RSA domain. More...

#include <givintrsa.h>

Inheritance diagram for IntRSADom< MyRandIter >:

Collaboration diagram for IntRSADom< MyRandIter >:

Public Types
typedef IntFactorDom< MyRandIter >::Element	Element

typedef IntFactorDom< MyRandIter >::random_generator	random_generator

using	Self_t = ZRing< Integer >

using	Parent_t = UnparametricZRing< Integer >

typedef Integer	Rep

typedef RandomIntegerIterator< false, false >	RandIter

typedef GeneralRingNonZeroRandIter< Self_t >	NonZeroRandIter

enum

using	Residu_t = Integer

using	Element_ptr = Element *

using	ConstElement_ptr = const Element *

typedef const Element	ConstElement

Public Member Functions
	IntRSADom (bool fi=false, MyRandIter g=MyRandIter())
	Constructors. More...

	IntRSADom (const int64_t s, bool fi=false, MyRandIter g=MyRandIter())

	IntRSADom (const int64_t p, const int64_t q, bool fi=false, MyRandIter g=MyRandIter())

	IntRSADom (const Element &n, const Element &e, const Element &d)

	IntRSADom (const Element &n, const Element &e)

const Element &	getn () const
	Accesses. More...

const Element &	gete () const

const Element &	getd () const

std::ostream &	encipher (std::ostream &, std::istream &) const
	Text conversions. More...

std::ostream &	decipher (std::ostream &, std::istream &)

Element &	strong_prime (random_generator &g, int64_t psize, Element &p) const
	Strong Primes. More...

void	keys_gen (random_generator &g, int64_t psize, int64_t qsize, Element &n, Element &e, Element &d, Element &p, Element &q) const
	Key gen. More...

void	keys_gen (random_generator &g, int64_t psize, int64_t qsize, Element &n, Element &e, Element &d) const

int64_t	log (const Element &n, const int64_t=10) const
	log[10] More...

std::ostream &	ecriture_str (std::ostream &, const Element &) const
	Text conversions. More...

std::ostream &	ecriture_str_last (std::ostream &, const Element &) const

std::ostream &	ecriture_Int (std::ostream &, const Element &) const

Element &	point_break (Element &u)
	Breaking codes : finding u knowing only m an k ... More...

Rep &	factor (Rep &r, const Rep &n, unsigned long loops=0) const

Rep &	iffactorprime (Rep &r, const Rep &n, unsigned long loops=0) const

Rep &	primefactor (Rep &r, const Rep &n) const

bool	set (Container1 &setint, Container2 &setpwd, const Rep &a, unsigned long loops=0) const
	Factors with primes. More...

void	set (Container &, const Rep &) const

void	Erathostene (Container &, const Rep &) const

Rep &	Erathostene (Rep &, const Rep &p) const
	returns a small factor More...

Container &	divisors (Container &L, const Cont2 &Lf, const Cont3 &Le) const

Container &	divisors (Container &, const Rep &) const

Rep &	Pollard (const GivRandom &, Rep &, const Rep &n, unsigned long threshold=0) const

Rep &	Lenstra (const GivRandom &, Rep &, const Rep &n, const Rep &B1=10000000, const unsigned long curves=30) const

std::ostream &	write (std::ostream &o, const Rep &n) const

std::ostream &	write (std::ostream &o, Array &, const Rep &n) const

std::ostream &	write (std::ostream &o) const

std::ostream &	write (std::ostream &os, const Element &a) const
	Print field element. More...

int	isprime (const Rep &n, int r=_GIVARO_ISPRIMETESTS_) const

unsigned int	isprimepower (Rep &, const Rep &) const

template<class MyRandIter >
unsigned int	Miller (MyRandIter &g, const Rep &n=_GIVARO_ISPRIMETESTS_) const

template<class MyRandIter >
Rep &	test_Lehmann (MyRandIter &g, Rep &, const Rep &n=_GIVARO_ISPRIMETESTS_) const

template<class MyRandIter >
int	Lehmann (MyRandIter &g, const Rep &n=_GIVARO_ISPRIMETESTS_) const

