How to prove knowledge of small secrets.
IACR Cryptology ePrint Archive(2016)
摘要
We propose a new zero-knowledge protocol applicable to additively homomorphic functions that map integer vectors to an Abelian group. The protocol demonstrates knowledge of a short preimage and achieves amortised efficiency comparable to the approach of Cramer and Damgård from Crypto 2010, but gives a much tighter bound on what we can extract from a dishonest prover. Towards achieving this result, we develop an analysis for bins-and-balls games that might be of independent interest. We also provide a general analysis of rewinding of a cut-and-choose protocol as well as a method to use Lyubachevsky's rejection sampling technique efficiently in an interactive protocol when many proofs are given simultaneously. Our new protocol yields improved proofs of plaintext knowledge for Ring-LWE-based cryptosystems, where such general techniques were not known before. Moreover, they can be extended to prove preimages of homomorphic hash functions as well.
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关键词
Proofs of plaintext knowledge,Lattice-based encryption,Homomorphic hashing,Integer commitments
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