BFV

In HomomorphicEncryption: BFV, BGV, CKKS Schema for Fully Homomorphic Encryption

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

Load libraries that will be used.

library(polynom)
library(HomomorphicEncryption)

Set some parameters.

d  =   4
n  =   2^d
p  =   (n/2)-1
q  = 874

Set a working seed for random numbers

set.seed(123)

Here we create the polynomial modulo.

pm = polynomial( coef=c(1, rep(0, n-1), 1 ) )
print(pm)

Create the secret key and the polynomials a and e, which will go into the public key

# generate a secret key
s = GenSecretKey(n)
print(s)

# generate a
a = GenA(n, q)
print(a)

Generate the error for the public key.

e = GenError(n)
print(e)

Generate the public key.

pk0 = GenPubKey0(a, s, e, pm, q)
print(pk0)

pk1 = GenPubKey1(a)

Create a polynomial message

# create a message
m = polynomial( coef=c(6, 4, 2) )

Create polynomials for the encryption

# polynomials for encryption
e1 = GenError(n)
e2 = GenError(n)
u  = GenU(n)
print(u)

Generate the ciphertext.

ct0 = EncryptPoly0(m, pk0, u, e1, p, pm, q)
print(ct0)

ct1 = EncryptPoly1(   pk1, u, e2,    pm, q)
print(ct1)

Decrypt

decrypt = (ct1 * s) + ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)

# rescale
decrypt = decrypt * p/q

Round (remove the error) then mod p

# round then mod p
decrypt = CoefMod(round(decrypt), p)
print(decrypt)

Which is indeed the message that we first encrypted.

Next, look at the vignette BFV-2 which does the exact same process, but unpacks all the functions used here into basic mathematical operations.

HomomorphicEncryption documentation built on May 29, 2024, 9:59 a.m.