int	isprime_Tabule (const int n) const

int	isprime_Tabule2 (const int n) const

Rep &	nextprime (Rep &, const Rep &, int r=_GIVARO_ISPRIMETESTS_) const

Rep &	prevprime (Rep &, const Rep &, int r=_GIVARO_ISPRIMETESTS_) const

Rep &	nextprimein (Rep &, int r=_GIVARO_ISPRIMETESTS_) const

Rep &	prevprimein (Rep &, int r=_GIVARO_ISPRIMETESTS_) const

int	local_prime (const Rep &n, int r=_GIVARO_ISPRIMETESTS_) const

int	operator== (const Self_t &) const

bool	operator== (const Self_t &F) const

int	operator!= (const Self_t &) const

bool	operator!= (const Self_t &F) const

template<class XXX >
XXX &	convert (XXX &x, const Rep &a) const

T &	convert (T &x, const Element &y) const

Rep &	mul (Rep &r, const Rep &a, const Rep &b) const

Rep &	mulin (Rep &r, const Rep &b) const

Rep &	div (Rep &r, const Rep &a, const Rep &b) const

Rep &	divin (Rep &r, const Rep &b) const

Rep &	mod (Rep &r, const Rep &a, const Rep &b) const

Rep &	modin (Rep &r, const Rep &b) const

Rep &	add (Rep &r, const Rep &a, const Rep &b) const

Rep &	addin (Rep &r, const Rep &b) const

Rep &	sub (Rep &r, const Rep &a, const Rep &b) const

Rep &	subin (Rep &r, const Rep &b) const

Rep &	divmod (Rep &q, Rep &r, const Rep &a, const Rep &b) const

Rep &	divexact (Rep &q, const Rep &a, const Rep &b) const

Rep &	axpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const

Rep &	maxpy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const

Rep &	maxpyin (Rep &r, const Rep &a, const Rep &b) const

Rep &	axmy (Rep &r, const Rep &a, const Rep &b, const Rep &c) const

Rep &	axpyin (Rep &r, const Rep &a, const Rep &b) const

Rep &	axmyin (Rep &r, const Rep &a, const Rep &b) const

Rep &	neg (Rep &r, const Rep &a) const

Rep &	negin (Rep &r) const

Element &	quo (Element &q, const Element &a, const Element &b) const

Element &	rem (Element &r, const Element &a, const Element &b) const

Element &	quoin (Element &a, const Element &b) const

Element &	remin (Element &a, const Element &b) const

void	quoRem (Element &q, Element &r, const Element &a, const Element &b) const

Element &	logtwo (Element &z, const Element &x) const

Rep &	gcd (Rep &g, Rep &u, Rep &v, const Rep &a, const Rep &b) const

Rep &	gcd (Rep &g, const Rep &a, const Rep &b) const

Rep &	gcdin (Rep &g, const Rep &a) const

Rep &	lcm (Rep &l, const Rep &a, const Rep &b) const

Rep &	lcmin (Rep &l, const Rep &a) const

Element &	dxgcd (Element &g, Element &s, Element &t, Element &u, Element &v, const Element &a, const Element &b) const

Rep &	inv (Rep &u, const Rep &a, const Rep &b) const

Rep &	invin (Rep &u, const Rep &b) const

Rep &	invmod (Rep &u, const Rep &a, const Rep &b) const

Rep &	invmodin (Rep &u, const Rep &b) const

bool	ratrecon (Rep &num, Rep &den, const Rep &f, const Rep &m, const Rep &numbound, bool forcereduce=true, bool recurs=true) const

bool	RationalReconstruction (Rep &, Rep &, const Rep &, const Rep &) const

bool	RationalReconstruction (Rep &, Rep &, const Rep &, const Rep &, const Rep &, bool=true, bool=true) const

bool	RationalReconstruction (Rep &, Rep &, const Rep &, const Rep &, const Rep &, const Rep &) const

Rep &	pow (Rep &r, const Rep &n, const int64_t l) const

Rep &	pow (Rep &r, const Rep &n, const uint64_t l) const

Rep &	pow (Rep &r, const Rep &n, const int32_t l) const

Rep &	pow (Rep &r, const Rep &n, const uint32_t l) const

Rep &	sqrt (Rep &s, const Rep &n) const

Rep &	sqrt (Rep &s, Rep &r, const Rep &n) const

int64_t	logp (const Rep &a, const Rep &p) const

Rep &	powmod (Rep &r, const Rep &n, const int64_t e, const Rep &m) const

Rep &	powmod (Rep &r, const Rep &n, const Rep &e, const Rep &m) const

uint64_t	length (const Rep &a) const

int	sign (const Rep &a) const

bool	isZero (const Rep &a) const

bool	isZero (const Element &a) const

bool	isOne (const Rep &a) const

bool	isOne (const Element &a) const

bool	isMOne (const Rep &a) const

bool	isMOne (const Element &a) const

bool	isUnit (const Rep &x) const
	isUnit More...

bool	isUnit (const Element &a) const

bool	isDivisor (const Element &a, const Element &b) const
	isDivisor (a, b) Test if b \| a. More...

