# CKKS encode encrypt

Load libraries that will be used.

library(polynom)
library(HomomorphicEncryption)

Set a working seed for random numbers (so that random numbers can be replicated exactly).

set.seed(123)

Set some parameters.

M     <- 8
N     <- M / 2
scale <- 200
xi    <- complex(real = cos(2 * pi / M), imaginary = sin(2 * pi / M))

Create the (complex) numbers we will encode.

z <- c(complex(real=3, imaginary=4), complex(real=2, imaginary=-1))
print(z)
#> [1] 3+4i 2-1i

Now we encode the vector of complex numbers to a polynomial.

m <- encode(xi, M, scale, z)

Let’s view the result.

print(m)
#> 500 + 283*x + 500*x^2 + 142*x^3

Set some parameters.

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

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, pm, q)
pk1 = GenPubKey1(a)

Create polynomials for the encryption

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

Generate the ciphertext

ct0 = CoefMod((pk0*u + e1 + m) %% pm, q)
ct1 = EncryptPoly1(pk1, u, e2, pm, q)

Decrypt

decrypt = (ct1 * s) + ct0
decrypt = decrypt %% pm
decrypt = CoefMod(decrypt, q)
print(decrypt[1:length(m)])
#> [1] 450 254 515 119

Let’s decode to obtain the original number:

decoded_z <- decode(xi, M, scale, polynomial(decrypt[1:length(m)]))
print(decoded_z)
#> [1] 2.727297+3.893754i 1.772703-1.256246i

The decoded z is indeed very close to the original z, we round the result to make the clearer.

round(decoded_z)
#> [1] 3+4i 2-1i