New Approach for Sine and Cosine in Secure Fixed-Point Arithmetic.

In this paper we present a new class of protocols for the secure computation of the sine and cosine functions. The precision for the underlying secure fixed-point arithmetic is parametrized by the number of fractional bits f and can be set to any desired value. We perform a rigorous error analysis to provide an exact bound for the absolute error of 2 - f in the worst case. Existing methods rely on polynomial approximations of the sine and cosine, whereas our approach relies on the random self-reducibility of the problem, using efficiently generated solved instances for uniformly random angles. As a consequence, most of the O ( f 2 ) secure multiplications can be done in preprocessing, leaving only O ( f ) work for the online part. The overall round complexity can be limited to O (1) using standard techniques. We have integrated our solution in MPyC.