Element &	abs (Element &x, const Element &a) const

Element	abs (const Element &a) const

Element &	abs (Element &x, const Element &a) const

Element	abs (const Element &a) const

int32_t	compare (const Rep &a, const Rep &b) const

long	compare (const Element &a, const Element &b) const

bool	areEqual (const Rep &a, const Rep &b) const

bool	areNEqual (const Rep &a, const Rep &b) const

bool	areAssociates (const Element &x, const Element &y) const

bool	isgeq (const Rep &a, const Rep &b) const

bool	isgeq (const int64_t b, const Rep &a) const

bool	isgeq (const Rep &a, const int64_t b) const

bool	isleq (const Rep &a, const Rep &b) const

bool	isleq (const int64_t b, const Rep &a) const

bool	isleq (const Rep &a, const int64_t b) const

bool	isgt (const Rep &a, const Rep &b) const

bool	isgt (const int64_t b, const Rep &a) const

bool	isgt (const Rep &a, const int64_t b) const

bool	islt (const Rep &a, const Rep &b) const

bool	islt (const int64_t b, const Rep &a) const

bool	islt (const Rep &a, const int64_t b) const

template<class MyRandIter >
Rep &	random (MyRandIter &, Rep &r, long s=1) const

template<class MyRandIter >
Rep &	random (MyRandIter &, Rep &r, const Rep &b) const

Element &	random (const Random &g, Element &r) const

template<class MyRandIter >
Rep &	nonzerorandom (MyRandIter &, Rep &r, long s=1) const

template<class MyRandIter >
Rep &	nonzerorandom (MyRandIter &, Rep &r, const Rep &b) const

Element &	nonzerorandom (const Random &g, Element &a) const

std::istream &	read (std::istream &i)

std::istream &	read (std::istream &is, Element &a) const
	Read field element. More...

Residu_t	residu () const

Residu_t	size () const

Residu_t	cardinality () const

T &	cardinality (T &c) const

Residu_t	characteristic () const

T &	characteristic (T &c) const

Element &	init (Element &x) const

Element &	init (Element &x, const T &s) const

Element &	assign (Element &x, const Element &y) const

Element &	reduce (Element &x, const Element &y) const

Element &	reduce (Element &x) const

Element	minElement () const

Element	maxElement () const

Input/Output Operations
std::ostream &	write (std::ostream &os, std::string F) const
	Read field. More...

std::istream &	read (std::istream &is) const
	Read field. More...

Arithmetic Operations
The first argument is set and is also the return value.
Element &	mul (Element &x, const Element &y, const Element &z) const
	x := y*z More...

Element &	div (Element &x, const Element &y, const Element &z) const
	x := y/z More...

Element &	mod (Element &x, const Element &y, const Element &z) const
	x := y mod z More...

Element &	add (Element &x, const Element &y, const Element &z) const
	x := y + z More...

Element &	sub (Element &x, const Element &y, const Element &z) const
	x := y - z More...

Element &	axpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x + y More...

Element &	maxpy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := y - a*x More...

Element &	maxpyin (Element &z, const Element &a, const Element &x) const
	z := z - a*x More...

Element &	axmy (Element &z, const Element &a, const Element &x, const Element &y) const
	z := a*x - y More...

Element &	axpyin (Element &z, const Element &a, const Element &x) const
	z := a*x + z More...

Element &	axmyin (Element &z, const Element &a, const Element &x) const
	z := a*x - z More...

Element &	neg (Element &x, const Element &y) const
	x := -y More...

Element &	inv (Element &x, const Element &y) const
	x := 1/y More...

Inplace Arithmetic Operations
The first argument is modified and the result is the return value.
Element &	mulin (Element &x, const Element &y) const
	x := x*y More...

Element &	divin (Element &x, const Element &y) const
	x := x/y More...

Element &	modin (Element &x, const Element &y) const
	x := x mod y More...

Element &	addin (Element &x, const Element &y) const
	x := x + y More...

Element &	subin (Element &x, const Element &y) const
	x := x - y More...

Element &	negin (Element &x) const
	x := -x More...

Element &	invin (Element &x) const
	x := 1/x More...

Comparison Predicates
bool	areEqual (const Element &x, const Element &y) const
	x == y More...

Static Public Member Functions
static Residu_t	maxCardinality ()

static Residu_t	minCardinality ()

static const std::string	type_string ()

Data Fields
const Element	one

const Element	zero

const Element	mOne

Protected Attributes
bool	_fast_impl
	Fast implementation. More...

GivRandom	_g

Detailed Description

template<class MyRandIter = GivRandom>
class Givaro::IntRSADom< MyRandIter >

RSA domain.

Member Typedef Documentation

◆ Element

typedef IntFactorDom<MyRandIter>::Element Element

◆ random_generator

typedef IntFactorDom<MyRandIter>::random_generator random_generator

Examples: examples/Integer/givaro-ssh-keygen.C.

◆ Self_t

using Self_t = ZRing<Integer>

inherited

◆ Parent_t

using Parent_t = UnparametricZRing<Integer>

inherited

◆ Rep

typedef Integer Rep

inherited

Examples: examples/Integer/RSA_decipher.C, and examples/Integer/RSA_encipher.C.

◆ RandIter

typedef RandomIntegerIterator<false,false> RandIter

inherited

◆ NonZeroRandIter

typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter

inherited

◆ Residu_t

using Residu_t = Integer

inherited

◆ Element_ptr

using Element_ptr = Element*

inherited

◆ ConstElement_ptr

using ConstElement_ptr = const Element*

inherited

◆ ConstElement

typedef const Element ConstElement

inherited

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

inherited

Constructor & Destructor Documentation

◆ IntRSADom() [1/5]

IntRSADom	(	bool	fi = `false`,
		MyRandIter	g = `MyRandIter()`
	)

inline

Constructors.

