c</em> (const) (e.g., <em >addMod</em> and <em >addModc</em>).
<p>
Almost all operators, members and constructors (except for the default
constructor) throw <em >Exception</em> exceptions on failure.
<p>
<h2 >INHERITS FROM</h2>
-
<p>
<h2 >TYPE</h2>
<p>
The class <strong >BigInt</strong> defines the type <em >Word</em>, which is equal to the type
<em >BN_ULONG</em> used by <em >OpenSSL</em> to store integral values of unlimited
precision. A <em >Word</em> is an <em >unsigned long</em>, which is, depending on the
architecture, usually 64 or 32 bits long.
<p>
<h2 >ENUMERATIONS</h2>
<strong >Msb</strong><br/>
This (most significant bit) enumeration is used when generating a
cryptographically strong random number. Its values are:
<ul>
<li> <strong >MSB_UNKNOWN</strong>:<br/>
The most significant bit may be 0 or 1.
<li> <strong >MSB_IS_ONE</strong>:<br/>
The most significant bit is guaranteed to be 1.
<li> <strong >TOP_TWO_BITS_ONE</strong>:<br/>
The two most significant bits are guaranteed to be 1, resulting in a
product of two values each containing <em >nBits</em> having <em >2 * nBits</em>
bits.
</ul>
<p>
<strong >Lsb</strong><br/>
This (least significant bit) enumeration is used when generating random
numbers, ensuring that the resulting value is either odd or even.
<ul>
<li> <strong >EVEN</strong>:<br/>
The random value will be an even value;
<li> <strong >ODD</strong>:<br/>
The random value will be an odd value.
</ul>
<p>
<h2 >CONSTRUCTORS</h2>
<p>
<ul>
<li> <strong >BigInt()</strong>:<br/>
The default constructor initializes a <em >BigInt</em> value to 0.
<li> <strong >explicit BigInt(BIGNUM const &value)</strong>:<br/>
This constructor initializes a <em >BigInt</em> from a <em >const BIGNUM</em>.
<li> <strong >explicit BigInt(BIGNUM const *value)</strong>:<br/>
This constructor initializes a <em >BigInt</em> from a pointer to a
<em >const BIGNUM</em>.
<li> <strong >explicit BigInt(BIGNUM *value)</strong>:<br/> This constructor initializes a
<em >BigInt</em> from a pointer to a <em >BIGNUM</em> (the <em >BIGNUM</em> value
pointed to by <em >value</em> is <em >not</em> mondified by the constructor.
This constructor is a mere wrapper around the previous constructor).
<li> <strong >BigInt(Type value)</strong>:<br/>
This constructor is defined as a member template. Any type that can be
converted using a static cast to an <em >unsigned long</em> can be used as argument
to this constructor. Promotion is allowed, so in many situations where
<em >BigInt</em>s are expected a plain numerical value can be used as well.
<li> <strong >BigInt(char const *bigEndian, size_t length, bool negative = false)</strong>:<br/>
This constructor initializes a <em >BigInt</em> from <em >length</em>
big-endian encoded bytes stored in <em >bigEndian</em>. This constructor interprets
the <em >char</em> values pointed at by <em >bigEndian</em> as unsigned values. Use this
constructor to reconstruct a <em >BigInt</em> object from the data made available by
the <em >bigEndian</em> member. If the number represents a negative value, then
provide a third argument <em >true</em>.
<li> <strong >explicit BigInt(std::string const &bigEndian, bool negative = false)</strong>:<br/>
This constructor initializes a <em >BigInt</em> from the bytes stored in
<em >bigEndian</em>, which must be big-endian encoded. This constructor interprets
the <em >char</em> values stored in <em >bigEndian</em> as unsigned values. If the number
that is stored in <em >bigEndian</em> represents a negative value, then provide a
second argument <em >true</em>.
</ul>
<p>
The standard copy constructor is available, the move constructor is not
available.
<p>
<h2 >MEMBER FUNCTIONS</h2>
<ul>
<li> <strong >BigInt &addMod(BigInt const &rhs, BigInt const &mod) </strong>:<br/>
<em >Rhs</em> is added (modulo <em >mod</em>) to the current object.
