# BGV-multiply

    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)

EvalMult

    multi_ct0 = m1_ct0 * m2_ct0
    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)
    multi_ct1 = multi_ct1 %% pm
    multi_ct1 = CoefMod(multi_ct1, q)
    multi_ct1 = round(multi_ct1)

    multi_ct2 = (m1_ct1 * m2_ct1)
    multi_ct2 = multi_ct2 %% pm
    multi_ct2 = CoefMod(multi_ct2, q)
    multi_ct2 = round(multi_ct2)

Decrypt

    decrypt = (multi_ct2 * s^2) + (multi_ct1 * s) + multi_ct0
    decrypt = decrypt %% pm
    decrypt = CoefMod(decrypt, q)
    decrypt = CoefMod(round(decrypt), p)
    print(decrypt)
    #> x + x^2 + x^3