Implementing polynomials (elements in the ring R_Q) in double-CRT form. More...

#include <DoubleCRT.h>

Inheritance diagram for helib::DoubleCRT:

Public Member Functions
	DoubleCRT (const DoubleCRT &other)=default

	DoubleCRT (const NTL::ZZX &poly, const Context &_context, const IndexSet &indexSet)
	Initializing DoubleCRT from a ZZX polynomial. More...

	DoubleCRT (const zzX &poly, const Context &_context, const IndexSet &indexSet)
	Same as above, but with zzX's. More...

	DoubleCRT (const Context &_context, const IndexSet &indexSet)
	Also specify the IndexSet explicitly. More...

DoubleCRT &	operator= (const DoubleCRT &other)

DoubleCRT &	operator= (const zzX &poly)

DoubleCRT &	operator= (const NTL::ZZX &poly)

DoubleCRT &	operator= (const NTL::ZZ &num)

DoubleCRT &	operator= (const long num)

long	getOneRow (NTL::Vec< long > &row, long idx, bool positive=false) const
	Get one row of a polynomial. More...

long	getOneRow (NTL::zz_pX &row, long idx) const

void	toPoly (NTL::ZZX &p, const IndexSet &s, bool positive=false) const
	Recovering the polynomial in coefficient representation. This yields an integer polynomial with coefficients in [-P/2,P/2], unless the positive flag is set to true, in which case we get coefficients in [0,P-1] (P is the product of all moduli used). Using the optional IndexSet param we compute the polynomial reduced modulo the product of only the primes in that set. More...

void	toPoly (NTL::ZZX &p, bool positive=false) const

bool	operator== (const DoubleCRT &other) const

bool	operator!= (const DoubleCRT &other) const

DoubleCRT &	SetZero ()

DoubleCRT &	SetOne ()

NTL::xdouble	breakIntoDigits (std::vector< DoubleCRT > &dgts) const
	Break into n digits,according to the primeSets in context.digits. See Section 3.1.6 of the design document (re-linearization) Returns the sum of the canonical embedding of the digits. More...

void	addPrimes (const IndexSet &s1, NTL::ZZX *poly_p=0)
	Expand the index set by s1. It is assumed that s1 is disjoint from the current index set. If poly_p != 0, then *poly_p will first be set to the result of applying toPoly. More...

double	addPrimesAndScale (const IndexSet &s1)
	Expand index set by s1, and multiply by Prod_{q in s1}. s1 is disjoint from the current index set, returns log(product). More...

void	removePrimes (const IndexSet &s1)
	Remove s1 from the index set. More...

void	setPrimes (const IndexSet &s1)
	@ brief make prime set equal to s1 More...

const Context &	getContext () const

const IndexMap< NTL::vec_long > &	getMap () const

const IndexSet &	getIndexSet () const

void	randomize (const NTL::ZZ *seed=nullptr)
	Fills each row i with random ints mod pi, uses NTL's PRG. More...

double	sampleSmall ()
	Coefficients are -1/0/1, Prob[0]=1/2. More...

double	sampleSmallBounded ()

double	sampleHWt (long Hwt)
	Coefficients are -1/0/1 with pre-specified number of nonzeros. More...

double	sampleHWtBounded (long Hwt)

double	sampleGaussian (double stdev=0.0)
	Coefficients are Gaussians Return a high probability bound on L-infty norm of canonical embedding. More...

double	sampleGaussianBounded (double stdev=0.0)

double	sampleUniform (long B)
	Coefficients are uniform in [-B..B]. More...

NTL::xdouble	sampleUniform (const NTL::ZZ &B)

void	scaleDownToSet (const IndexSet &s, long ptxtSpace, NTL::ZZX &delta)

void	FFT (const NTL::ZZX &poly, const IndexSet &s)

void	FFT (const zzX &poly, const IndexSet &s)

void	reduce () const

void	read (std::istream &str)

void	write (std::ostream &str) const

Arithmetic operation
Only the "destructive" versions are used, i.e., a += b is implemented but not a + b.
DoubleCRT &	Negate (const DoubleCRT &other)

DoubleCRT &	Negate ()

DoubleCRT &	operator+= (const DoubleCRT &other)

DoubleCRT &	operator+= (const NTL::ZZX &poly)

DoubleCRT &	operator+= (const NTL::ZZ &num)

DoubleCRT &	operator+= (long num)

DoubleCRT &	operator-= (const DoubleCRT &other)

DoubleCRT &	operator-= (const NTL::ZZX &poly)

DoubleCRT &	operator-= (const NTL::ZZ &num)

DoubleCRT &	operator-= (long num)

DoubleCRT &	operator++ ()

DoubleCRT &	operator-- ()

void	operator++ (int)

void	operator-- (int)