<p>
<li> <strong >BigInt addModc(BigInt const &rhs, BigInt const &mod) </strong>:<br/>
The sum (modulo <em >mod</em>) of the current object and <em >rhs</em> is returned.
<p>
<li> <strong >BigInt::Word at(size_t index) const</strong>:<br/>
Returns the <em >Word</em> at <em >index</em>. E.g., on a 32 bit architecture, if
the <strong >BigInt</strong> value equals 2<sup >33</sup>, then <em >at(0)</em> returns 0, and
<em >at(1)</em> returns 2. If <em >index</em> equals or exceeds the value returned
by <em >nWords</em> an <em >FBB::Exception</em> is thrown.
<p>
<li> <strong >BIGNUM const &bignum() const</strong>:<br/>
A reference to the <em >BIGNUM</em> value maintained by the current
<em >BigInt</em> object is returned.
<p>
<li> <strong >char *bigEndian() const</strong>:<br/> The value represented by the current object
is stored in a series of <em >char</em> typed values in big-endian order. If
a value consists of 5 <em >char</em>s the eight most significant bits will
be stored in the <em >char</em> having index value 0, the eight least
significant bits will be stored in the <em >char</em> having index value
4. When needed simply swap <em >char[i]</em> with <em >char[j]</em> (i = 0
.. nBytes/2, j = nBytes-1 .. nBytes/2) to convert to little-endian
order. The return value consists of a series of <em >sizeInBytes()</em> (see
below) dynamically allocated <em >char</em> values. The caller of
<em >bigEndian</em> owns the allocated memory and should eventually delete
it again using <em >delete[]</em>. Note that the current object's <em >sign</em>
cannot be inferred from the return value.
<p>
<li> <strong >BigInt &clearBit(size_t index)</strong>:<br/>
The current object's bit at index position <em >index</em> is cleared.
<p>
<li> <strong >BigInt clearBit(size_t index) const</strong>:<br/>
A copy of the current object having its bit at index position
<em >index</em> cleared.
<p>
<li> <strong >long long diophantus(long long *factor1, long long *factor2,
long long value1, long long value2)</strong>:<br/>
The integral solution of <em >factor1 * value1 + factor2 * value2 = gcd</em>
is computed. The function returns the greatest common divisor
(<em >gcd</em>) of <em >value1</em> and <em >value2</em>, and returns their
multiplication factors in, respectively, <em >*factor1</em> and
<em >*factor2</em>. The solution is not unique: another solution is obtained
by adding <em >k * value2</em> to <em >factor1</em> and subtracting <em >k * value1</em>
from <em >factor2</em>. For values exceeding <em >std::numeric_limits<long,
long>::max()</em> the next member can be used.
<p>
<li> <strong >BigInt diophantus(BigInt *factor1, BigInt *factor2,
BigInt const &value1, BigInt const &value2)</strong>:<br/>
The integral solution of <em >factor1 * value1 + factor2 * value2 = gcd</em>
is computed. The function returns the greatest common divisor
(<em >gcd</em>) of <em >value1</em> and <em >value2</em>, and returns their
multiplication factors in, respectively, <em >*factor1</em> and
<em >*factor2</em>. The solution is not unique: another solution is obtained
by adding <em >k * value2</em> to <em >factor1</em> and subtracting <em >k * value1</em>
from <em >factor2</em>.
<p>
<li> <strong >BigInt &div(BigInt *remainder, BigInt const &rhs)</strong>:<br/>
The current object is divided by <em >rhs</em>. The division's remainder
is returned in <em >*remainder</em>.
<p>
<li> <strong >BigInt divc(BigInt *remainder, BigInt const &rhs) const</strong>:<br/>
The quotient of the current object and <em >rhs</em> is returned. The
division's remainder is returned in <em >*remainder</em>.
<p>
<li> <strong >int compare(BigInt const &rsh) const</strong>:<br/>
Using signed values, if the current object is smaller than <em >rhs</em> -1
is returned; if they are equal 0 is returned; if the current object is
larger than <em >ths</em> 1 is returned (see also <em >uCompare</em>).
<p>
<li> <strong >BigInt &exp(BigInt const &exponent)</strong>:<br/>
The current object is raised to the power <em >exponent</em>.
