Load libraries that will be used.

Set some parameters.

Set a working seed for random numbers

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.

Create polynomials for the encryption

Now create to messages to add.

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