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
m1 = polynomial( coef=c(1, 1, 1) )
m2 = polynomial( coef=c(0, 1   ) )

Create polynomials for the encryption

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

Generate the ciphertext

m1_ct0 = pk0*u + p*e1 + m1
m1_ct0 = m1_ct0 %% pm
m1_ct0 = CoefMod(m1_ct0, q)

m1_ct1 = pk1*u + p*e2
m1_ct1 = m1_ct1 %% pm
m1_ct1 = CoefMod(m1_ct1, q)

m2_ct0 = pk0*u + p*e1 + m2
m2_ct0 = m2_ct0 %% pm
m2_ct0 = CoefMod(m2_ct0, q)

m2_ct1 = pk1*u + p*e2
m2_ct1 = m2_ct1 %% pm
m2_ct1 = CoefMod(m2_ct1, q)

sum_ct0 = m1_ct0 + m2_ct0
sum_ct1 = m1_ct1 + m2_ct1
decrypt = (sum_ct1 * s) + sum_ct0
#> 1 + 2*x + x^2