Secure Numerical and Logical Multi Party Operations

TL;DR

This paper presents efficient, secure algorithms for numerical and logical multi-party computations, achieving significant speed-ups over previous methods while ensuring strong security guarantees.

Contribution

It introduces novel algorithms for secure trigonometric, division, and logarithmic functions, and enhances logical operations with perfect security in multi-party settings.

Findings

Speed-ups of more than 100x for evaluated operations

Secure computation of trigonometric functions, division, and logarithms

Logical operations like comparisons and AND gates are perfectly secure

Abstract

We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our algorithms for trigonometric functions, we use basic mathematical laws in combination with properties of the additive encryption scheme in a novel way. For division and logarithm we use a new approach to compute a Taylor series at a fixed point for all numbers. All our logical operations such as comparisons and large fan-in AND gates are perfectly secure. Our empirical evaluation yields speed-ups of more than a factor of 100 for the evaluated operations compared to the state-of-the-art.