Paper 2008/367 Original: eprint.iacr.org/2008/367 ↗

Threshold Homomorphic Encryption in the Universally Composable Cryptographic Library

Abstract

Protocol security analysis has become an active research topic in recent years. Researchers have been trying to build sufficient theories for building automated tools, which give security proofs for cryptographic protocols. There are two approaches for analysing protocols: formal and computational. The former, often called Dolev-Yao style, uses abstract terms to model cryptographic messages with an assumption about perfect security of the cryptographic primitives. The latter mathematically uses indistinguishability to prove that adversaries with computational resources bounds cannot gain anything significantly. The first method is easy to be automated while the second one can give sound proofs of security. Therefore there is a demand to bridge the gap between two methods in order to have better security-proof tools. One idea is to prove that some Dolev-Yao style cryptographic primitives used in formal tools are computationally sound for arbitrary active attacks in arbitrary reactive environments, i.e universally composable. As a consequence, protocols that use such primitives can also be proved secure by formal tools. In this paper, we prove that a homomorphic encryption used together with a non-interactive zero-knowledge proof in Dolev-Yao style are sound abstractions for the real implementation under certain conditions. It helps to automatically design and analyze a class of protocols that use homomorphic encryptions together with non-interactive zero-knowledge proofs, such as e-voting.