Load libraries that will be used.
library(HomomorphicEncryption)
library(polynom)Set some parameters.
d = 4
n = 2^d
p = (n/2)-1
q = 424242
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.
# generate the public key
pk0 = GenPubKey0(a, s, e, pm, q)
pk1 = GenPubKey1(a)Create polynomials for the encryption
# polynomials for encryption
e1 = GenError(n)
e2 = GenError(n)
u = GenU(n)Now create to messages to add.
m1 = polynomial(c(1, 1, 1))
m2 = polynomial(c(0, 1 ))m1_ct0 = EncryptPoly0(m1, pk0, u, e1, p, pm, q)
m1_ct1 = EncryptPoly1( pk1, u, e2, pm, q)
m2_ct0 = EncryptPoly0(m2, pk0, u, e1, p, pm, q)
m2_ct1 = EncryptPoly1( pk1, u, e2, pm, q)Multiply the encrypted messages.
multi_ct0 = m1_ct0 * m2_ct0 * (p/q)
multi_ct0 = multi_ct0 %% pm
multi_ct0 = CoefMod(multi_ct0, q)
multi_ct0 = round(multi_ct0)
multi_ct1 = (m1_ct0 * m2_ct1 + m1_ct1 * m2_ct0) * (p/q)
multi_ct1 = multi_ct1 %% pm
multi_ct1 = CoefMod(multi_ct1, q)
multi_ct1 = round(multi_ct1)
multi_ct2 = (m1_ct1 * m2_ct1) * (p/q)
multi_ct2 = multi_ct2 %% pm
multi_ct2 = CoefMod(multi_ct2, q)
multi_ct2 = round(multi_ct2)Decrypt the sum
decrypt = (multi_ct2 * s^2) + (multi_ct1 * s) + multi_ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)
# rescale
decrypt = decrypt * p/q
# round then mod p
decrypt = CoefMod(round(decrypt), p)
print(decrypt)
#> x + x^2 + x^3