Secret, verifiable auctions from elections

Abstract

Auctions and elections are seemingly disjoint. Nevertheless, similar cryptographic primitives are used in both domains. For instance, mixnets, homomorphic encryption and trapdoor bit-commitments have been used by state-of-the-art schemes in both domains. These developments have appeared independently. For example, the adoption of mixnets in elections preceded a similar adoption in auctions by over two decades. In this paper, we demonstrate a relation between auctions and elections: we present a generic construction for auctions from election schemes. Moreover, we show that the construction guarantees secrecy and verifiability, assuming the underlying election scheme satisfies analogous security properties. We demonstrate the applicability of our work by deriving auction schemes from the Helios family of election schemes. Our results advance the unification of auctions and elections, thereby facilitating the progression of both domains.

Verifiability of Helios Mixnet

“…An asymmetric encryption scheme Π = (Gen, Enc, Dec) is homomorphic, with respect to ternary operators , ⊕, and ⊗, 29 if there exists a negligible function negl, such that for all security parameters κ, we have the following. 30 First, for all messages m 1 and m 2 we have Pr[(pk , sk , m) ← Gen(κ); c 1 ← Enc(pk , m 1 ); c 2 ← Enc(pk , m 2 ) :…”

“…The tallying and verification algorithms in Definition 9 adapt (unpublished) algorithms prepared by Quaglia & Smyth in the context of[30]. Quaglia & Smyth have since incorporated these adaptations into their work to take advantage of the results presented in this manuscript.…”

Authentication with Weaker Trust Assumptions for Voting Systems

“…We demonstrate applicability of Theorem 2 using a construction for election schemes from asymmetric encryption. 7,8 Definition 4 (Enc2Vote [32]). Given a perfectly correct asymmetric encryption scheme Π = (Gen, Enc, Dec) satisfying IND-CPA, election scheme with external authentication Enc2Vote(Π) is defined as follows:…”

“…, the system must be complete: there exists a negligible function negl, such that for all statement and witnesses (s, w) ∈ R and security parameters κ, we have Pr[σ ← Prove(s, w, κ) : Verify(s, σ, κ) = 1] > 1 − negl(κ).Definition 9 (Fiat-Shamir transformation[18]). Given a sigma protocol Σ = (Comm, Chal, Resp, Verify Σ ) for relation R and a hash function H, the Fiat-Shamir transformation, denoted FS(Σ, H), is the non-interactive proof system (Prove, Verify), defined as follows:Prove(s, w, κ) = (comm, t) ← Comm(s, w, κ); chal ← H(comm, s); resp ← Resp(chal, t, κ); return (comm, resp) Verify(s, (comm, resp), κ) =chal ← H(comm, s); return Verify Σ (s, (comm, chal, resp), κ)Definition 10 (Zero-knowledge (as formalized in[32])). Let ∆ = (Prove, Verify) be a non-interactive proof system for a relation R, derived by application of the Fiat-Shamir transformation[18] to a random oracle H and the sigma protocol.…”

An Improved and Efficient Coercion-resistant Measure for Electronic Voting System

“…Based on the proposal of Wu et al [2,41], they represented that the issues of bribery and coercion can be protected as long as the modus applied to perform bribery and coercion can make people comprehend clearly. As a result, the methods that applied to the system of bribe and coercion can be divided into five levels: Level-1: Receipt Checking Making the voters believe their vote is efficiently accepted and calculated, there are several e-voting systems offer the voting evidence and receipts to voters [3,4,5,[6][7][8][9][10][11]. Through checking the voting receipts from the e-voting systems, the briber and the coercer can exam whether a voter has followed their rules or not.…”