Oblivious Polynomial Evaluation and Oblivious Neural Learning [chapter]

Yan-Cheng Chang, Chi-Jen Lu
2001 Lecture Notes in Computer Science  
We study the problem of Oblivious Polynomial Evaluation (OPE). There are two parties, Alice who has a polynomial P , and Bob who has an input x. The goal is for Bob to compute P (x) in such way that Alice learns nothing about x and Bob learns only what can be inferred from P (x). Previously existing protocols are based on some intractability assumptions that have not been well studied [15, 14] , and these protocols are only applicable for polynomials over finite fields. In this paper, we
more » ... efficient OPE protocols which are based on Oblivious Transfer only. Unlike that of [15] , slight modifications to our protocols immediately give protocols to handle multi-variate polynomials and 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 [14] . As an example, we give a protocol for the problem of Oblivious Neural Learning, where one party has a neural network and the other, with some training set, wants to train the neural network in an oblivious way. 1 Actually they use 2kd + 1 invocations of 1-out-of-m oblivious transfer, denoted as OT m 1 . It is known that one OT m 1 can be simulated by log m calls to OT 2 1 , together with several evaluations of a pseudo-random function [15] .
doi:10.1007/3-540-45682-1_22 fatcat:cfxijlfvtrhzhfpeqngcck7xfu