◆ IntRSADom() [2/5]

IntRSADom	(	const int64_t	s,
		bool	fi = `false`,
		MyRandIter	g = `MyRandIter()`
	)

inline

◆ IntRSADom() [3/5]

IntRSADom	(	const int64_t	p,
		const int64_t	q,
		bool	fi = `false`,
		MyRandIter	g = `MyRandIter()`
	)

inline

◆ IntRSADom() [4/5]

IntRSADom	(	const Element &	n,
		const Element &	e,
		const Element &	d
	)

inline

◆ IntRSADom() [5/5]

IntRSADom	(	const Element &	n,
		const Element &	e
	)

inline

Member Function Documentation

◆ getn()

const Element& getn ( ) const

inline

Accesses.

◆ gete()

const Element& gete ( ) const

inline

◆ getd()

const Element& getd ( ) const

inline

◆ encipher()

std::ostream & encipher	(	std::ostream &	o,
		std::istream &	in
	)		const

Text conversions.

◆ decipher()

std::ostream & decipher	(	std::ostream &	o,
		std::istream &	in
	)

◆ strong_prime()

IntRSADom< MyRandIter >::Element & strong_prime	(	random_generator &	g,
		int64_t	psize,
		Element &	p
	)		const

Strong Primes.

Bibliography:

J. Gordon, Strong Primes Are Easy to Find, EUROCRYPT'84, LNCS 209.

◆ keys_gen() [1/2]

void keys_gen	(	random_generator &	g,
		int64_t	psize,
		int64_t	qsize,
		Element &	n,
		Element &	e,
		Element &	d,
		Element &	p,
		Element &	q
	)		const

Key gen.

Here m = p*q p and q are prime numbers of respective sizes psize, qsize Moreover p-1 and q-1 have one prime factor of respective size 2/3 since k.u = 1 mod (p-1)(q-1)

◆ keys_gen() [2/2]

void keys_gen	(	random_generator &	g,
		int64_t	psize,
		int64_t	qsize,
		Element &	n,
		Element &	e,
		Element &	d
	)		const

◆ log()

int64_t log	(	const Element &	n,
		const int64_t	b = `10`
	)		const

log[10]

◆ ecriture_str()

std::ostream & ecriture_str	(	std::ostream &	o,
		const Element &	n
	)		const

Text conversions.

◆ ecriture_str_last()

std::ostream & ecriture_str_last	(	std::ostream &	o,
		const Element &	n
	)		const

◆ ecriture_Int()

std::ostream & ecriture_Int	(	std::ostream &	o,
		const Element &	p
	)		const

◆ point_break()

IntRSADom< MyRandIter >::Element & point_break ( Element & u )

Breaking codes : finding u knowing only m an k ...

◆ factor()

Rep& factor	(	Rep &	r,
		const Rep &	n,
		unsigned long	loops = `0`
	)		const

inlineinherited

◆ iffactorprime()

Rep& iffactorprime	(	Rep &	r,
		const Rep &	n,
		unsigned long	loops = `0`
	)		const

inlineinherited

◆ primefactor()

Rep& primefactor	(	Rep &	r,
		const Rep &	n
	)		const

inlineinherited

◆ set() [1/2]

bool set	(	Container1 &	setint,
		Container2 &	setpwd,
		const Rep &	a,
		unsigned long	loops = `0`
	)		const

inherited

Factors with primes.

◆ set() [2/2]

void set	(	Container &	Lf,
		const Rep &	n
	)		const

inherited

◆ Erathostene() [1/2]

void Erathostene	(	Container &	Lf,
		const Rep &	p
	)		const

inherited

◆ Erathostene() [2/2]

Rep& Erathostene	(	Rep &	,
		const Rep &	p
	)		const

inherited

returns a small factor

◆ divisors() [1/2]

Container & divisors	(	Container &	L,
		const Cont2 &	Lf,
		const Cont3 &	Le
	)		const

inherited

◆ divisors() [2/2]

Container & divisors	(	Container &	L,
		const Rep &	n
	)		const

inherited

◆ Pollard()

IntFactorDom< GivRandom >::Rep & Pollard	(	const MyRandIter &	gen,
		Rep &	g,
		const Rep &	n,
		unsigned long	threshold = `0`
	)		const

inherited

◆ Lenstra()

IntFactorDom< GivRandom >::Rep & Lenstra	(	const MyRandIter &	gen,
		Rep &	g,
		const Rep &	n,
		const Rep &	B1 = `10000000`,
		const unsigned long	curves = `30`
	)		const

inherited

◆ write() [1/5]

std::ostream & write	(	std::ostream &	o,
		const Rep &	n
	)		const

inherited

◆ write() [2/5]

std::ostream & write	(	std::ostream &	o,
		Array &	Lf,
		const Rep &	n
	)		const

inherited

◆ write() [3/5]

std::ostream& write ( std::ostream & o ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

Examples: examples/Integer/lambda.C, examples/Integer/lambda_inv.C, examples/Integer/phi.C, examples/Integer/primitiveelement.C, and examples/Integer/probable_primroot.C.

