Efficient Cryptographic Protocol Design Based on Distributed El Gamal Encryption

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Abstract

We propose a set of primitives based on El Gamal encryption that can be used to construct efficient multiparty computation protocols for certain low-complexity functions. In particular, we show how to privately count the number of true Boolean disjunctions of literals and pairwise exclusive disjunctions of literals. Applications include efficient two-party protocols for computing the Hamming distance of two bitstrings and the greater-than function. The resulting protocols only require 6 rounds of interaction (in the random oracle model) and their communication complexity is \(\mathcal{O}(kQ)\) where k is the length of bit-strings and Q is a security parameter. The protocols are secure against active adversaries but do not provide fairness. Security relies on the decisional Diffie-Hellman assumption and error probability is negligible in Q.