ringqp

package
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 Go to latest Published: Nov 28, 2023 License: Apache-2.0 Imports: 9 Imported by: 9

Documentation

Overview

Package ringqp is implements a wrapper for both the ringQ and ringP.

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

This section is empty.

Types

type Poly 

type Poly struct {
	Q, P ring.Poly
}

Poly represents a polynomial in the ring of polynomial modulo Q*P. This type is simply the union type between two ring.Poly, each one containing the modulus Q and P coefficients of that polynomial. The modulus Q represent the ciphertext modulus and the modulus P the special primes for the RNS decomposition during homomorphic operations involving keys.

func NewPoly 

func NewPoly(N, levelQ, levelP int) Poly

NewPoly creates a new polynomial at the given levels. If levelQ or levelP are negative, the corresponding polynomial will be nil.

func (Poly) BinarySize 

func (p Poly) BinarySize() (dataLen int)

BinarySize returns the serialized size of the object in bytes. It assumes that each coefficient takes 8 bytes.

func (*Poly) Copy 

func (p *Poly) Copy(other Poly)

Copy copies the coefficients of other on the target polynomial. This method simply calls the Copy method for each of its sub-polynomials.

func (*Poly) CopyLvl 

func (p *Poly) CopyLvl(levelQ, levelP int, other Poly)

CopyLvl copies the values of other on the target polynomial. The operation is performed at levelQ for the ringQ and levelP for the ringP.

func (Poly) CopyNew 

func (p Poly) CopyNew() *Poly

CopyNew creates an exact copy of the target polynomial.

func (Poly) Equal 

func (p Poly) Equal(other *Poly) (v bool)

Equal returns true if the receiver Poly is equal to the provided other Poly.

func (Poly) LevelP 

func (p Poly) LevelP() int

LevelP returns the level of the polynomial modulo P. Returns -1 if the modulus P is absent.

func (Poly) LevelQ 

func (p Poly) LevelQ() int

LevelQ returns the level of the polynomial modulo Q. Returns -1 if the modulus Q is absent.

func (Poly) MarshalBinary 

func (p Poly) MarshalBinary() (data []byte, err error)

MarshalBinary encodes the object into a binary form on a newly allocated slice of bytes.

func (*Poly) ReadFrom 

func (p *Poly) ReadFrom(r io.Reader) (n int64, err error)

ReadFrom reads on the object from an io.Writer. It implements the io.ReaderFrom interface.

Unless r implements the buffer.Reader interface (see see lattigo/utils/buffer/reader.go), it will be wrapped into a bufio.Reader. Since this requires allocation, it is preferable to pass a buffer.Reader directly:

  • When reading multiple values from a io.Reader, it is preferable to first first wrap io.Reader in a pre-allocated bufio.Reader.
  • When reading from a var b []byte, it is preferable to pass a buffer.NewBuffer(b) as w (see lattigo/utils/buffer/buffer.go).

func (*Poly) Resize 

func (p *Poly) Resize(levelQ, levelP int)

Resize resizes the levels of the target polynomial to the provided levels. If the provided level is larger than the current level, then allocates zero coefficients, otherwise dereferences the coefficients above the provided level. Nil polynomials are unaffected.

func (*Poly) UnmarshalBinary 

func (p *Poly) UnmarshalBinary(data []byte) (err error)

UnmarshalBinary decodes a slice of bytes generated by MarshalBinary or WriteTo on the object.

func (Poly) WriteTo 

func (p Poly) WriteTo(w io.Writer) (n int64, err error)

WriteTo writes the object on an io.Writer. It implements the io.WriterTo interface, and will write exactly object.BinarySize() bytes on w.

Unless w implements the buffer.Writer interface (see lattigo/utils/buffer/writer.go), it will be wrapped into a bufio.Writer. Since this requires allocations, it is preferable to pass a buffer.Writer directly:

  • When writing multiple times to a io.Writer, it is preferable to first wrap the io.Writer in a pre-allocated bufio.Writer.
  • When writing to a pre-allocated var b []byte, it is preferable to pass buffer.NewBuffer(b) as w (see lattigo/utils/buffer/buffer.go).

type Ring 

type Ring struct {
	RingQ, RingP *ring.Ring
}

Ring is a structure that implements the operation in the ring R_QP. This type is simply a union type between the two Ring types representing R_Q and R_P.

func (Ring) Add 

func (r Ring) Add(p1, p2, p3 Poly)

Add adds p1 to p2 coefficient-wise and writes the result on p3.

func (Ring) AddLazy 

func (r Ring) AddLazy(p1, p2, p3 Poly)

AddLazy adds p1 to p2 coefficient-wise and writes the result on p3 without modular reduction.

