Efficient Homomorphic Integer Polynomial Evaluation based on GSW FHE

In this paper, we introduce new methods to evaluate integer polynomials with GSW FHE. Our solution has much slower noise growth and per homomorphic integer multiplication cost, which is only O( (log k) w+1 kw·n ) percent of the original GSW scheme, where k is the input plaintext width, n is the LWE dimention, and ω = 2.373. Technically, we reduce the integer multiplication noise by performing the evaluation between two kinds of ciphertexts, one in Zq and the other in F qe 2 . To achieve generality, we propose an integer bootstrapping scheme which converts these two kinds of ciphertexts into each other. To solve the ciphertext expansion problem due to ciphertexts in F qe 2 , we propose a solution based on symmetric encryption with stream ciphers.