◆ write() [4/5]

std::ostream& write	(	std::ostream &	os,
		const Element &	x
	)		const

inlinevirtualinherited

Print field element.

Returns: output stream to which field element is written.

Parameters

os	output stream to which field element is written.
x	field element.

Reimplemented from UnparametricOperations< _Element >.

◆ write() [5/5]

std::ostream& write	(	std::ostream &	os,
		std::string	F
	)		const

inlineinherited

Read field.

Returns: input stream from which field is read.

Parameters

is	input stream from which field is read.

◆ isprime()

int isprime	(	const Rep &	n,
		int	r = `_GIVARO_ISPRIMETESTS_`
	)		const

inlineinherited

Examples: examples/Integer/ModularSquareRoot.C, examples/Integer/primitiveroot.C, and examples/Integer/probable_primroot.C.

◆ isprimepower()

unsigned int isprimepower	(	Rep &	q,
		const Rep &	u
	)		const

inherited

Examples: examples/Integer/ispower.C.

◆ Miller()

unsigned int Miller	(	MyRandIter &	g,
		const Rep &	n = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ test_Lehmann()

IntPrimeDom::Rep & test_Lehmann	(	MyRandIter &	g,
		Rep &	r,
		const Rep &	n = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ Lehmann()

int Lehmann	(	MyRandIter &	g,
		const Rep &	n = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ isprime_Tabule()

int isprime_Tabule ( const int n ) const

inherited

◆ isprime_Tabule2()

int isprime_Tabule2 ( const int n ) const

inherited

◆ nextprime()

IntPrimeDom::Rep & nextprime	(	Rep &	,
		const Rep &	,
		int	r = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ prevprime()

IntPrimeDom::Rep & prevprime	(	Rep &	n,
		const Rep &	p,
		int	r = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ nextprimein()

IntPrimeDom::Rep & nextprimein	(	Rep &	,
		int	r = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ prevprimein()

IntPrimeDom::Rep & prevprimein	(	Rep &	n,
		int	r = `_GIVARO_ISPRIMETESTS_`
	)		const

inherited

◆ local_prime()

int local_prime	(	const Rep &	n,
		int	r = `_GIVARO_ISPRIMETESTS_`
	)		const

inlineinherited

◆ operator==() [1/2]

int operator== ( const Self_t & ) const

inlineinherited

◆ operator==() [2/2]

bool operator== ( const Self_t & F ) const

inlineinherited

◆ operator!=() [1/2]

int operator!= ( const Self_t & ) const

inlineinherited

◆ operator!=() [2/2]

bool operator!= ( const Self_t & F ) const

inlineinherited

◆ convert() [1/2]

XXX& convert	(	XXX &	x,
		const Rep &	a
	)		const

inlineinherited

◆ convert() [2/2]

T& convert	(	T &	x,
		const Element &	y
	)		const

inlineinherited

◆ mul() [1/2]

Rep& mul	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ mul() [2/2]

Element& mul	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inlinevirtualinherited

x := y*z

Implements RingInterface< _Element >.

◆ mulin() [1/2]

Rep& mulin	(	Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ mulin() [2/2]

Element& mulin	(	Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

x := x*y

Implements RingInterface< _Element >.

◆ div() [1/2]

Rep& div	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ div() [2/2]

Element& div	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inlineinherited

x := y/z

◆ divin() [1/2]

Rep& divin	(	Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ divin() [2/2]

Element& divin	(	Element &	x,
		const Element &	y
	)		const

inlineinherited

x := x/y

◆ mod() [1/2]

Rep& mod	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ mod() [2/2]

Element& mod	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inlineinherited

x := y mod z

◆ modin() [1/2]

Rep& modin	(	Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ modin() [2/2]

Element& modin	(	Element &	x,
		const Element &	y
	)		const

inlineinherited

x := x mod y

◆ add() [1/2]

Rep& add	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ add() [2/2]

Element& add	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inlinevirtualinherited

x := y + z

Implements RingInterface< _Element >.

◆ addin() [1/2]

Rep& addin	(	Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ addin() [2/2]

Element& addin	(	Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

x := x + y

Implements RingInterface< _Element >.

◆ sub() [1/2]

Rep& sub	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Examples: examples/Integer/primitiveroot.C.

◆ sub() [2/2]

Element& sub	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inlinevirtualinherited

x := y - z

Implements RingInterface< _Element >.

◆ subin() [1/2]

Rep& subin	(	Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ subin() [2/2]

Element& subin	(	Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

x := x - y

Implements RingInterface< _Element >.