<p>
<li> <strong >BigInt expc(BigInt const &exponent) const</strong>:<br/>
The current object raised to the power <em >exponent</em> is returned.
<p>
<li> <strong >BigInt &expMod(BigInt const &exponent, BigInt const &mod)</strong>:<br/>
The current object is raised to the power <em >exponent</em> modulo <em >mod</em>.
<p>
<li> <strong >BigInt expModc(BigInt const &exponent, BigInt const &mod) const</strong>:<br/>
The current object raised to the power <em >exponent</em> modulo <em >mod</em> is
returned.
<p>
<li> <strong >BigInt &gcd(BigInt const &rhs)</strong>:<br/>
The greatest common divisor (gcd) of the current object and <em >rhs</em> is
assigned to the current object. To compute the least common multiple
(lcm) the following relationship can be used:
<pre>
lcm(a, b) = a * b / a.gcd(b)
</pre>
<p>
<li> <strong >BigInt gcdc(BigInt const &rhs) const</strong>:<br/>
The greatest common divisor (gcd) of the current object and <em >rhs</em> is
returned. To compute the least common multiple (lcm) the following
relationship can be used:
<pre>
lcm(a, b) = a * b / a.gcd(b)
</pre>
<p>
<li> <strong >bool hasBit(size_t index)</strong>:<br/>
<em >True</em> is returned if the bit at index position <em >index</em> has been
set, <em >false</em> otherwise.
<p>
<li> <strong >BigInt &inverseMod(BigInt const &mod)</strong>:<br/>
The inverse of the current object modulo <em >mod</em> is assigned to the
current object. This is the value <em >ret</em> for which the following
expression holds true:
<pre>
(*this * ret) % mod = 1
</pre>
<p>
<li> <strong >BigInt inverseModc(BigInt const &mod) const</strong>:<br/>
This inverse of the current object modulo <em >mod</em> is returned.
<p>
<li> <strong >bool isNegative() const</strong>:<br/>
Returns <em >true</em> if the current object contains a negative value.
<p>
<li> <strong >bool isOdd() const</strong>:<br/>
Returns <em >true</em> if the current object is an odd value.
<p>
<li> <strong >bool isOne() const</strong>:<br/>
Returns <em >true</em> if the current object equals one (1).
<p>
<li> <strong >BigInt &isqrt()</strong>:<br/>
The current object's integer square root value is assigned to the
current object. The integer square root of a value <em >x</em> is the
biggest integral value whose square does not exceed <em >x</em>. E.g.,
<em >isqrt(17) == 4</em>. An <em >Exception</em> exception is thrown if the current
object's value is smaller than one.
<p>
<li> <strong >BigInt isqrtc() const</strong>:<br/>
The integer square root of the current object is returned. An
<em >Exception</em> exception is thrown if the current object's value is smaller
than one.
<p>
<li> <strong >bool isZero() const</strong>:<br/>
Returns <em >true</em> if the current object equals zero (0).
<p>
<li> <strong >BigInt &lshift()</strong>:<br/>
The current object's bits are shifted one bit to the left. The object's
sign remains unaltered.
<p>
<li> <strong >BigInt lshiftc()</strong>:<br/>
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.
<p>
<li> <strong >BigInt &lshift(size_t nBits)</strong>:<br/>
The current object's bits are shifted <em >nBits</em> to the left. The
object's sign remains unaltered.
<p>
<li> <strong >BigInt lshiftc(size_t nBits) const</strong>:<br/>
The current object's bits shifted <em >nBits</em> bit to the left are
returned. The object's sign will be equal to the current object's
sign.
<p>
<li> <strong >BigInt &maskBits(size_t lowerNBits)</strong>:<br/>
The current object's <em >lowerNBits</em> lower bits are kept, its
higher order bits are cleared. The object's sign is not affected.
<p>
<li> <strong >BigInt maskBitsc(size_t lowerNBits) const</strong>:<br/>
A copy of the current object is returned having all but its
<em >lowerNBits</em> lower bits cleared. The sign of the returned object
will be equal to the current object's sign.
<p>
<li> <strong >size_t maxWordIndex() const</strong>:<br/>
Returns the maximum <em >Word</em>-index that can be used with the <em >at</em>
and <em >setWord</em> members for the current <strong >BigInt</strong> value.
