LNCS

We construct a perfectly binding string commitment scheme whose security is based on the learning parity with noise (LPN) assumption, or equivalently, the hardness of decoding random linear codes. Our scheme not only allows for a simple and efficient zero-knowledge proof of knowledge for committed values (essentially a Σ-protocol), but also for such proofs showing any kind of relation amongst committed values, i.e. proving that messages m_0,...,m_u, are such that m_0=C(m_1,...,m_u) for any circuit C. To get soundness which is exponentially small in a security parameter t, and when the zero-knowledge property relies on the LPN problem with secrets of length l, our 3 round protocol has communication complexity O(t|C|l log(l)) and computational complexity of O(t|C|l) bit operations. The hidden constants are small, and the computation consists mostly of computing inner products of bit-vectors

Design and Implementation of Cast-as-Intended Verifiability for a Blockchain-Based Voting System

Digitization of electoral processes depends on confident systems that produce verifiable evidence. The design and implementation of voting systems has been widely studied in prior research, bringing together expertise in many fields. Switzerland is organized in a federal, decentralized structure of independent governmental entities. Thus, its decentralized structure is a real-world example for implementing an electronic voting system, where trust is distributed among multiple authorities. This work outlines the design and implementation of a blockchain-based electronic voting system providing cast-as-intended verifiability. The generation of non-interactive zero-knowledge proofs of knowledge enables every voter to verify the encrypted vote, while maintaining the secrecy of the ballot. The Public Bulletin Board (PBB) is a crucial component of every electronic voting system, serving as a publicly verifiable log of communication and ballots - here a blockchain is used as the PBB. Also, the required cryptographic operations are in linear relation to the number of voters, making the outlined system fit for large-scale elections

Advances in Cryptology - ASIACRYPT 2012

International audience18th International Conference on the Theory and Application of Cryptology and Information Security, Beijing, China, December 2-6, 2012. Proceeding

An Efficient Scheme for Proving a Shuffle

Abstract. In this paper, we propose a novel and efficient protocol for proving the correctness of a shuffle, without leaking how the shuffle was performed. Using this protocol, we can prove the correctness of a shuffle of n data with roughly 18n exponentiations, where as the protocol of Sako-Kilian[SK95] required 642n and that of Abe[Ab99] required 22n log n. The length of proof will be only 2 11 n bits in our protocol, opposed to 2 18 n bits and 2 14 n log n bits required by Sako-Kilian and Abe, respectively. The proposed protocol will be a building block of an efficient, universally verifiable mix-net, whose application to voting system is prominent