Single-Server Delegation of Small-Exponent Exponentiation from Quasilinear-Time Clients and Applications

Motivated by reducing the cost of public-key encryption on resource-constrained devices, we investigate the problem of delegating operations in cryptography schemes from client devices that only perform quasilinear-time or lower-order computations (e.g., modular additions and subtractions, multiplications with a small modulus, etc.) to a single, possibly malicious, server. Almost all of previous work considered clients capable of computing higher-order operations, such as fully homomorphic encryption, group exponentiations or several group multiplications with a large modulus. We show the (first in this model) single-server protocols to efficiently delegate the computation of small-exponent ring exponentiation, while satisfying desirable result correctness, input privacy and result security requirements. Small-exponent exponentiation is part of, for instance, the exponential El Gamal encryption algorithm. The asymptotic improvements in our delegation protocols are also backed up by concrete implementation results, showing that the improvements hold also for parameter values of practical interest. As an application example, we show that our protocols can be used to delegate encryption in the exponential El Gamal public-key cryptosystem, which can in turn be used for confidential transfer of, for instance, the average of multiple data values measured by a group of IoT client devices, with remarkable communication efficiency (i.e., a single public-key encryption ciphertext for each group).