The Application Of LWE Homomorphic Encryption Algorithm In Electronic Voting System

With the fast development of the mobile network,many onsite activities can be accomplished through the internet now,and the electronic voting is one of the examples.Because of the high efficiency,low cost and low human error rate,many countries and areas have carried out a number of large-scale trials.And the great convenience of electronic voting can improve the attendance and thus promote the process of democratization.Most electronic voting systems for the moment are based on traditional cryptosystems such as the Paillier cryptosystem,and the appearance of quantum computers severely threats the security of those traditional electronic voting systems.There are few electronic voting systems newly promoted and most of them suffer from strong security assumptions or low efficiency.The LWE algorithm is considered as a post-quantum cryptosystem with provable security and high efficiency,but compared with those traditional cryptography schemes,the application of the LWE is still in its infancy.Therefore,exploring a way to utilize the homomorphism of the LWE to construct an efficient and verifiable electronic voting system,and in the meantime facilitating the use of post-quantum cryptography are of great theoretical and practical meaning.Regarding the current issues,we propose a homomorphic LWE-based data verification scheme,an interactive zero-knowledge proof in this paper and adopt them to construct an efficient verifiable post-quantum electronic voting system.The system utilizes the homomorphic property of the LWE to tally the votes.By the data verification scheme,the system can verify the validity of a ballot while keeping the content of the ballot secret.Besides,by the interactive zero-knowledge proof,anyone can interact with the tally server to verify the correctness of tally results,making sure that these tally results are not modified,so as to guarantee the correctness and verifiability of the voting system.We implement the electronic voting system and carry out a series of experiments.In general,it takes only 2.8ms for a voter to generate a ballot ciphertext.In terms of ballot verification,the verification servers can complete the verification of more than 2000 ballots within 0.8s.In terms of homomorphic tallying,the time required to homomorphically tally 1000000 ballots is only about 1.8s and it takes 0.07 ms for the tally server to decrypt a tally result.Furthermore,we analyze and prove the properties of our voting system,showing that our system is not inferior to those traditional electronic voting systems in terms of the basic cryptographic properties and it can resist quantum attacks.The experiments and analyses show that the LWE can be well applied to electronic voting systems,and our system is a secure and practical post-quantum electronic voting system with high efficiency and complete cryptographic properties.