Verifiable Evaluation of Private Polynomials

Polynomial evaluation is an important tool in constructing many cryptographic protocols, such as proof of retrievability and verifiable keyword search. However, for the high degree polynomials derived from very large datasets, polynomial evaluation becomes an intractable problem, especially for resource limited devices. In this paper, we firstly propose practically efficient verifiable evaluation of private polynomial schemes without utilizing homomorphic encryption. We propose a novel method to blind the original polynomial and deblind the result returned from the server. To obtain and verify the correctness of the final evaluation of the polynomial, the user only needs to solve a linear congruence equation problem using Chinese Remainder Theorem(CRT). Extensive analysis shows that our schemes are secure in the proposed security model, that is, they satisfy the security requirements of verifiability, function privacy, and output privacy.