Maintaining the parameters. More...

#include <Context.h>

Public Member Functions
double noiseBoundForUniform (double magBound, long degBound) const

NTL::xdouble noiseBoundForUniform (NTL::xdouble magBound, long degBound) const

double noiseBoundForMod (long modulus, long degBound) const

double noiseBoundForGaussian (double sigma, long degBound) const

double noiseBoundForSmall (double prob, long degBound) const

double noiseBoundForHWt (long hwt, UNUSED long degBound) const

double stdDevForRecryption (long skHwt=0) const
NOTE: this is a bit heuristic. See design document for details. More...

double boundForRecryption (long skHwt=0) const

void setModSizeTable ()

Context (unsigned long m, unsigned long p, unsigned long r, const std::vector< long > &gens=std::vector< long >(), const std::vector< long > &ords=std::vector< long >())

void makeBootstrappable (const NTL::Vec< long > &mvec, long skWht=0, bool build_cache=false, bool alsoThick=true)

bool isBootstrappable () const

IndexSet fullPrimes () const

IndexSet allPrimes () const

IndexSet getCtxtPrimes (long nprimes) const

long BPL () const

bool operator== (const Context &other) const

bool operator!= (const Context &other) const

long ithPrime (unsigned long i) const
The ith small prime in the modulus chain. More...

const Cmodulus & ithModulus (unsigned long i) const
Cmodulus object corresponding to ith small prime in the chain. More...

long numPrimes () const
Total number of small prime in the chain. More...

bool isZeroDivisor (const NTL::ZZ &num) const
Is num divisible by any of the primes in the chain? More...

bool inChain (long p) const
Is p already in the chain? More...

double logOfPrime (unsigned long i) const
Returns the natural logarithm of the ith prime. More...

double logOfProduct (const IndexSet &s) const
Returns the natural logarithm of productOfPrimes(s) More...

long bitSizeOfQ () const
Size in bits of Q. More...

double securityLevel (int hwt=0) const
An estimate for the security-level. This has a lower bound of 0. More...

void printout (std::ostream &out=std::cout) const
print out algebra and other important info More...

void AddSmallPrime (long q)
Just add the given prime to the chain. More...

void AddCtxtPrime (long q)

void AddSpecialPrime (long q)


void productOfPrimes (NTL::ZZ &p, const IndexSet &s) const
The product of all the primes in the given set. More...

NTL::ZZ productOfPrimes (const IndexSet &s) const

Public Attributes
PAlgebra zMStar
The structure of Zm*. More...

PAlgebraMod alMod
The structure of Z[X]/(Phi_m(X),p^r) More...

std::shared_ptr< const EncryptedArray > ea
A default EncryptedArray. More...

std::shared_ptr< const PowerfulDCRT > pwfl_converter

std::shared_ptr< PolyModRing > slotRing
The structure of a single slot of the plaintext space. More...

NTL::xdouble stdev
sqrt(variance) of the LWE error (default=3.2) More...

double scale

IndexSet ctxtPrimes

IndexSet specialPrimes

IndexSet smallPrimes

ModuliSizes modSizes
A helper table to map required modulo-sizes to primeSets. More...

std::vector< IndexSet > digits
The set of primes for the digits. More...

ThinRecryptData rcData
Bootstrapping-related data in the context. More...

Friends
void writeContextBinary (std::ostream &str, const Context &context)

void readContextBinary (std::istream &str, Context &context)

I/O routines
To write out all the data associated with a context, do the following: writeContextBase(str, context); str << context; The first function call writes out just [m p r gens ords], which is the data needed to invoke the context constructor. The second call writes out all other information, including the stdev field, the prime sequence (including which primes are "special"), and the digits info. To read in all the data associated with a context, do the following: unsigned long m, p, r; std::vector<long> gens, ords; readContextBase(str, m, p, r, gens, ords); Context context(m, p, r, gens, ords); str >> context; The call to readContextBase just reads the values m, p, r and the set of generators in Zm* /(p) and their order. Then, after constructing the context, the >> operator reads in and attaches all other information.
void writeContextBase (std::ostream &str, const Context &context)
write [m p r] data More...

std::ostream & operator<< (std::ostream &str, const Context &context)
Write all other data. More...

void readContextBase (std::istream &str, unsigned long &m, unsigned long &p, unsigned long &r, std::vector< long > &gens, std::vector< long > &ords)
read [m p r] data, needed to construct context More...

std::istream & operator>> (std::istream &str, Context &context)
read all other data associated with context More...

