Symmetric Variant of the BFV scheme

Question

Is it possible to encrypt a plaintext using the secret key in SEAL?
Does the symmetric variant help in increasing the noise budget of the ciphertext, or improve the homomorphic evaluation in some other way?

Answer 1

No symmetric key primitives are implemented in SEAL 3.2. There are some benefits:

• Smaller initial noise;
• Possibility to replace half of a freshly encrypted ciphertext with a random seed, resulting in ~ 50% reduction in message expansion (but only in fresh ciphertexts). This can be significant.

The only problem with the symmetric key schemes is that the ciphertexts can't easily be re-randomized since without the public key there isn't any easy way to create fresh encryptions of zero. As a result, it might be hard or impossible to create provably secure protocols where the computation depends on the private data coming from other sources than the secret key owner (through multiply_plain and add_plain).