Post-quantum secure instantiation of the Ordinos e-voting system

Abstract

The end-to-end verifiable e-voting system Ordinos [26] is primarily characterized by its tally-hiding property, which ensures that only the actual election result, e. g., the winner of the election, is revealed while the full tally consisting of the aggregated votes stays hidden. Ordinos is an abstract model that guarantees tally-hiding, verifiability and vote privacy if the underlying cryptographic primitives satisfy certain requirements. It uses a multi-party-computation protocol over an additively homomorphic encryption scheme and guarantees active security with zero-knowledge proofs. Ordinos has already been instantiated for several election systems using the Paillier [35] encryption scheme, which can be broken by Shor’s algorithm [41]. The aim of this thesis is to instantiate Ordinos post-quantum secure using a variant of Regev’s LWE-based cryptosystem [39], which is adapted to realize an actively secure threshold encryption scheme over an arbitrary plaintext space. Then a noise analysis of the arithmetic and logical components used in the MPC-protocol of the Paillier instantiation is conducted, and the components are slightly adapted to restrict the noise growth. Additionally, valid zero-knowledge proofs are provided and a concrete instantiation achieving a security level of 128 bits is shown.