Detailed Description

Maintaining the parameters.

Constructor & Destructor Documentation

◆ Context()

helib::Context::Context	(	unsigned long	m,
		unsigned long	p,
		unsigned long	r,
		const std::vector< long > &	gens = `std::vector<long>()`,
		const std::vector< long > &	ords = `std::vector<long>()`
	)

Member Function Documentation

◆ AddCtxtPrime()

void helib::Context::AddCtxtPrime ( long q )

◆ AddSmallPrime()

void helib::Context::AddSmallPrime ( long q )

Just add the given prime to the chain.

◆ AddSpecialPrime()

void helib::Context::AddSpecialPrime ( long q )

◆ allPrimes()

IndexSet helib::Context::allPrimes ( ) const

inline

◆ bitSizeOfQ()

long helib::Context::bitSizeOfQ ( ) const

inline

Size in bits of Q.

◆ boundForRecryption()

double helib::Context::boundForRecryption ( long skHwt = 0 ) const

inline

◆ BPL()

long helib::Context::BPL ( ) const

inline

◆ fullPrimes()

IndexSet helib::Context::fullPrimes ( ) const

inline

◆ getCtxtPrimes()

IndexSet helib::Context::getCtxtPrimes ( long nprimes ) const

inline

◆ inChain()

bool helib::Context::inChain ( long p ) const

inline

Is p already in the chain?

◆ isBootstrappable()

bool helib::Context::isBootstrappable ( ) const

inline

◆ isZeroDivisor()

bool helib::Context::isZeroDivisor ( const NTL::ZZ & num ) const

inline

Is num divisible by any of the primes in the chain?

◆ ithModulus()

const Cmodulus& helib::Context::ithModulus ( unsigned long i ) const

inline

Cmodulus object corresponding to ith small prime in the chain.

◆ ithPrime()

long helib::Context::ithPrime ( unsigned long i ) const

inline

The ith small prime in the modulus chain.

◆ logOfPrime()

double helib::Context::logOfPrime ( unsigned long i ) const

inline

Returns the natural logarithm of the ith prime.

◆ logOfProduct()

double helib::Context::logOfProduct ( const IndexSet & s ) const

inline

Returns the natural logarithm of productOfPrimes(s)

◆ makeBootstrappable()

void helib::Context::makeBootstrappable	(	const NTL::Vec< long > &	mvec,
		long	skWht = `0`,
		bool	build_cache = `false`,
		bool	alsoThick = `true`
	)

inline

◆ noiseBoundForGaussian()

double helib::Context::noiseBoundForGaussian	(	double	sigma,
		long	degBound
	)		const

inline

Assume the polynomial f(x) = sum_{i < k} f_i x^i is chosen so that each f_i is chosen uniformly and independently from N(0, sigma^2), and that k = degBound. This returns a bound B such that the L-infty norm of the canonical embedding exceeds B with probability at most epsilon.

◆ noiseBoundForHWt()

double helib::Context::noiseBoundForHWt	(	long	hwt,
		UNUSED long	degBound
	)		const

inline

Assume the polynomial f(x) = sum_{i < k} f_i x^i is chosen hwt coefficients are chosen to \pm 1, and the remainder zero. This returns a bound B such that the L-infty norm of the canonical embedding exceeds B with probability at most epsilon.

◆ noiseBoundForMod()

double helib::Context::noiseBoundForMod	(	long	modulus,
		long	degBound
	)		const

inline

Assume the polynomial f(x) = sum_{i < k} f_i x^i is chosen so that each f_i is chosen uniformly and independently from the from the set of balanced residues modulo the given modulus. This returns a bound B such that the L-infty norm of the canonical embedding exceeds B with probability at most epsilon.

◆ noiseBoundForSmall()

double helib::Context::noiseBoundForSmall	(	double	prob,
		long	degBound
	)		const

inline

Assume the polynomial f(x) = sum_{i < k} f_i x^i is chosen so that each f_i is zero with probability 1-prob, 1 with probability prob/2, and -1 with probability prob/2. This returns a bound B such that the L-infty norm of the canonical embedding exceeds B with probability at most epsilon.

