On the Homomorphic Computation of Symmetric Cryptographic Primitives

We present an analysis on the homomorphic computability of different symmetric cryptographic primitives, with the goal of understanding their characteristics with respect to the homomorphic evaluation according to the BGV scheme. Specifically, we start from the framework presented by Gentry, Halevi and Smart for evaluating AES. We provide an improvement of it, then we perform a detailed evaluation on the homomorphic computation of cryptographic algorithms of different families (Salsa20 stream cipher, SHA-256 hash function and Keccak sponge function). After the analysis, we report the performance results of the primitives we have implemented using the recently released HElib. In the conclusions we discuss our findings for the different primitives we have analyzed to draw a general conclusion on the homomorphic evaluation of symmetric cryptographic primitives.