# BFV-multiply

Load libraries that will be used.

    library(polynom)
    library(HomomorphicEncryption)

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 multiply.

    m1 = polynomial(c(3, 2, 2))
    m2 = polynomial(c(0, 2   ))

Encrypt the two messages (i.e. genete the ct0 and ct1 part for each m1 and m2).

    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 multiple

    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)
    #> 6*x + 4*x^2 + 4*x^3