# BGV-addition

    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)

EvalAdd

    sum_ct0 = m1_ct0 + m2_ct0
    sum_ct1 = m1_ct1 + m2_ct1

Decrypt

    decrypt = (sum_ct1 * s) + sum_ct0
    decrypt = decrypt %% pm
    decrypt = CoefMod(decrypt, q)
    decrypt = CoefMod(round(decrypt), p)
    print(decrypt)
    #> 1 + 2*x + x^2