Non-interactive Exponential Homomorphic Encryption Algorithm

Homomorphic encryption can be applied to non-interactive evaluation of encrypted functions. The known homomorphism includes homomorphism of addition, subtraction, multiplication, division, and so on. They are able to encrypt coefficients of polynomial functions, but cannot encrypt exponents so that the skeleton of the encrypted polynomial function is leaked. This paper presents the concept of exponential homomorphism and proposes an exponential homomorphic encryption algorithm based on RSA. The correctness and the security of the proposed exponential homomorphism are analyzed. The exponential homomorphism is also an algebraic homomorphic encryption algorithm. The proof and the example show the proposed algorithm can encrypt coefficients and exponents of polynomial functions, hide the skeleton of the encrypted polynomial, and implement non-interactive evaluation of encrypted exponential functions and polynomial functions.