Polynomial Functional Encryption Scheme with Linear Ciphertext Size

Abstract

In this paper, we suggest a new selective secure functional encryption scheme for degree $d$ polynomial. The number of ciphertexts for a message with length $\ell$ in our scheme is $O(\ell)$ regardless of $d$, while it is at least $\ell^{d/2}$ in the previous works. Our main idea is to generically combine two abstract encryption schemes that satisfies some special properties. We also gives an instantiation of our scheme by combining ElGamal scheme and Ring-LWE based homomorphic encryption scheme, whose ciphertext length is exactly $2\ell+1,$ for any degree $d.