DoubleCRT &	operator*= (const DoubleCRT &other)

DoubleCRT &	operator*= (const NTL::ZZX &poly)

DoubleCRT &	operator*= (const NTL::ZZ &num)

DoubleCRT &	operator*= (long num)

void	Add (const DoubleCRT &other, bool matchIndexSets=true)

void	Sub (const DoubleCRT &other, bool matchIndexSets=true)

void	Mul (const DoubleCRT &other, bool matchIndexSets=true)

DoubleCRT &	operator/= (const NTL::ZZ &num)

DoubleCRT &	operator/= (long num)

void	Exp (long k)
	Small-exponent polynomial exponentiation. More...

void	automorph (long k)
	Apply the automorphism F(X) --> F(X^k) (with gcd(k,m)=1) More...

DoubleCRT &	operator>>= (long k)

void	complexConj ()
	Compute the complex conjugate, the same as automorph(m-1) More...

Friends
std::ostream &	operator<< (std::ostream &s, const DoubleCRT &d)

std::istream &	operator>> (std::istream &s, DoubleCRT &d)

Detailed Description

Implementing polynomials (elements in the ring R_Q) in double-CRT form.

Double-CRT form is a matrix of L rows and phi(m) columns. The i'th row contains the FFT of the element wrt the ith prime, i.e. the evaluations of the polynomial at the primitive mth roots of unity mod the ith prime. The polynomial thus represented is defined modulo the product of all the primes in use.

The list of primes is defined by the data member indexMap. indexMap.getIndexSet() defines the set of indices of primes associated with this DoubleCRT object: they index the primes stored in the associated Context.

Arithmetic operations are computed modulo the product of the primes in use and also modulo Phi_m(X). Arithmetic operations can only be applied to DoubleCRT objects relative to the same context, trying to add/multiply objects that have different Context objects will raise an error.

Constructor & Destructor Documentation

◆ DoubleCRT() [1/4]

helib::DoubleCRT::DoubleCRT ( const DoubleCRT & other )

default

◆ DoubleCRT() [2/4]

helib::DoubleCRT::DoubleCRT	(	const NTL::ZZX &	poly,
		const Context &	_context,
		const IndexSet &	indexSet
	)

Initializing DoubleCRT from a ZZX polynomial.

Parameters

poly	The ring element itself, zero if not specified
_context	The context for this DoubleCRT object, use "current active context" if not specified
indexSet	Which primes to use for this object, if not specified then use all of them

◆ DoubleCRT() [3/4]

helib::DoubleCRT::DoubleCRT	(	const zzX &	poly,
		const Context &	_context,
		const IndexSet &	indexSet
	)

Same as above, but with zzX's.

◆ DoubleCRT() [4/4]

helib::DoubleCRT::DoubleCRT	(	const Context &	_context,
		const IndexSet &	indexSet
	)

Also specify the IndexSet explicitly.

Member Function Documentation

◆ Add()

void helib::DoubleCRT::Add	(	const DoubleCRT &	other,
		bool	matchIndexSets = `true`
	)

inline

◆ addPrimes()

void helib::DoubleCRT::addPrimes	(	const IndexSet &	s1,
		NTL::ZZX *	poly_p = `0`
	)

Expand the index set by s1. It is assumed that s1 is disjoint from the current index set. If poly_p != 0, then *poly_p will first be set to the result of applying toPoly.

◆ addPrimesAndScale()

double helib::DoubleCRT::addPrimesAndScale ( const IndexSet & s1 )

Expand index set by s1, and multiply by Prod_{q in s1}. s1 is disjoint from the current index set, returns log(product).

◆ automorph()

void helib::DoubleCRT::automorph ( long k )

Apply the automorphism F(X) --> F(X^k) (with gcd(k,m)=1)

◆ breakIntoDigits()

NTL::xdouble helib::DoubleCRT::breakIntoDigits ( std::vector< DoubleCRT > & dgts ) const

Break into n digits,according to the primeSets in context.digits. See Section 3.1.6 of the design document (re-linearization) Returns the sum of the canonical embedding of the digits.

◆ complexConj()

void helib::DoubleCRT::complexConj ( )

Compute the complex conjugate, the same as automorph(m-1)

◆ Exp()

void helib::DoubleCRT::Exp ( long k )

Small-exponent polynomial exponentiation.

