Properties of two-layer FHE and their applications

Abstract

Homomorphic equality test is a process, which was present in CRYPTO'2014 as a tool of refresh in a FHE (Alperin-Sheriff and Peikert, 2014), and has been used to test whether the plaintext of a given ciphertext is equal to a certain number. In fact, this powerful function induced many new applications about homomorphic encryption, in theory and practice, especially when homomorphic comparison and arithmetic functions are needed. Firstly, this paper extended three useful processes to Alperin-Sheriff and Peikert (2014), HTG, FDDec and negative, which are essential to many applications. HTG can transform a HEPerm ciphertext, a ciphertext of permutation matrix in Alperin-Sheriff and Peikert (2014), to a small GSW ciphertext. FDDec can decrypt a HEPerm ciphertext directly. Secondly, this paper concluded the rules of application about our scheme and constructed an efficiency l' bits comparator as an example of application. Lastly, this paper finds a solution, based on the equality test, for the problem of password leakage, which can protect the password and preserve the bypass function, when the database of password was compromised.