func (Ring) AtLevel 

func (r Ring) AtLevel(levelQ, levelP int) Ring

AtLevel returns a shallow copy of the target ring configured to carry on operations at the specified levels.

func (Ring) Automorphism 

func (r Ring) Automorphism(p1 Poly, galEl uint64, p2 Poly)

Automorphism applies the automorphism X^{i} -> X^{i*gen} on p1 and writes the result on p2. Method is not in place.

func (Ring) AutomorphismNTT 

func (r Ring) AutomorphismNTT(p1 Poly, galEl uint64, p2 Poly)

AutomorphismNTT applies the automorphism X^{i} -> X^{i*gen} on p1 and writes the result on p2. Method is not in place. Inputs are assumed to be in the NTT domain.

func (Ring) AutomorphismNTTWithIndex 

func (r Ring) AutomorphismNTTWithIndex(p1 Poly, index []uint64, p2 Poly)

AutomorphismNTTWithIndex applies the automorphism X^{i} -> X^{i*gen} on p1 and writes the result on p2. Index of automorphism must be provided. Method is not in place.

func (Ring) AutomorphismNTTWithIndexThenAddLazy 

func (r Ring) AutomorphismNTTWithIndexThenAddLazy(p1 Poly, index []uint64, p2 Poly)

AutomorphismNTTWithIndexThenAddLazy applies the automorphism X^{i} -> X^{i*gen} on p1 and adds the result on p2. Index of automorphism must be provided. Method is not in place.

func (Ring) Equal 

func (r Ring) Equal(p1, p2 Poly) (v bool)

func (Ring) EvalPolyScalar 

func (r Ring) EvalPolyScalar(pol []Poly, pt uint64, p3 Poly)

EvalPolyScalar evaluate the polynomial pol at pt and writes the result in p3

func (Ring) ExtendBasisSmallNormAndCenter 

func (r Ring) ExtendBasisSmallNormAndCenter(polyInQ ring.Poly, levelP int, polyOutQ, polyOutP ring.Poly)

ExtendBasisSmallNormAndCenter extends a small-norm polynomial polQ in R_Q to a polynomial polQP in R_QP.

func (Ring) IMForm 

func (r Ring) IMForm(p1, p2 Poly)

IMForm switches back p1 from the Montgomery domain to the conventional domain and writes the result on p2.

func (Ring) INTT 

func (r Ring) INTT(p1, p2 Poly)

INTT computes the inverse-NTT of p1 and returns the result on p2.

func (Ring) INTTLazy 

func (r Ring) INTTLazy(p1, p2 Poly)

INTTLazy computes the inverse-NTT of p1 and returns the result on p2. Output values are in the range [0, 2q-1].

func (Ring) Inverse 

func (r Ring) Inverse(scalar ring.RNSScalar)

Inverse computes the modular inverse of a scalar a expressed in a CRT decomposition. The inversion is done in-place and assumes that a is in Montgomery form.

func (Ring) LevelP 

func (r Ring) LevelP() int

LevelP returns the level at which the target ring operates for the modulus P.

func (Ring) LevelQ 

func (r Ring) LevelQ() int

LevelQ returns the level at which the target ring operates for the modulus Q.

func (Ring) Log2OfStandardDeviation 

func (r Ring) Log2OfStandardDeviation(poly Poly) (std float64)

Log2OfStandardDeviation returns base 2 logarithm of the standard deviation of the coefficients of the polynomial.

func (Ring) MForm 

func (r Ring) MForm(p1, p2 Poly)

MForm switches p1 to the Montgomery domain and writes the result on p2.

func (Ring) MulCoeffsMontgomery 

func (r Ring) MulCoeffsMontgomery(p1, p2, p3 Poly)

MulCoeffsMontgomery multiplies p1 by p2 coefficient-wise with a Montgomery modular reduction.

func (Ring) MulCoeffsMontgomeryLazy 

func (r Ring) MulCoeffsMontgomeryLazy(p1, p2, p3 Poly)

MulCoeffsMontgomeryLazy multiplies p1 by p2 coefficient-wise with a constant-time Montgomery modular reduction. Result is within [0, 2q-1].

func (Ring) MulCoeffsMontgomeryLazyThenAddLazy 

func (r Ring) MulCoeffsMontgomeryLazyThenAddLazy(p1, p2, p3 Poly)

MulCoeffsMontgomeryLazyThenAddLazy multiplies p1 by p2 coefficient-wise with a constant-time Montgomery modular reduction and adds the result on p3. Result is within [0, 2q-1]

func (Ring) MulCoeffsMontgomeryLazyThenSubLazy 

func (r Ring) MulCoeffsMontgomeryLazyThenSubLazy(p1, p2, p3 Poly)