◆ divmod()

Rep& divmod	(	Rep &	q,
		Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ divexact()

Rep& divexact	(	Rep &	q,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ axpy() [1/2]

Rep& axpy	(	Rep &	r,
		const Rep &	a,
		const Rep &	b,
		const Rep &	c
	)		const

inlineinherited

◆ axpy() [2/2]

Element& axpy	(	Element &	z,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

z := a*x + y

Implements RingInterface< _Element >.

◆ maxpy() [1/2]

Rep& maxpy	(	Rep &	r,
		const Rep &	a,
		const Rep &	b,
		const Rep &	c
	)		const

inlineinherited

◆ maxpy() [2/2]

Element& maxpy	(	Element &	z,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

z := y - a*x

Implements RingInterface< _Element >.

◆ maxpyin() [1/2]

Rep& maxpyin	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ maxpyin() [2/2]

Element& maxpyin	(	Element &	z,
		const Element &	a,
		const Element &	x
	)		const

inlinevirtualinherited

z := z - a*x

Implements RingInterface< _Element >.

◆ axmy() [1/2]

Rep& axmy	(	Rep &	r,
		const Rep &	a,
		const Rep &	b,
		const Rep &	c
	)		const

inlineinherited

◆ axmy() [2/2]

Element& axmy	(	Element &	z,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

z := a*x - y

Implements RingInterface< _Element >.

◆ axpyin() [1/2]

Rep& axpyin	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ axpyin() [2/2]

Element& axpyin	(	Element &	z,
		const Element &	a,
		const Element &	x
	)		const

inlinevirtualinherited

z := a*x + z

Implements RingInterface< _Element >.

◆ axmyin() [1/2]

Rep& axmyin	(	Rep &	r,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ axmyin() [2/2]

Element& axmyin	(	Element &	z,
		const Element &	a,
		const Element &	x
	)		const

inlinevirtualinherited

z := a*x - z

Implements RingInterface< _Element >.

◆ neg() [1/2]

Rep& neg	(	Rep &	r,
		const Rep &	a
	)		const

inlineinherited

◆ neg() [2/2]

Element& neg	(	Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

x := -y

Implements RingInterface< _Element >.

◆ negin() [1/2]

Rep& negin ( Rep & r ) const

inlineinherited

◆ negin() [2/2]

Element& negin ( Element & x ) const

inlinevirtualinherited

x := -x

Implements RingInterface< _Element >.

◆ quo()

Element& quo	(	Element &	q,
		const Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ rem()

Element& rem	(	Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ quoin()

Element& quoin	(	Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ remin()

Element& remin	(	Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ quoRem()

void quoRem	(	Element &	q,
		Element &	r,
		const Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ logtwo()

Element& logtwo	(	Element &	z,
		const Element &	x
	)		const

inlineinherited

◆ gcd() [1/2]

Rep& gcd	(	Rep &	g,
		Rep &	u,
		Rep &	v,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

Examples: examples/Integer/probable_primroot.C.

◆ gcd() [2/2]

Rep& gcd	(	Rep &	g,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ gcdin()

Rep& gcdin	(	Rep &	g,
		const Rep &	a
	)		const

inlineinherited

◆ lcm()

Rep& lcm	(	Rep &	l,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ lcmin()

Rep& lcmin	(	Rep &	l,
		const Rep &	a
	)		const

inlineinherited

◆ dxgcd()

Element& dxgcd	(	Element &	g,
		Element &	s,
		Element &	t,
		Element &	u,
		Element &	v,
		const Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ inv() [1/2]

Rep& inv	(	Rep &	u,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ inv() [2/2]

Element& inv	(	Element &	x,
		const Element &	y
	)		const

inlineinherited

x := 1/y

◆ invin() [1/2]

Rep& invin	(	Rep &	u,
		const Rep &	b
	)		const

inlineinherited

◆ invin() [2/2]

Element& invin ( Element & x ) const

inlineinherited

x := 1/x

◆ invmod()

Rep& invmod	(	Rep &	u,
		const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ invmodin()

Rep& invmodin	(	Rep &	u,
		const Rep &	b
	)		const

inlineinherited

◆ ratrecon()

bool ratrecon	(	Rep &	num,
		Rep &	den,
		const Rep &	f,
		const Rep &	m,
		const Rep &	numbound,
		bool	forcereduce = `true`,
		bool	recurs = `true`
	)		const

inherited

◆ RationalReconstruction() [1/3]

bool RationalReconstruction	(	Rep &	a,
		Rep &	b,
		const Rep &	x,
		const Rep &	m
	)		const

inherited

◆ RationalReconstruction() [2/3]

bool RationalReconstruction	(	Rep &	a,
		Rep &	b,
		const Rep &	x,
		const Rep &	m,
		const Rep &	bound,
		bool	forcereduce = `true`,
		bool	recurs = `true`
	)		const

inherited

◆ RationalReconstruction() [3/3]

bool RationalReconstruction	(	Rep &	a,
		Rep &	b,
		const Rep &	x,
		const Rep &	m,
		const Rep &	a_bound,
		const Rep &	b_bound
	)		const

inherited

◆ pow() [1/4]

