Cryptology ePrint Archive: Report 2009/391

Threshold Decryption and Zero-Knowledge Proofs for Lattice-Based Cryptosystems

Rikke Bendlin and Ivan Damgård

Abstract: We present a variant of Regev's cryptosystem, but with a new choice of parameters. By a recent classical reduction by Peikert we prove the scheme semantically secure based on the worst-case lattice problem GapSVP. From this we construct a threshold cryptosystem which has a very efficient and non-interactive decryption protocol. We prove the threshold cryptosystem secure against passive adversaries corrupting all but one of the players, and againts active adversaries corrupting less than one third of the players. We also describe how one can build a distributed key generation protocol. In the final part of the paper, we show how one can, in zero-knowledge - prove knowledge of the plaintext contained in a given ciphertext from Regev's original cryptosystem or our variant. The proof is of size only a constant times the size of a ciphertext.

Category / Keywords: public-key cryptography / lattice techniques and threshold cryptography

Publication Info: This is a more complete version of the paper published in the proceedings of TCC 2010.

Date: received 11 Aug 2009, last revised 29 Mar 2010

Contact author: rikkeb at cs au dk

Available format(s): PDF | BibTeX Citation

Note: This version includes a more general discussion of the choice of parameters, and how these choices are influenced by the underlying lattice assumptions.

Version: 20100329:105645 (All versions of this report)

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