Single-Server Delegation of Ring Multiplications from Quasilinear-time Clients

We investigate the problem of delegating operations in cryptography solutions from client devices that only perform quasilinear-time or lower-order computations (e.g., additions/subtractions, modular reductions with a small modulus, etc.) to a single, possibly malicious, server. All previous work considered clients capable of computing higher-order operations, such as fully homomorphic encryption, group exponentiations or several group multiplications. In this model, we show protocols to delegate the computation of ring multiplications while satisfying desirable result correctness, input privacy and result security requirements. The main technical component, of independent interest, is a family of probabilistic tests that extends a classical test by Pippenger. The asymptotic improvement in our multiplication delegation protocols is also backed up by concrete implementation results, demonstrating that the client's online computation is strictly smaller than non-delegated computation of the same function, for input lengths of interest in cryptography solutions.