BGV

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High-Performance Open-Source Archive

BGV

library(polynom)
library(HomomorphicEncryption)

Set some parameters.

d  =   4
n  =   2^d
p  =   (n/2)-1
t  =   p
q  = 868
pm = GenPolyMod(n)

Set a working seed for random numbers

set.seed(123)

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

# generate a secret key
s = GenSecretKey(n)

# generate a
a = GenA(n, q)

# generate the error
e = GenError(n)

Generate the public key.

pk0 = GenPubKey0(a, s, e*p, pm, q)
pk1 = GenPubKey1(a)

Create a polynomial message

# create a message
m = polynomial( coef=c(1, 1, 1) )

Create polynomials for the encryption

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

Generate the ciphertext

ct0 = pk0*u + p*e1 + m
ct0 = ct0 %% pm
ct0 = CoefMod(ct0, q)
  
ct1 = pk1*u + p*e2
ct1 = ct1 %% pm
ct1 = CoefMod(ct1, q)

Decrypt

decrypt = (ct1 * s) + ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)
decrypt = CoefMod(round(decrypt), p)
print(decrypt)
#> 1 + x + x^2

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