Information-Theoretically Secure Three-Party Computation with One Corrupted Party

TL;DR

This paper characterizes unconditionally secure three-party computation protocols with one potentially malicious party, providing a protocol for Hamming distance computation and illustrating security differences between active and passive models.

Contribution

It offers an information-theoretic framework for secure computation with one active adversary and presents a secure protocol for Hamming distance calculation.

Findings

Protocol for Hamming distance is unconditionally secure under both models.

Security distinctions between active and passive models are demonstrated.

BGW protocol is secure under passive but not active adversarial models.

Abstract

The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference between the notions of security under the active and passive behavioral models is illustrated through the BGW protocol for computing quadratic and Hamming distances; this protocol is secure under the passive model, but is shown to be not secure under the active model.