Secure Numerical and Logical Multi Party Operations
Johannes Schneider, Bin Lu

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.
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Taxonomy
TopicsCryptography and Data Security · Complexity and Algorithms in Graphs · Cryptography and Residue Arithmetic
