Memory-Bounded Randomness for Hardware-Constrained Encrypted Computation

Encrypted computation enables processing sensitive data directly in the encrypted domain, which allows outsourcing to third parties without compromising privacy. Recent solutions that leverage partial homomorphic encryption, however, require excessive lookup tables or obfuscated software oracles to implement branching over encrypted control values. To address these limitations and make encrypted computations more practical on memory-constrained systems, we present a novel approach for limiting the amount of randomness in probabilistic ciphertexts, using number theory primitives and hash tables. This allows de-randomizing probabilistic ciphertexts and define a new encrypted abstract machine that is memory-friendly to the target system. Compared to obfuscated oracles in previous work, our method performs control flow decisions over ciphertexts twice as fast, while requiring selectively small lookup tables.