Practical Parameters for Somewhat Homomorphic Encryption Schemes on Binary Circuits

Post-quantum cryptography gets increasing attention lately, as we have to prepare alternative cryptographic solutions that will resist attacks from quantum computers. A very large effort is being done to replace the usual primitives such as encryption, signature or authentication. This effort also pulls new cryptographic features such as Somewhat or Fully Homomorphic Encryption schemes, based on lattices. Since their introduction in 2009, lots of the burden has been overcome and real applications now become possible. However many papers suffer from the fast constant pace of evolution on the attack side, so their parameter analysis is usually incomplete or obsolete. In this work we present a thorough study of two schemes that have proven their worth: FV and SHIELD, providing a deep analysis of how to setup and size their parameters, to ensure both correctness and security. Our overall aim is to provide easy-to-use guidelines for implementation purposes.