◆ noiseBoundForUniform() [1/2]

double helib::Context::noiseBoundForUniform	(	double	magBound,
		long	degBound
	)		const

inline

erfc(scale/sqrt(2)) * phi(m) should be less than some negligible parameter epsilon. The default value of 10 should be good enough for most applications. NOTE: -log(erfc(8/sqrt(2)))/log(2) = 49.5 -log(erfc(10/sqrt(2)))/log(2) = 75.8 -log(erfc(11/sqrt(2)))/log(2) = 91.1 -log(erfc(12/sqrt(2)))/log(2) =107.8 The way this is used is as follows. If we have a normal random variable X with variance sigma^2, then the probability that that X lies outside the interval [-scale*sigma, scale*sigma] is delta=erfc(scale/sqrt(2)). We will usually apply the union bound to a vector of phi(m) such random variables (one for each primitive m-th root of unity), so that the probability that that the L-infty norm exceeds scale*sigma is at most epsilon=phim*delta. Thus, scale*sigma will be used as a high-probability bound on the L-infty norm of such vectors. Assume the polynomial f(x) = sum_{i < k} f_i x^i is chosen so that each f_i is chosen uniformly and independently from the interval [-magBound, magBound], and that k = degBound. This returns a bound B such that the L-infty norm of the canonical embedding exceeds B with probability at most epsilon.

◆ noiseBoundForUniform() [2/2]

NTL::xdouble helib::Context::noiseBoundForUniform	(	NTL::xdouble	magBound,
		long	degBound
	)		const

inline

◆ numPrimes()

long helib::Context::numPrimes ( ) const

inline

Total number of small prime in the chain.

◆ operator!=()

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

inline

◆ operator==()

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

◆ printout()

void helib::Context::printout ( std::ostream & out = std::cout ) const

print out algebra and other important info

◆ productOfPrimes() [1/2]

NTL::ZZ helib::Context::productOfPrimes ( const IndexSet & s ) const

inline

◆ productOfPrimes() [2/2]

void helib::Context::productOfPrimes	(	NTL::ZZ &	p,
		const IndexSet &	s
	)		const

The product of all the primes in the given set.

◆ securityLevel()

double helib::Context::securityLevel ( int hwt = 0 ) const

inline

An estimate for the security-level. This has a lower bound of 0.

This function uses experimental affine approximations to the lwe-estimator from https://bitbucket.org/malb/lwe-estimator/raw/HEAD/estimator.py, from Aug-2020 (see script in misc/estimator/lwe-estimator.sage).

Let s=3.2 if m is a power of two, or s=3.2*sqrt(m) otherwise. For the estimator we use alpha=s/q (so log2AlphaInv = log_2(q/s)), and n=phi(m).

◆ setModSizeTable()

void helib::Context::setModSizeTable ( )

inline

◆ stdDevForRecryption()

double helib::Context::stdDevForRecryption ( long skHwt = 0 ) const

inline

NOTE: this is a bit heuristic. See design document for details.

This computes a high probability bound on the L-infty norm of x0+s*x1 in the pwrfl basis, assuming is chosen with coeffs in the pwrfl basis uniformly and independently dist'd over [-1/2,1/2], x0 has arbitrary coeffs over [-1/2,1/2] in the pwrfl basis, and assuming s is chosen with skHwt nonzero coeffs mod X^m-1 in the power basis (uniformly and independently over {-1,1}). The bound should be satisfied with probability epsilon. NOTE: this is still valid even when m is a power of 2

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	str,
		const Context &	context
	)

friend

Write all other data.

◆ operator>>

std::istream& operator>>	(	std::istream &	str,
		Context &	context
	)

friend

read all other data associated with context

◆ readContextBase

void readContextBase	(	std::istream &	str,
		unsigned long &	m,
		unsigned long &	p,
		unsigned long &	r,
		std::vector< long > &	gens,
		std::vector< long > &	ords
	)

friend

read [m p r] data, needed to construct context

◆ readContextBinary

void readContextBinary	(	std::istream &	str,
		Context &	context
	)

friend

◆ writeContextBase

void writeContextBase	(	std::ostream &	str,
		const Context &	context
	)

friend

write [m p r] data

◆ writeContextBinary

void writeContextBinary	(	std::ostream &	str,
		const Context &	context
	)

friend

Member Data Documentation

◆ alMod

PAlgebraMod helib::Context::alMod

The structure of Z[X]/(Phi_m(X),p^r)

◆ ctxtPrimes

IndexSet helib::Context::ctxtPrimes

The "ciphertext primes" are the "normal" primes that are used to represent the public encryption key and ciphertexts. These are all "large" single=precision primes, or bit-size roughly NTL_SP_SIZE bits.

