# 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