Abstract
Sander, Young and Yung recently exhibited a protocol for computing on encrypted inputs, for functions computable in NC 1. In their variant of secure function evaluation, Bob (the “CryptoComputer”) accepts homomorphically-encrypted inputs (x) from client Alice, and then returns a string from which Alice can extract f(x; y) (where y is Bob’s input, or e.g. the function f itself). Alice must not learn more about y than what f(x, y) reveals by itself. We extend their result to encompass NLOGSPACE (nondeterministic log-space functions). In the domain of multiparty computations, constant-round protocols have been known for years [BB89,FKN95]. This paper introduces novel parallelization techniques that, coupled with the [SYY99] methods, reduce the constant to 1 with preprocessing. This resolves the conjecture that NLOGSPACE subcomputations (including log-slices of circuit computation) can be evaluated with latency 1 (as opposed to just O(1))
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Beaver, D. (2000). Minimal-Latency Secure Function Evaluation. In: Preneel, B. (eds) Advances in Cryptology — EUROCRYPT 2000. EUROCRYPT 2000. Lecture Notes in Computer Science, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45539-6_23
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DOI: https://doi.org/10.1007/3-540-45539-6_23
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