◆ FFT() [1/2]

void helib::DoubleCRT::FFT	(	const NTL::ZZX &	poly,
		const IndexSet &	s
	)

◆ FFT() [2/2]

void helib::DoubleCRT::FFT	(	const zzX &	poly,
		const IndexSet &	s
	)

◆ getContext()

const Context& helib::DoubleCRT::getContext ( ) const

inline

◆ getIndexSet()

const IndexSet& helib::DoubleCRT::getIndexSet ( ) const

inline

◆ getMap()

const IndexMap<NTL::vec_long>& helib::DoubleCRT::getMap ( ) const

inline

◆ getOneRow() [1/2]

long helib::DoubleCRT::getOneRow	(	NTL::Vec< long > &	row,
		long	idx,
		bool	positive = `false`
	)		const

Get one row of a polynomial.

◆ getOneRow() [2/2]

long helib::DoubleCRT::getOneRow	(	NTL::zz_pX &	row,
		long	idx
	)		const

◆ Mul()

void helib::DoubleCRT::Mul	(	const DoubleCRT &	other,
		bool	matchIndexSets = `true`
	)

inline

◆ Negate() [1/2]

DoubleCRT& helib::DoubleCRT::Negate ( )

inline

◆ Negate() [2/2]

DoubleCRT & helib::DoubleCRT::Negate ( const DoubleCRT & other )

◆ operator!=()

bool helib::DoubleCRT::operator!= ( const DoubleCRT & other ) const

inline

◆ operator*=() [1/4]

DoubleCRT& helib::DoubleCRT::operator*= ( const DoubleCRT & other )

inline

◆ operator*=() [2/4]

DoubleCRT& helib::DoubleCRT::operator*= ( const NTL::ZZ & num )

inline

◆ operator*=() [3/4]

DoubleCRT& helib::DoubleCRT::operator*= ( const NTL::ZZX & poly )

inline

◆ operator*=() [4/4]

DoubleCRT& helib::DoubleCRT::operator*= ( long num )

inline

◆ operator++() [1/2]

DoubleCRT& helib::DoubleCRT::operator++ ( )

inline

◆ operator++() [2/2]

void helib::DoubleCRT::operator++ ( int )

inline

◆ operator+=() [1/4]

DoubleCRT& helib::DoubleCRT::operator+= ( const DoubleCRT & other )

inline

◆ operator+=() [2/4]

DoubleCRT& helib::DoubleCRT::operator+= ( const NTL::ZZ & num )

inline

◆ operator+=() [3/4]

DoubleCRT& helib::DoubleCRT::operator+= ( const NTL::ZZX & poly )

inline

◆ operator+=() [4/4]

DoubleCRT& helib::DoubleCRT::operator+= ( long num )

inline

◆ operator--() [1/2]

DoubleCRT& helib::DoubleCRT::operator-- ( )

inline

◆ operator--() [2/2]

void helib::DoubleCRT::operator-- ( int )

inline

◆ operator-=() [1/4]

DoubleCRT& helib::DoubleCRT::operator-= ( const DoubleCRT & other )

inline

◆ operator-=() [2/4]

DoubleCRT& helib::DoubleCRT::operator-= ( const NTL::ZZ & num )

inline

◆ operator-=() [3/4]

DoubleCRT& helib::DoubleCRT::operator-= ( const NTL::ZZX & poly )

inline

◆ operator-=() [4/4]

DoubleCRT& helib::DoubleCRT::operator-= ( long num )

inline

◆ operator/=() [1/2]

DoubleCRT & helib::DoubleCRT::operator/= ( const NTL::ZZ & num )

◆ operator/=() [2/2]

DoubleCRT& helib::DoubleCRT::operator/= ( long num )

inline

◆ operator=() [1/5]

DoubleCRT & helib::DoubleCRT::operator= ( const DoubleCRT & other )

◆ operator=() [2/5]

DoubleCRT& helib::DoubleCRT::operator= ( const long num )

inline

◆ operator=() [3/5]

DoubleCRT & helib::DoubleCRT::operator= ( const NTL::ZZ & num )

◆ operator=() [4/5]

DoubleCRT & helib::DoubleCRT::operator= ( const NTL::ZZX & poly )

◆ operator=() [5/5]

DoubleCRT & helib::DoubleCRT::operator= ( const zzX & poly )

◆ operator==()

bool helib::DoubleCRT::operator== ( const DoubleCRT & other ) const

inline

◆ operator>>=()

DoubleCRT& helib::DoubleCRT::operator>>= ( long k )

inline

◆ randomize()

void helib::DoubleCRT::randomize ( const NTL::ZZ * seed = nullptr )

Fills each row i with random ints mod pi, uses NTL's PRG.

◆ read()

void helib::DoubleCRT::read ( std::istream & str )

◆ reduce()

void helib::DoubleCRT::reduce ( ) const

inline

◆ removePrimes()

void helib::DoubleCRT::removePrimes ( const IndexSet & s1 )

inline

Remove s1 from the index set.

◆ sampleGaussian()

double helib::DoubleCRT::sampleGaussian ( double stdev = 0.0 )

Coefficients are Gaussians Return a high probability bound on L-infty norm of canonical embedding.

