Oblivious Multi-variate Polynomial Evaluation

In this paper, we propose a protocol for Oblivious Polynomial Evaluation (OPE) considering a multi-variate polynomial. There are two parties, Alice who has a secret multi-variate polynomial f and Bob who has an input x = (x(1), ..., x(T)). Thus, Bob wants to compute f(x) without any information leakage: Alice learns nothing about x and Bob learns only what can be inferred from f (x). In [4], the authors proposed a solution for this problem using Oblivious Transfer (OT) protocol only. In this paper, we propose efficient OPE protocols for the multi-variate case based upon additive and multiplicative homomorphic encryption schemes defined on the same domain. Our protocol only reveals the number of monomials.