<p>
<li> <strong >BigInt &mulMod(BigInt const &rhs, BigInt const &mod)</strong>:<br/>
The current object is multiplied (modulo <em >mod</em>) by <em >rhs</em>.
<p>
<li> <strong >BigInt mulModc(BigInt const &rhs, BigInt const &mod) const</strong>:<br/>
The current object multiplied (modulo <em >mod</em>) by <em >rhs</em> is returned.
<p>
<li> <strong >BigInt &negate()</strong>:<br/>
The current object's value is negated (i.e., the value changes its
sign).
<p>
<li> <strong >BigInt negatec() const</strong>:<br/>
The negated value of the current object is returned.
<p>
<li> <strong >size_t nWords() const</strong>:<br/>
The number of `words' required to store the <strong >BigInt</strong> value is
returned. Note that the returned value depends on the architecture's
number of bytes per word. For 32-bit architectures there are four
bytes per word, for 64-bit architectures eight bytes per word.
<p>
<li> <strong >BigInt &rshift()</strong>:<br/>
The current object's bits are shifted one bit to the right. The object's
sign remains unaltered.
<p>
<li> <strong >BigInt rshiftc()</strong>:<br/>
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.
<p>
<li> <strong >BigInt &rshift(size_t nBits)</strong>:<br/>
The current object's bits are shifted <em >nBits</em> to the right. The
object's sign remains unaltered.
<p>
<li> <strong >BigInt rshiftc(size_t nBits) const</strong>:<br/>
The current object's bits shifted <em >nBits</em> bit to the right are
returned. The object's sign will be equal to the current object's
sign.
<p>
<li> <strong >BigInt &setBit(size_t index)</strong>:<br/>
The bit at index position <em >index</em> is set.
<p>
<li> <strong >BigInt setBitc(size_t index) const</strong>:<br/>
A copy of the current object is returned having its bit at index
position <em >index</em> set.
<p>
<li> <strong >BigInt &setBit(size_t index, bool value)</strong>:<br/>
The bit at index position <em >index</em> is set to <em >value</em>.
<p>
<li> <strong >BigInt setBitc(size_t index, bool value) const</strong>:<br/>
A copy of the current object is returned having its bit at index
position <em >index</em> set to <em >value</em>.
<p>
<li> <strong >BigInt &setNegative(bool negative)</strong>:<br/>
The current object's sign will be set to negative if the function's
argument is <em >true</em>, it will be set to positive if the function's
argument is <em >false</em>.
<p>
<li> <strong >BigInt setNegativec(bool negative) const</strong>:<br/>
A copy of the current object is return having a negative sign if the
function's argument is <em >true</em> and a positive sign if the function's
argument is <em >false</em>.
<p>
<li> <strong >void setWord(size_t index, BigInt::Word value)</strong>:<br/>
Assigns <em >value</em> to the <em >Word</em> at <em >index</em>. E.g., on a 32 bit
architecture, if the <strong >BigInt</strong> value equals 2<sup >33</sup>, then
after <em >setWord(1, 1)</em> the value has become 2<sup >32</sup>. If <em >index</em>
exceeds the value returned by <em >nWords</em> an <em >FBB::Exception</em> is
thrown.
<p>
<li> <strong >size_t size() const</strong>:<br/>
The number of significant <em >bits</em> required to store the current
<em >BIGNUM</em> value is returned.
<p>
<li> <strong >size_t sizeInBytes() const</strong>:<br/>
The number of bytes required to store the current <em >BIGNUM</em> value is
returned (returns the same value as the <em >size</em> memeber does).
<p>
<li> <strong >size_t constexpr sizeOfWord() const</strong>:<br/>
<strong >BigInt</strong> values are stored in units of `words', which are unsigned
long values. These values may consist of, e.g., 32 or 64 bits. The
number of bytes occupied by a `word' is returned: 4 for a 32 bit
value, 8 for a 64 bit value, and possibly other values, depending on
specific architecture peculiarities. The value returned by this
member, therefore, is architecture dependent.
<p>
<li> <strong >BigInt &sqr()</strong>:<br/>
The current object's value is squared.