MulCoeffsMontgomeryLazyThenSubLazy multiplies p1 by p2 coefficient-wise with a Montgomery modular reduction and subtracts the result from p3.

func (Ring) MulCoeffsMontgomeryThenAdd 

func (r Ring) MulCoeffsMontgomeryThenAdd(p1, p2, p3 Poly)

MulCoeffsMontgomeryThenAdd multiplies p1 by p2 coefficient-wise with a Montgomery modular reduction and adds the result to p3.

func (Ring) MulCoeffsMontgomeryThenSub 

func (r Ring) MulCoeffsMontgomeryThenSub(p1, p2, p3 Poly)

MulCoeffsMontgomeryThenSub multiplies p1 by p2 coefficient-wise with a Montgomery modular reduction and subtracts the result from p3.

func (Ring) MulRNSScalar 

func (r Ring) MulRNSScalar(s1, s2, sout ring.RNSScalar)

MulRNSScalar multiplies s1 and s2 and stores the result in sout.

func (Ring) MulRNSScalarMontgomery 

func (r Ring) MulRNSScalarMontgomery(p Poly, scalar []uint64, pOut Poly)

MulRNSScalarMontgomery multiplies p with a scalar value expressed in the CRT decomposition. It assumes the scalar decomposition to be in Montgomery form.

func (Ring) MulScalar 

func (r Ring) MulScalar(p1 Poly, scalar uint64, p2 Poly)

MulScalar multiplies p1 by scalar and returns the result in p2.

func (Ring) N 

func (r Ring) N() int

func (Ring) NTT 

func (r Ring) NTT(p1, p2 Poly)

NTT computes the NTT of p1 and returns the result on p2.

func (Ring) NTTLazy 

func (r Ring) NTTLazy(p1, p2 Poly)

NTTLazy computes the NTT of p1 and returns the result on p2. Output values are in the range [0, 2q-1].

func (Ring) Neg 

func (r Ring) Neg(p1, p2 Poly)

Neg negates p1 coefficient-wise and writes the result on p2.

func (Ring) NewPoly 

func (r Ring) NewPoly() Poly

NewPoly creates a new polynomial with all coefficients set to 0.

func (Ring) NewRNSScalar 

func (r Ring) NewRNSScalar() ring.RNSScalar

NewRNSScalar creates a new Scalar value (i.e., a degree-0 polynomial) in the RingQP.

func (Ring) NewRNSScalarFromUInt64 

func (r Ring) NewRNSScalarFromUInt64(v uint64) ring.RNSScalar

NewRNSScalarFromUInt64 creates a new Scalar in the RingQP initialized with value v.

func (Ring) PolyToBigintCentered 

func (r Ring) PolyToBigintCentered(p1 Poly, gap int, coeffsBigint []*big.Int)

PolyToBigintCentered reconstructs p1 and returns the result in an array of Int. Coefficients are centered around Q/2 gap defines coefficients X^{i*gap} that will be reconstructed. For example, if gap = 1, then all coefficients are reconstructed, while if gap = 2 then only coefficients X^{2*i} are reconstructed.

func (Ring) Reduce 

func (r Ring) Reduce(p1, p2 Poly)

Reduce applies the modular reduction on the coefficients of p1 and returns the result on p2.

func (Ring) Sub 

func (r Ring) Sub(p1, p2, p3 Poly)

Sub subtracts p2 to p1 coefficient-wise and writes the result on p3.

func (Ring) SubRNSScalar 

func (r Ring) SubRNSScalar(s1, s2, sout ring.RNSScalar)

SubRNSScalar subtracts s2 to s1 and stores the result in sout.

type UniformSampler 

type UniformSampler struct {
	// contains filtered or unexported fields
}

UniformSampler is a type for sampling polynomials in Ring.

func NewUniformSampler 

func NewUniformSampler(prng sampling.PRNG, r Ring) (s UniformSampler)

NewUniformSampler instantiates a new UniformSampler from a given PRNG.

func (UniformSampler) AtLevel 

func (s UniformSampler) AtLevel(levelQ, levelP int) UniformSampler

AtLevel returns a shallow copy of the target sampler that operates at the specified levels.

func (UniformSampler) Read 

func (s UniformSampler) Read(p Poly)

Read samples a new polynomial with uniform distribution and stores it into p.

func (UniformSampler) ReadNew 

func (s UniformSampler) ReadNew() (p Poly)

ReadNew samples a new polynomial with uniform distribution and returns it.

func (UniformSampler) WithPRNG 

func (s UniformSampler) WithPRNG(prng sampling.PRNG) UniformSampler

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