Secure Computation of Randomized Functions

TL;DR

This paper studies secure computation protocols for randomized functions where only one user computes the output, providing rate-optimal solutions under perfect and asymptotic security conditions.

Contribution

It extends Kilian's characterization to asymptotic security and introduces rate-optimal protocols for both privacy scenarios in secure randomized function computation.

Findings

Characterization of securely computable randomized functions in perfect security.

Rate-optimal protocols for both privacy scenarios.

Single-letter rate expressions in asymptotic security.

Abstract

Two user secure computation of randomized functions is considered, where only one user computes the output. Both the users are semi-honest; and computation is such that no user learns any additional information about the other user's input and output other than what cannot be inferred from its own input and output. First we consider a scenario, where privacy conditions are against both the users. In perfect security setting Kilian [STOC 2000] gave a characterization of securely computable randomized functions, and we provide rate-optimal protocols for such functions. We prove that the same characterization holds in asymptotic security setting as well and give a rate-optimal protocol. In another scenario, where privacy condition is only against the user who is not computing the function, we provide rate-optimal protocols. For perfect security in both the scenarios, our results are in terms of chromatic entropies of different graphs. In asymptotic security setting, we get single-letter expressions of rates in both the scenarios.