Paper 2017/458

Fully Homomorphic Encryption Using Multivariate Polynomials

Matthew Tamayo-Rios and Jean-Charles Faugère and Ludovic Perret and Peng Hui How and Robin Zhang

Abstract

Efficient and secure third party computation has many practical applications in cloud computing. We develop new approach for building fully homomorphic encryption (FHE) schemes, by starting with the intuition of using algebraic descriptions of the encryption and decryption functions to construct a functionally complete set of homomorphic boolean operators. We use this approach to design a compact efficient asymmetric cryptosystem that supports secure third party evaluation of arbitrary boolean functions. In the process, we introduce a new hard problem that is a more difficult variant of of the classical Isomorphism of Polynomials (IP) that we call the Obfuscated-IP.