Oblivious Polynomial Evaluation and Oblivious Neural Learning

We study the problem of Oblivious Polynomial Evaluation (OPE), where one party has a polynomial P and the other party, with an input x, wants to learn P (x) in an oblivious way. Previously existing protocols are based on some intractability assumptions that have not been well studied [10, 9], and these protocols are only applicable for polynomials over finite fields. In this paper, we propose efficient OPE protocols which are based on Oblivious Transfer only. Slight modifications to our protocols immediately give protocols to handle polynomials over floating-point numbers. Many important real-world applications deal with floating-point numbers, instead of integers or arbitrary finite fields, and our protocols have the advantage of operating directly on floating-point numbers, instead of going through finite field simulation as that of [9]. As an example, we study the problem of Oblivious Neural Learning where a party has a neural network and the other party wants to train the neural network in an oblivious way with some training set. We give an efficient protocol for this problem, and in a sense it says that one can get smarter in an oblivious way.