Weighing Coins and Keeping Secrets

TL;DR

This paper explores privacy-preserving strategies for counterfeit coin problems, introducing new solution classes, conditions for their existence, and metrics to quantify information revealed, laying groundwork for future research.

Contribution

It introduces two new classes of privacy-preserving solutions for counterfeit coin problems and develops metrics to evaluate their effectiveness.

Findings

Six strategies categorized into two classes

Conditions for solution existence established

Metrics for information revelation defined

Abstract

In this expository paper we discuss a relatively new counterfeit coin problem with an unusual goal: maintaining the privacy of, rather than revealing, counterfeit coins in a set of both fake and real coins. We introduce two classes of solutions to this problem --- one that respects the privacy of all the coins and one that respects the privacy of only the fake coins --- and give several results regarding each. We describe and generalize 6 unique strategies that fall into these two categories. Furthermore, we explain conditions for the existence of a solution, as well as showing proof of a solution's optimality in select cases. In order to quantify exactly how much information is revealed by a given solution, we also define the revealing factor and revealing coefficient; these two values additionally act as a means of comparing the relative effectiveness of different solutions. Most importantly, by introducing an array of new concepts, we lay the foundation for future analysis of this very interesting problem, as well as many other problems related to privacy and the transfer of information.