Secure aggregation of distributed information: How a team of agents can safely share secrets in front of a spy

TL;DR

This paper introduces combinatorial protocols for secure aggregation of distributed information, enabling a team to share secrets without revealing individual card holdings to an eavesdropper.

Contribution

It presents a novel combinatorial construction and an iterative reduction technique to solve a broad class of secure aggregation problems involving distributed information.

Findings

Protocols work for large, balanced card distributions

Methods ensure secrecy against eavesdroppers

Provides a direct solution for a wide range of SADI problems

Abstract

We consider the generic problem of Secure Aggregation of Distributed Information (SADI), where several agents acting as a team have information distributed among them, modeled by means of a publicly known deck of cards distributed among the agents, so that each of them knows only her cards. The agents have to exchange and aggregate the information about how the cards are distributed among them by means of public announcements over insecure communication channels, intercepted by an adversary "eavesdropper", in such a way that the adversary does not learn who holds any of the cards. We present a combinatorial construction of protocols that provides a direct solution of a class of SADI problems and develop a technique of iterated reduction of SADI problems to smaller ones which are eventually solvable directly. We show that our methods provide a solution to a large class of SADI problems, including all SADI problems with sufficiently large size and sufficiently balanced card distributions.