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const int64_t	l
	)		const

inlineinherited

◆ pow() [2/4]

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const uint64_t	l
	)		const

inlineinherited

◆ pow() [3/4]

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const int32_t	l
	)		const

inlineinherited

◆ pow() [4/4]

Rep& pow	(	Rep &	r,
		const Rep &	n,
		const uint32_t	l
	)		const

inlineinherited

◆ sqrt() [1/2]

Rep& sqrt	(	Rep &	s,
		const Rep &	n
	)		const

inlineinherited

◆ sqrt() [2/2]

Rep& sqrt	(	Rep &	s,
		Rep &	r,
		const Rep &	n
	)		const

inlineinherited

◆ logp()

int64_t logp	(	const Rep &	a,
		const Rep &	p
	)		const

inlineinherited

◆ powmod() [1/2]

Rep& powmod	(	Rep &	r,
		const Rep &	n,
		const int64_t	e,
		const Rep &	m
	)		const

inlineinherited

◆ powmod() [2/2]

Rep& powmod	(	Rep &	r,
		const Rep &	n,
		const Rep &	e,
		const Rep &	m
	)		const

inlineinherited

◆ length()

uint64_t length ( const Rep & a ) const

inlineinherited

◆ sign()

int sign ( const Rep & a ) const

inlineinherited

◆ isZero() [1/2]

bool isZero ( const Rep & a ) const

inlineinherited

◆ isZero() [2/2]

bool isZero ( const Element & a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

◆ isOne() [1/2]

bool isOne ( const Rep & a ) const

inlineinherited

◆ isOne() [2/2]

bool isOne ( const Element & a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

◆ isMOne() [1/2]

bool isMOne ( const Rep & a ) const

inlineinherited

◆ isMOne() [2/2]

bool isMOne ( const Element & a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

◆ isUnit() [1/2]

bool isUnit ( const Rep & x ) const

inlineinherited

isUnit

◆ isUnit() [2/2]

bool isUnit ( const Element & a ) const

inlinevirtualinherited

Implements RingInterface< _Element >.

◆ isDivisor()

bool isDivisor	(	const Element &	a,
		const Element &	b
	)		const

inlineinherited

isDivisor (a, b) Test if b | a.

◆ abs() [1/4]

Element& abs	(	Element &	x,
		const Element &	a
	)		const

inlineinherited

◆ abs() [2/4]

Element abs ( const Element & a ) const

inlineinherited

◆ abs() [3/4]

Element& abs	(	Element &	x,
		const Element &	a
	)		const

inlineinherited

◆ abs() [4/4]

Element abs ( const Element & a ) const

inlineinherited

◆ compare() [1/2]

int32_t compare	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ compare() [2/2]

long compare	(	const Element &	a,
		const Element &	b
	)		const

inlineinherited

◆ areEqual() [1/2]

bool areEqual	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ areEqual() [2/2]

bool areEqual	(	const Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

x == y

Implements RingInterface< _Element >.

◆ areNEqual()

bool areNEqual	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ areAssociates()

bool areAssociates	(	const Element &	x,
		const Element &	y
	)		const

inlineinherited

◆ isgeq() [1/3]

bool isgeq	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ isgeq() [2/3]

bool isgeq	(	const int64_t	b,
		const Rep &	a
	)		const

inlineinherited

◆ isgeq() [3/3]

bool isgeq	(	const Rep &	a,
		const int64_t	b
	)		const

inlineinherited

◆ isleq() [1/3]

bool isleq	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ isleq() [2/3]

bool isleq	(	const int64_t	b,
		const Rep &	a
	)		const

inlineinherited

◆ isleq() [3/3]

bool isleq	(	const Rep &	a,
		const int64_t	b
	)		const

inlineinherited

◆ isgt() [1/3]

bool isgt	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ isgt() [2/3]

bool isgt	(	const int64_t	b,
		const Rep &	a
	)		const

inlineinherited

◆ isgt() [3/3]

bool isgt	(	const Rep &	a,
		const int64_t	b
	)		const

inlineinherited

◆ islt() [1/3]

bool islt	(	const Rep &	a,
		const Rep &	b
	)		const

inlineinherited

◆ islt() [2/3]

bool islt	(	const int64_t	b,
		const Rep &	a
	)		const

inlineinherited

◆ islt() [3/3]

bool islt	(	const Rep &	a,
		const int64_t	b
	)		const

inlineinherited

◆ random() [1/3]

Rep& random	(	MyRandIter &	,
		Rep &	r,
		long	s = `1`
	)		const

inlineinherited

◆ random() [2/3]

Rep& random	(	MyRandIter &	,
		Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ random() [3/3]

Element& random	(	const Random &	g,
		Element &	r
	)		const

inlineinherited

◆ nonzerorandom() [1/3]

Rep& nonzerorandom	(	MyRandIter &	,
		Rep &	r,
		long	s = `1`
	)		const

inlineinherited

◆ nonzerorandom() [2/3]

Rep& nonzerorandom	(	MyRandIter &	,
		Rep &	r,
		const Rep &	b
	)		const

inlineinherited

◆ nonzerorandom() [3/3]

Element& nonzerorandom	(	const Random &	g,
		Element &	a
	)		const

inlineinherited

◆ read() [1/3]

std::istream& read ( std::istream & i )

inlineinherited

◆ read() [2/3]

std::istream& read	(	std::istream &	is,
		Element &	x
	)		const

inlinevirtualinherited

Read field element.