◆ sampleGaussianBounded()

double helib::DoubleCRT::sampleGaussianBounded ( double stdev = 0.0 )

◆ sampleHWt()

double helib::DoubleCRT::sampleHWt ( long Hwt )

Coefficients are -1/0/1 with pre-specified number of nonzeros.

◆ sampleHWtBounded()

double helib::DoubleCRT::sampleHWtBounded ( long Hwt )

◆ sampleSmall()

double helib::DoubleCRT::sampleSmall ( )

Coefficients are -1/0/1, Prob[0]=1/2.

Sampling routines: Each of these return a high probability bound on L-infty norm of canonical embedding

◆ sampleSmallBounded()

double helib::DoubleCRT::sampleSmallBounded ( )

◆ sampleUniform() [1/2]

NTL::xdouble helib::DoubleCRT::sampleUniform ( const NTL::ZZ & B )

◆ sampleUniform() [2/2]

double helib::DoubleCRT::sampleUniform ( long B )

Coefficients are uniform in [-B..B].

◆ scaleDownToSet()

void helib::DoubleCRT::scaleDownToSet	(	const IndexSet &	s,
		long	ptxtSpace,
		NTL::ZZX &	delta
	)

◆ SetOne()

DoubleCRT& helib::DoubleCRT::SetOne ( )

inline

◆ setPrimes()

void helib::DoubleCRT::setPrimes ( const IndexSet & s1 )

inline

@ brief make prime set equal to s1

◆ SetZero()

DoubleCRT& helib::DoubleCRT::SetZero ( )

inline

◆ Sub()

void helib::DoubleCRT::Sub	(	const DoubleCRT &	other,
		bool	matchIndexSets = `true`
	)

inline

◆ toPoly() [1/2]

void helib::DoubleCRT::toPoly	(	NTL::ZZX &	p,
		bool	positive = `false`
	)		const

◆ toPoly() [2/2]

void helib::DoubleCRT::toPoly	(	NTL::ZZX &	p,
		const IndexSet &	s,
		bool	positive = `false`
	)		const

Recovering the polynomial in coefficient representation. This yields an integer polynomial with coefficients in [-P/2,P/2], unless the positive flag is set to true, in which case we get coefficients in [0,P-1] (P is the product of all moduli used). Using the optional IndexSet param we compute the polynomial reduced modulo the product of only the primes in that set.

◆ write()

void helib::DoubleCRT::write ( std::ostream & str ) const

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	s,
		const DoubleCRT &	d
	)

friend

◆ operator>>

std::istream& operator>>	(	std::istream &	s,
		DoubleCRT &	d
	)

friend

Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ DoubleCRT() [1/4]

◆ DoubleCRT() [2/4]

◆ DoubleCRT() [3/4]

◆ DoubleCRT() [4/4]

Member Function Documentation

◆ Add()

◆ addPrimes()

◆ addPrimesAndScale()

◆ automorph()

◆ breakIntoDigits()

◆ complexConj()

◆ Exp()

◆ FFT() [1/2]

◆ FFT() [2/2]

◆ getContext()

◆ getIndexSet()

◆ getMap()

◆ getOneRow() [1/2]

◆ getOneRow() [2/2]

◆ Mul()

◆ Negate() [1/2]

◆ Negate() [2/2]

◆ operator!=()

◆ operator*=() [1/4]

◆ operator*=() [2/4]

◆ operator*=() [3/4]

◆ operator*=() [4/4]

◆ operator++() [1/2]

◆ operator++() [2/2]

◆ operator+=() [1/4]

◆ operator+=() [2/4]

◆ operator+=() [3/4]

◆ operator+=() [4/4]

◆ operator--() [1/2]

◆ operator--() [2/2]

◆ operator-=() [1/4]

◆ operator-=() [2/4]

◆ operator-=() [3/4]

◆ operator-=() [4/4]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator=() [1/5]

◆ operator=() [2/5]

◆ operator=() [3/5]

◆ operator=() [4/5]

◆ operator=() [5/5]

◆ operator==()

◆ operator>>=()

◆ randomize()

◆ read()

◆ reduce()

◆ removePrimes()

◆ sampleGaussian()

◆ sampleGaussianBounded()

◆ sampleHWt()

◆ sampleHWtBounded()

◆ sampleSmall()

◆ sampleSmallBounded()

◆ sampleUniform() [1/2]

◆ sampleUniform() [2/2]

◆ scaleDownToSet()

◆ SetOne()

◆ setPrimes()

◆ SetZero()

◆ Sub()

◆ toPoly() [1/2]

◆ toPoly() [2/2]

◆ write()

Friends And Related Function Documentation

◆ operator<<

◆ operator>>