◆ digits

std::vector<IndexSet> helib::Context::digits

The set of primes for the digits.

The different columns in any key-switching matrix contain encryptions of multiplies of the secret key, sk, B1*sk, B2*B1*sk, B3*B2*B1*sk,... with each Bi a product of a few "non-special" primes in the chain. The digits data member indicate which primes correspond to each of the Bi's. These are all IndexSet objects, whose union is the subset ctxtPrimes.

The number of Bi's is one less than the number of columns in the key switching matrices (since the 1st column encrypts sk, without any Bi's), but we keep in the digits std::vector also an entry for the primes that do not participate in any Bi (so digits.size() is the same as the number of columns in the key switching matrices). See section 3.1.6 in the design document (key-switching).

◆ ea

std::shared_ptr<const EncryptedArray> helib::Context::ea

A default EncryptedArray.

◆ modSizes

ModuliSizes helib::Context::modSizes

A helper table to map required modulo-sizes to primeSets.

◆ pwfl_converter

std::shared_ptr<const PowerfulDCRT> helib::Context::pwfl_converter

◆ rcData

ThinRecryptData helib::Context::rcData

Bootstrapping-related data in the context.

◆ scale

double helib::Context::scale

◆ slotRing

std::shared_ptr<PolyModRing> helib::Context::slotRing

The structure of a single slot of the plaintext space.

This will be Z[X]/(G(x),p^r) for some irreducible factor G of Phi_m(X).

◆ smallPrimes

IndexSet helib::Context::smallPrimes

Yet a third set of primes, aimed at allowing modulus-switching with higher resolution. These are somewhat smaller single-precision primes, of size from NTL_SP_SIZE-20 to NTL_SP_SIZE-1.

◆ specialPrimes

IndexSet helib::Context::specialPrimes

A disjoint set of primes, used for key switching. See section 3.1.6 in the design document (key-switching). These too are "large" single=precision primes, or bit-size close to NTL_SP_SIZE bits.

◆ stdev

NTL::xdouble helib::Context::stdev

sqrt(variance) of the LWE error (default=3.2)

◆ zMStar

PAlgebra helib::Context::zMStar

The structure of Zm*.

Search Results

Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Context()

Member Function Documentation

◆ AddCtxtPrime()

◆ AddSmallPrime()

◆ AddSpecialPrime()

◆ allPrimes()

◆ bitSizeOfQ()

◆ boundForRecryption()

◆ BPL()

◆ fullPrimes()

◆ getCtxtPrimes()

◆ inChain()

◆ isBootstrappable()

◆ isZeroDivisor()

◆ ithModulus()

◆ ithPrime()

◆ logOfPrime()

◆ logOfProduct()

◆ makeBootstrappable()

◆ noiseBoundForGaussian()

◆ noiseBoundForHWt()

◆ noiseBoundForMod()

◆ noiseBoundForSmall()

◆ noiseBoundForUniform() [1/2]

◆ noiseBoundForUniform() [2/2]

◆ numPrimes()

◆ operator!=()

◆ operator==()

◆ printout()

◆ productOfPrimes() [1/2]

◆ productOfPrimes() [2/2]

◆ securityLevel()

◆ setModSizeTable()

◆ stdDevForRecryption()

Friends And Related Function Documentation

◆ operator<<

◆ operator>>

◆ readContextBase

◆ readContextBinary

◆ writeContextBase

◆ writeContextBinary

Member Data Documentation

◆ alMod

◆ ctxtPrimes

◆ digits

◆ ea

◆ modSizes

◆ pwfl_converter

◆ rcData

◆ scale

◆ slotRing

◆ smallPrimes

◆ specialPrimes

◆ stdev

◆ zMStar