<p>
<li> <strong >BigInt sqrc() const</strong>:<br/>
The square of the current object is returned.
<p>
<li> <strong >BigInt &sqrMod(BigInt const &mod) const</strong>:<br/>
The current object's value is squared modulo <em >mod</em>.
<p>
<li> <strong >BigInt sqrModc(BigInt const &mod) const</strong>:<br/>
The square (modulo <em >mod</em>) of the current object is returned.
<p>
<li> <strong >BigInt &subMod(BigInt const &rhs, BigInt const &mod)</strong>:<br/>
<em >Rhs</em> is subtracted modulo <em >mod</em> from the current object.
<p>
<li> <strong >BigInt subModc(BigInt const &rhs, BigInt const &mod) const</strong>:<br/>
The difference (modulo <em >mod</em>) of the current object and <em >rhs</em> is
returned.
<p>
<li> <strong >void swap(BigInt &other)</strong>:<br/>
The current object swaps its value with <em >other</em>.
<p>
<li> <strong >BigInt &tildeBits()</strong>:<br/>
All the bits in
the bytes of the current object and the sign of the current object
are toggled.
So, after
<pre>
Bigint b(5);
b.tildeBits();
</pre>
<em >b</em> contains the value -250. Also see the discussion with
<em >operator~()</em> below.
<p>
<li> <strong >BigInt tildeBitsc() const</strong>:<br/>
A copy of the current object whose bits are toggled is returned.
<p>
<li> <strong >BigInt &tildeInt()</strong>:<br/>
The `tilde' operation is performed on the current object using the
standard <em >int</em> semantics. E.g., ~5 results in -6. Also see the
discussion with <em >operator~()</em> below.
<p>
<li> <strong >BigInt tildeIntc() const</strong>:<br/>
A copy of the current object is returned to which the `tilde' operation
has been performed using the standard <em >int</em> semantics.
<p>
<li> <strong >unsigned long ulong() const</strong>:<br/>
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 <em >0xffffffffL</em>.
<p>
<li> <strong >int uCompare(BigInt const &rsh) const</strong>:<br/>
Using absolute values, if the current object is smaller than <em >rhs</em> -1
is returned; if they are equal 0 is returned; if the current object is
larger than <em >ths</em> 1 is returned (see also <em >uCompare</em>).
</ul>
<p>
<h2 >OVERLOADED OPERATORS</h2>
<p>
Except for some operators all operators perform their intuitive
operations. Where that isn't completely true an explanatory remark is
provided. E.g., <em >operator*()</em> multiplies two <em >BigInt</em>s, possibly promoting
one of the operands; <em >operator*=()</em> multiplies the lhs by the rhs
<em >BigInt</em>, possibly promoting the rhs operand.
<p>
Here are the available operators:
<p>
<strong >Unary operators:</strong>
<p>
<ul>
<li> <strong >bool operator bool() const</strong>:<br/>
Returns <em >true</em> if the <em >BigInt</em> value is unequal zero, otherwise
<em >false</em> is returned.
<p>
<li> <strong >BigInt &operator++()</strong>:<br/>
<li> <strong >BigInt operator++(int)</strong>:<br/>
<li> <strong >BigInt &operator--()</strong>:<br/>
<li> <strong >BigInt operator--(int)</strong>:<br/>
<li> <strong >BigInt operator-()</strong>:<br/>
<li> <strong >int operator[](size_t idx) const</strong>:<br/>
With <em >BigInt</em> objects it returns the bit-value of the object's
<em >idx</em>th bit as the value 0 or 1.
<p>
<li> <strong >BigInt::Bit operator[](size_t idx)</strong>:<br/>
With non-const <em >BigInt</em> objects it returns a reference to the
bit-value of the object's <em >idx</em>th bit. When used as <em >lvalue</em>
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 (<em >|=</em>), binary and
(<em >&=</em>) or binary xor (<em >^=</em>). When used as <em >rvalue</em> the value of
the object's <em >idx</em>th bit is returned as a <em >bool</em> value. When
inseerted into a <em >std::ostream</em> the bit's value is displayed as 0 or
1.
<p>
<li> <strong >BigInt operator~()</strong>:<br/>
This operator is <em >not</em> implemented as it cannot be implemented so
that it matches the actions of this operator when applied to <em >int</em>
type values.
