# BFV-addition

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   ))

Encrypt the messages.

    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)

Sum the encrypted messages.

    sum_ct0 = m1_ct0 + m2_ct0
    sum_ct1 = m1_ct1 + m2_ct1

    sum_ct0 = sum_ct0 %% pm
    sum_ct0 = CoefMod(sum_ct0, q)

    sum_ct1 = sum_ct1 %% pm
    sum_ct1 = CoefMod(sum_ct1, q)

Decrypt the sum

    decrypt = (sum_ct1 * s) + sum_ct0
    decrypt = decrypt %% pm
    decrypt = CoefMod(decrypt, q)

    # rescale
    decrypt = decrypt * p/q

    # round then mod p
    decrypt = CoefMod(round(decrypt), p)
    print(decrypt)
    #> 1 + 2*x + x^2