Returns: input stream from which field element is read.

Parameters

is	input stream from which field element is read.
x	field element.

Reimplemented from UnparametricOperations< _Element >.

◆ read() [3/3]

std::istream& read ( std::istream & is ) const

inlineinherited

Read field.

Returns: input stream from which field is read.

Parameters

is	input stream from which field is read.

◆ residu()

Residu_t residu ( ) const

inlineinherited

◆ size()

Residu_t size ( ) const

inlineinherited

◆ cardinality() [1/2]

Residu_t cardinality ( ) const

inlineinherited

◆ cardinality() [2/2]

T& cardinality ( T & c ) const

inlineinherited

◆ characteristic() [1/2]

Residu_t characteristic ( ) const

inlineinherited

◆ characteristic() [2/2]

T& characteristic ( T & c ) const

inlineinherited

◆ maxCardinality()

static Residu_t maxCardinality ( )

inlinestaticinherited

◆ minCardinality()

static Residu_t minCardinality ( )

inlinestaticinherited

◆ init() [1/2]

Element& init ( Element & x ) const

inlinevirtualinherited

Reimplemented from UnparametricOperations< _Element >.

◆ init() [2/2]

Element& init	(	Element &	x,
		const T &	s
	)		const

inlineinherited

◆ assign()

Element& assign	(	Element &	x,
		const Element &	y
	)		const

inlinevirtualinherited

Reimplemented from UnparametricOperations< _Element >.

◆ reduce() [1/2]

Element& reduce	(	Element &	x,
		const Element &	y
	)		const

inlineinherited

◆ reduce() [2/2]

Element& reduce ( Element & x ) const

inlineinherited

◆ minElement()

Element minElement ( ) const

inlineinherited

◆ maxElement()

Element maxElement ( ) const

inlineinherited

◆ type_string()

static const std::string type_string ( )

inlinestaticinherited

Field Documentation

◆ _fast_impl

bool _fast_impl

protected

Fast implementation.

Means simple enciphering key, and deciphering via chinese remaindering.

Warning: this means less security !

◆ _g

GivRandom _g

protectedinherited

◆ one

const Element one

inherited

Examples: examples/Integer/primitiveroot.C.

◆ zero

const Element zero

inherited

◆ mOne

const Element mOne

inherited

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Static Public Member Functions

Data Fields

Protected Attributes

Detailed Description

template<class MyRandIter = GivRandom> class Givaro::IntRSADom< MyRandIter >

Member Typedef Documentation

◆ Element

◆ random_generator

◆ Self_t

◆ Parent_t

◆ Rep

◆ RandIter

◆ NonZeroRandIter

◆ Residu_t

◆ Element_ptr

◆ ConstElement_ptr

◆ ConstElement

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ IntRSADom() [1/5]

◆ IntRSADom() [2/5]

◆ IntRSADom() [3/5]

◆ IntRSADom() [4/5]

◆ IntRSADom() [5/5]

Member Function Documentation

◆ getn()

◆ gete()

◆ getd()

◆ encipher()

◆ decipher()

◆ strong_prime()

◆ keys_gen() [1/2]

◆ keys_gen() [2/2]

◆ log()

◆ ecriture_str()

◆ ecriture_str_last()

◆ ecriture_Int()

◆ point_break()

◆ factor()

◆ iffactorprime()

◆ primefactor()

◆ set() [1/2]

◆ set() [2/2]

◆ Erathostene() [1/2]

◆ Erathostene() [2/2]

◆ divisors() [1/2]

◆ divisors() [2/2]

◆ Pollard()

◆ Lenstra()

◆ write() [1/5]

◆ write() [2/5]

◆ write() [3/5]

◆ write() [4/5]

◆ write() [5/5]

◆ isprime()

◆ isprimepower()

◆ Miller()

◆ test_Lehmann()

◆ Lehmann()

◆ isprime_Tabule()

◆ isprime_Tabule2()

◆ nextprime()

◆ prevprime()

◆ nextprimein()

◆ prevprimein()

◆ local_prime()

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ convert() [1/2]

◆ convert() [2/2]

◆ mul() [1/2]

◆ mul() [2/2]

◆ mulin() [1/2]

◆ mulin() [2/2]

◆ div() [1/2]

template<class MyRandIter = GivRandom>
class Givaro::IntRSADom< MyRandIter >