<p>
When used on <em >int</em> values this operator toggles all the <em >int</em>'s
bits. E.g., ~5 represents -6, and ~-6 again equals five. The -6 is the
result of the sign bit of <em >int</em> values. The obvious implementation
of <em >BigInt::operator~()</em> 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 <em >int</em> constant ~5:
when constructing <em >BigInt(~5)</em>, the value -6 is obtained.
<p>
It is possible to change the implementation. E.g., after
<pre>
Bigint b(5);
b = ~b;
</pre>
<em >~b</em> could be implemented so that it results in the value -6. But
this too leads to unexpected results. While <em >5 & ~5 == 0</em>, this
would no longer hold true for <em >BigInt</em> objects: Assuming <em >b</em>
contains 5 then <em >b & ~b</em> would expand to (binary) <em >101 &
(negative)110</em> which equals (binary) 100.
<p>
Since either implementation produces unexpected results
<em >BigInt::operator~()</em> was not implemented. Instead two members are
offered: <em >tildeBits()</em>, toggling all the bits of all the
<em >BigInt</em> bytes and toggling its sign (so
<pre>
Bigint b(5);
b.tildeBits();
</pre>
changes <em >b</em>'s value into -250), and <em >tildeInt()</em> changing the
object's value into the value that would have been obtained if a
<em >BigInt</em> was a mere <em >int</em> (so
<pre>
Bigint b(5);
b.tildeInt();
</pre>
changes <em >b</em>'s value into -6).
</ul>
<p>
<strong >Binary operators:</strong>
<p>
<ul>
<li> <strong >BigInt operator*(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt operator/(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
This operator returns the quotient of the <em >lhs</em> object divided by the
<em >rhs</em> object. The remainder is lost (The member <em >div</em> performs the
division and makes the remainder available as well).
<li> <strong >BigInt operator%(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt operator+(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt operator-(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt operator<<(BigInt const &lhs, size_t nBits)</strong>:<br/>
See also the <em >lshift</em> members. If <em >lhs</em> is positive,
<li> <strong >BigInt operator>>=(BigInt const &lhs, size_t nBits)</strong>:<br/>
See also the <em >rshift</em> members.
<li> <strong >BigInt operator&(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
This operator returns a <em >BigInt</em> value consisting of the
<em >bit_and</em>-ed bits and sign flags of lhs and rhs
operands. Consequently, if one operand is positive, the resulting
value will be positive.
<li> <strong >BigInt operator|(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
This operator returns a <em >BigInt</em> value consisting of the
<em >bit_or</em>-ed bits and sign flags of lhs and rhs
operands. Consequently, if either operand is negative, the result will
be negative.
<li> <strong >BigInt operator^(BigInt const &lhs, BigInt const &rhs)</strong>:<br/>
This operator returns a <em >BigInt</em> value consisting of the
<em >bit_xor</em>-ed bits and sign flags of lhs and rhs
operands. Consequently, if exactly one operand is negative, the result
will be negative.
</ul>
<p>
<strong >(Arithmetic) assignment operator(s):</strong>
<p>
<ul>
<li> <strong >BigInt &operator=(BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt &operator*=(BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt &operator/=(BigInt const &rhs)</strong>:<br/>
This operator assigns the result of the (integer) division of the current
<em >BigInt</em> object by <em >ths</em> to the current object. The remainder is
lost. The member <em >div</em> divides and makes the remainder available as
well.
<li> <strong >BigInt &operator%=(BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt &operator+=(BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt &operator-=(BigInt const &rhs)</strong>:<br/>
<li> <strong >BigInt &operator<<=(size_t nBits)</strong>:<br/>
See also the <em >lshift</em> members.
<li> <strong >BigInt &operator>>=(size_t nBits)</strong>:<br/>
See also the <em >rshift</em> members.
<li> <strong >BigInt &operator&=(BigInt const &rhs)</strong>:<br/>
This operator <em >bit_and</em>s the bits and sign flags of the current
object and the rhs operand.
<li> <strong >BigInt &operator|=(BigInt const &rhs)</strong>:<br/>
This operator <em >bit_or</em>s the bits and sign flags of the current
object and the rhs operand.
