A SYMMETRIC KEY FULLY HOMOMORPHIC ENCRYPTION SCHEME USING GENERAL CHINESE REMAINDER THEOREM

Abstract

The Fully Homomorphic Encryption (FHE) was an open problem up to 2009. In 2009, Gentry solved the problem. After Gentry's solution, a lot of work have made on FHE. In 2012, Xiao et al suggested a new FHE scheme with symmetric keys. They proved that security of their scheme depends on large integer factorization. In their scheme, they used 2m prime numbers in keygen algorithm and they used Chinese Remainder Theorem (CRT) in encryption algorithm. In 2014, Vaudenay et al broken this scheme. In this paper we present a new FHE scheme with symmetric keys which is a little di erent from Xiao et al scheme. We extend the approach with using General Chinese Remainder Theorem (GCRT). With using GCRT, we obtained a new FHE scheme and also we achieved to avoid choosing 2m prime/mutually prime numbers. Our scheme works with random numbers.

Keywords

• Fully Homomorphic Encryption,Large Integer Factorization,General Chinese Remainder Theorem

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