In cryptography, the open vote network is a secure multi-party computation protocol to compute the boolean-count function: namely, given a set of binary values 0/1 in the input, compute the total count of ones without revealing each individual value. This protocol was proposed by Feng Hao, Peter Ryan, and Piotr Zieliński in 2010. It extends Hao and Zieliński's anonymous veto network protocol by allowing each participant to count the number of veto votes while preserving the anonymity of those who have voted. The protocol can be generalized to support a wider range of inputs beyond just the binary values 0 and 1.
Description
All participants agree on a group with a generator of prime order in which the discrete logarithm problem is hard. For example, a Schnorr group can be used. Assume there are participants. Unlike other secure multi-party computation protocols that typically require pairwise secret and authenticated channels between participants in addition to an authenticated public channel, OV-net only requires an authenticated public channel available to every participant. Such a channel may be realized by using digital signatures. The protocol runs in two rounds. Round 1: each participant selects a random value and publishes the ephemeral public key together with a zero-knowledge proof for the proof of the knowledge of the exponent. Such proofs may be realized by using Schnorr non-interactive zero-knowledge proofs as described in RFC 8235. After this round, each participant computes: Round 2: each participant publishes where is either 0 or 1, together with a 1-out-of-2 zero knowledge proof for the proof that is one of. Such 1-out-of-2 proofs may be realized by using Cramer, Gennaro, and Schoenmakers' zero-knowledge proof technique. After round 2, each participant computes. Note that all values vanish because. The exponent represents the count of ones. As it is usually a small number, the count can be computed by exhaustive search. Overall, the 2-round efficiency is the theoretically best possible. In terms of the computational load and bandwidth usage, OV-net is also the most efficient among related techniques.
Maximum secrecy
The OV-net protocol guarantees the secrecy of an input bit unless all other input bits are known. The protection of secrecy is the maximum since when all other bits are known, the remaining bit can always be computed by subtracting the values of known input bits from the output of the boolean-count function.
Applications
A straightforward application of OV-net is to build a boardroom voting system, where the election is run by voters themselves. For a single candidate election, each voter sends either "No" or "Yes", which correspond to 0 and 1. Every voter, as well as an observer, can tally the "Yes" votes by themselves without needing any tallying authority. There are standard methods to extend a single-candidate election to support multiple candidates. A straightforward method is to run the single-candidate election in parallel for multiple candidates, and each voter casts "Yes/No" to each of the candidates. Additional zero-knowledge proofs are needed if the voter is limited to vote for only one candidate. Another method is to modify the encoding of candidates: instead of using 0 and 1 for "No" and "Yes" in a single-candidate election, encode each candidate with a unique number such that the tally for each candidate can be unambiguously computed. In this case, a more general 1-out-of-n zero-knowledge proof is used instead where n is the number of candidates.
Implementation
A prototype implementation of OV-net was presented by McCorry, Shahandashti, and Hao at Financial Cryptography'17 as a smart contract over Ethereum's blockchain. The source code is . This implementation forms part of the Newcastle University team's solution on "", which was awarded third place in the jointly organized by The Economist and Kaspersky Lab.