<li> <strong >BigInt &operator^=(BigInt const &rhs)</strong>:<br/>
This operator <em >bit_xor</em>s the bits and sign flags of the current
object and the rhs operand.
</ul>
<p>
Note that the move operator is not available
<p>
<h2 >STATIC MEMBERS</h2>
<p>
All members returning a <em >BigInt</em> computed from a set of arguments and
not requiring an existing <em >BigInt</em> object are defined as static members.
<p>
<ul>
<li> <strong >BigInt fromText(std::string text, int mode = 0)</strong>:<br/>
This member converts a textual representation of a number to a
<em >BigInt</em> value. Conversion continues until the end of <em >text</em> or
until a character outside of an expected range is encountered.
<p>
The expected range may be preset by specifying <em >mode</em> as <em >ios::dec,
ios::oct,</em> or <em >ios::hex</em> or (the default) the expected range is
determined by <em >fromText</em> itself by inspecting the characters in
<em >text</em>.
<p>
By default if <em >text</em> contains hexadecimal characters then
<em >fromText</em> assumes that the number is represented as a hexadecimal
value (e.g., <em >"abc"</em> is converted to the (decimal) value 2748); if
<em >text</em> starts with 0 and contains only characters in the range 0
until (including) 7 then <em >fromText</em> assumes the number is
represented as an octal value (e.g., <em >"01234"</em> is converted to the
(decimal) value 668). Otherwise a decimal value is assumed.
<p>
If the text does not represent a valid numerical value (of the
given extraction mode) then a <em >FBB::Exception</em> exception is thrown
(<em >fromText: text does not represent a BigInt value</em>).
<p>
<li> <strong >BigInt rand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb = ODD)</strong>:<br/>
This member returns a cryptographically strong pseudo-random number
of <em >size</em> bits. The most significant bit(s) can be controlled by
<em >msb</em> (by default <strong >MSB_IS_ONE</strong>), the least significant bit can be
controlled by <em >lsb</em> (by default <strong >ODD</strong>). Before calling this
member the random number generator must have been seeded.
<p>
From the <strong >RAND_add</strong>(3ssl) man-page:
<p>
OpenSSL makes sure that the PRNG state is unique for each thread. On
systems that provide <em >/dev/urandom</em>, the randomness device is used
to seed the PRNG transparently. However, on all other systems, the
application is responsible for seeding the PRNG by calling
<strong >RAND_add</strong>(3ssl), <strong >RAND_egd</strong>(3ssl), <strong >RAND_load_file</strong>(3ssl), or
<strong >RAND_seed</strong>(3ssl).
<p>
<li> <strong >BigInt randRange(BigInt const &max)</strong>:<br/>
This member returns a cryptographically strong pseudo-random
number in the range <em >0 <= number < max</em>. Before calling this
member the random number generator must have been seeded (see also
<strong >rand</strong>, described above).
<p>
<li> <strong >BigInt setBigEndian(std::string const &bytes)</strong>:<br/>
The <em >bytes.length()</em> bytes of <em >bytes</em> are used to compute a
<em >BigInt</em> object which is returned by this function. The characters
in <em >bytes</em> are interpreted as a series of bytes in big-endian
order. See also the member function <em >bigEndian()</em> above. The
returned <em >BigInt</em> has a positive value.
<p>
<li> <strong >BigInt prime(size_t nBits,
BigInt const *mod = 0, BigInt const *rem = 0,
PrimeType primeType = ANY)</strong>:<br/>
This member returns a prime number of <em >bBits</em> bits. If both <em >mod</em>
and <em >rem</em> are non-zero, the condition prime % mod == rem.
(E.g., use <em >prime % mod == 1</em> in order to suit a given
generator). The parameter <em >primeType</em> can be <em >ANY</em>, <em >(prime - 1)
/ 2</em> may or may not be a prime. If it is <em >SAFE</em> then <em >(prime - 1)
/ 2</em> will be a (so-called <em >safe</em>) prime.
