Title: BFV, BGV, CKKS Schema for Fully Homomorphic Encryption
Version: 0.9.0
Description: Implements the Brakerski-Fan-Vercauteren (BFV, 2012) https://eprint.iacr.org/2012/144, Brakerski-Gentry-Vaikuntanathan (BGV, 2014) <doi:10.1145/2633600>, and Cheon-Kim-Kim-Song (CKKS, 2016) https://eprint.iacr.org/2016/421.pdf schema for Fully Homomorphic Encryption. The included vignettes demonstrate the encryption procedures.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.2.3
Depends: polynom, stats, HEtools
Suggests: covr, knitr, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2024-01-09 13:16:35 UTC; bquast
Author: Bastiaan Quast ORCID iD [aut, cre]
Maintainer: Bastiaan Quast <bquast@gmail.com>
Repository: CRAN
Date/Publication: 2024-01-09 13:40:05 UTC

Brakerski / Fan-Vercauteren

Description

Brakerski / Fan-Vercauteren

Usage

BFV_KeyGen(d = 4, q = 424242)

Arguments

d

the d input

q

the q input

Value

polynomial

Examples

d  =      4
n  =      2^d
p  =     (n/2)-1
q  = 424242
GenPolyMod(n)

BFV encryption

Description

BFV encryption

Usage

BFV_encrypt(m, pk)

Arguments

m

message

pk

public key

Value

polynomial

Encrypt Polynomial Message Part 0

Description

Encrypt Polynomial Message Part 0

Usage

EncryptPoly0(m, pk0, u, e1, p, pm, q)

Arguments

m

message

pk0

public key part 0

u

u

e1

e1

p

p

pm

pm

q

q

Value

polynomial which contains the message in ciphertext

Encrypt Polynomial Message Part 1

Description

Encrypt Polynomial Message Part 1

Usage

EncryptPoly1(pk1, u, e2, pm, q)

Arguments

pk1

public key part 1

u

u

e2

e2

pm

pm

q

q

Value

polynomial which contains the message in ciphertext

Generate a

Description

Generate a

Usage

GenA(n, q)

Arguments

n

the order

q

the ciphermod of coefficients

Value

polynomial of order x^^n with coefficients 0,..,q

Examples

n = 16
q =  7
GenA(n, q)

Generate a

Description

Generate a

Usage

GenError(n)

Arguments

n

the order

Value

polynomial of order x^^n with discrete Gaussian distribution, bounded (not strictly true) by -n,n

Examples

n = 16
GenError(n)

Generate the Evaluation Key

Description

Generate the Evaluation Key

Usage

GenEvalKey0(a, s, e)

Arguments

a

a

s

s

e

e

Value

polynomial

Generate Polynomial Modulo

Description

These objects are imported from other packages. Follow the links below to see their documentation.

HEtools

CoefMod

Arguments

n

the order

Value

polynomial of the form x^^n + 1

Generate the Public Key

Description

Generate the Public Key

Usage

GenPubKey(a, n, e, pm, q)

Arguments

a

a

n

n

e

e

pm

pm

q

q

Value

list with the two polynomials that form the public key

Generate part 0 of the Public Key

Description

Generate part 0 of the Public Key

Usage

GenPubKey0(a, s, e, pm, q)

Arguments

a

a

s

s

e

e

pm

pm

q

q

Value

polynomial

Generate part 1 of the Public Key

Description

Generate part 1 of the Public Key

Usage

GenPubKey1(a)

Arguments

a

a

Value

polynomial

Generate Secret key

Description

Generate Secret key

Usage

GenSecretKey(n)

Arguments

n

the order

Value

polynomial of order x^^n with coefficients (-1,-,1)

Examples

n = 16
GenSecretKey(n)

Generate u

Description

Generate u

Usage

GenU(n)

Arguments

n

the order

Value

polynomial of order x^^n-1 with coefficients (-1,-,1)

Examples

n = 16
GenU

compute basis coordinates

Description

Compute basis coordinates

Usage

compute_basis_coordinates(sigma_R_basis, z)

Arguments

sigma_R_basis

sigma_R_basis

z

z

Value

basis coordinates

coordinate-wise random rounding

Description

Coordinate-wise random rounding

Usage

coordinate_wise_random_rounding(coordinates)

Arguments

coordinates

coordinates

Value

rounded coordinates

decode

Description

Decode

Usage

decode(xi, M, scale, p)

Arguments

xi

xi

M

M

scale

scale

p

p

Value

decoded xi

encode

Description

Encode

Usage

encode(xi, M, scale, z)

Arguments

xi

xi

M

M

scale

scale

z

z

Value

encode polynomial

pi function

Description

Pi function

Usage

pi_function(M, z)

Arguments

M

M

z

z

Value

Pi of M

pi inverse function

Description

Pi inverse function

Usage

pi_inverse(z)

Arguments

z

z

Value

inverse of z

round coordinates

Description

Round coordinates

Usage

round_coordinates(coordinates)

Arguments

coordinates

coordinates

Value

rounded coordinates

sigma discretization

Description

Sigma discretization

Usage

sigma_R_discretization(xi, M, z)

Arguments

xi

xi

M

M

z

z

Value

sigma R discretization

sigma function

Description

Sigma

Usage

sigma_function(xi, M, p)

Arguments

xi

xi

M

M

p

p

Value

sigma of xi

sigma inverse

Description

Sigma inverse

Usage

sigma_inverse(xi, M, b)

Arguments

xi

xi

M

M

b

b

Value

sigma inverse of xi

vandermonde

Description

Vandermonde

Usage

vandermonde(xi, M)

Arguments

xi

xi

M

M

Value

The Vandermonde matrix