Mooney, Vincent John, III

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Lattice-Based Encryption Schemes and its Applications to Homomorphic Encryption

2020-12 , Bin Ahmad Shahrir, Ahmad Faris Durrani , Pan, Leyan , Hutto, Kevin , Mooney, Vincent John, III

Homomorphic encryption is a type of encryption that allows performing operations on the ciphertext without having access to the plaintext. While the algorithm is still not efficient enough for practical applications, homomorphic encryption has potential in many areas such as voting, storage of sensitive personal information, and analyzing demo-graphical data. In 2009, Gentry proposed the first plausible algorithm for fully homomorphic encryption, and various improvements have been built upon this result, significantly increasing the efficiency of homomorphic encryption. In Gentry’s original implementation, lattice-based cryptography is used as a basis of the Homomorphic encryption scheme. Lattice-based cryptography still lies at the heart of many fully homomorphic encryption schemes. In this report, we build on previous VIP works and illustrate various lattice-based encryption schemes, and briefly describe how Gentry used lattice-based cryptography to construct the first fully homomorphic encryption scheme. In addition, this sub-team hopes the incoming VIP sub-teams would make use of this report and expand upon our research into homomorphic encryption.