<p>
<li> <strong >BigInt pseudoRand(size_t size, Msb msb = MSB_IS_ONE, Lsb lsb =
ODD)</strong>:<br/>
This member returns a potentially predictable pseudo-random number of
<em >size</em> bits. The most significant bit(s) can be controlled by
<em >msb</em> (by default <strong >MSB_IS_ONE</strong>), the least significant bit can be
controlled by <em >lsb</em> (by default <strong >ODD</strong>). It can be used for
non-cryptographic purposes and for certain purposes in cryptographic
protocols, but usually not for key generation.
<p>
<li> <strong >BigInt pseudoRandRange(BigInt const &max)</strong>:<br/>
This member returns a potentially predictable pseudo-random
number in the range <em >0 <= number < max</em>.
</ul>
<p>
<h2 >FREE FUNCTIONS IN THE FBB NAMESPACE</h2>
<p>
<ul>
<li> <strong >std::ostream &operator<<(ostream &out, BigInt const &value)</strong>:<br/>
Inserts <em >value</em> into the provided <em >ostream</em>. If the <em >hex</em>
manipulator has been inserted into the stream before inserting the <em >BigInt</em>
value the value will be displayed as a hexadecimal value (without a leading
<em >0x</em>); if the <em >oct</em> 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 <em >dec</em> manipulator is active. If the
<em >BigInt</em> value is negative its value will be preceded by a minus
character.
<li> <strong >std::istream &operator>>(istream &in, BigInt &value)</strong>:<br/>
Extracts <em >value</em> from the provided <em >istream</em>. Depending on the
currently set extraction mode (<em >dec, oct,</em> or <em >hex</em>) the matching
set of characters will be extracted from <em >in</em> and converted to a
number which is stored in <em >value</em>. 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 <em >failbit</em> is set. The extracted value may be preceded
by a minus character, resulting in an extracted negative value.
</ul>
<p>
<h2 >EXAMPLE</h2>
<pre>
#include <iostream>
#include <bobcat/bigint>
using namespace std;
using namespace FBB;
int main()
{
BigInt value(BigInt::prime(100));
BigInt mod(BigInt::rand(50));
BigInt inverse(value.inverseModc(mod));
cout << '(' << value << " * " << inverse << ") % " << mod << " = " <<
( value * inverse ) % mod << endl;
}
</pre>
<p>
<h2 >FILES</h2>
<em >bobcat/bigint</em> - defines the class interface
<p>
<h2 >SEE ALSO</h2>
<strong >bobcat</strong>(7), <strong >diffiehellman</strong>(3bobcat),
<strong >RAND_add</strong>(3ssl), <strong >RAND_egd</strong>(3ssl),
<strong >RAND_load_file</strong>(3ssl), <strong >RAND_seed</strong>(3).
<p>
<h2 >BUGS</h2>
<p>
Sep/Oct 2013: due to a change in library handling by the linker
(cf. <a href="http://fedoraproject.org/wiki/UnderstandingDSOLinkChange">http://fedoraproject.org/wiki/UnderstandingDSOLinkChange</a> and
<a href="https://wiki.debian.org/ToolChain/DSOLinking">https://wiki.debian.org/ToolChain/DSOLinking</a>) libraries that are
indirectly required are no longer automatically linked to your program. With
<strong >BigInt</strong> this is <em >libcrypto</em>, which requires programs to link to both
<em >bobcat</em> and <em >crypto</em>.
<p>
<h2 >DISTRIBUTION FILES</h2>
<ul>
<li> <em >bobcat_4.04.00-x.dsc</em>: detached signature;
<li> <em >bobcat_4.04.00-x.tar.gz</em>: source archive;
<li> <em >bobcat_4.04.00-x_i386.changes</em>: change log;
<li> <em >libbobcat1_4.04.00-x_*.deb</em>: debian package holding the
libraries;
<li> <em >libbobcat1-dev_4.04.00-x_*.deb</em>: debian package holding the
libraries, headers and manual pages;
<li> <em >http://sourceforge.net/projects/bobcat</em>: public archive location;
</ul>
<p>
<h2 >BOBCAT</h2>
Bobcat is an acronym of `Brokken's Own Base Classes And Templates'.
<p>
<h2 >COPYRIGHT</h2>
This is free software, distributed under the terms of the
GNU General Public License (GPL).
<p>
<h2 >AUTHOR</h2>
Frank B. Brokken (<strong >f.b.brokken@rug.nl</strong>).
<p>
|