Cooking Cryptographers: Secure Multiparty Computation Based on Balls and Bags

Imagine two cryptographers wishing to securely compute the AND value of their secret input bits. They are in the kitchen, where all they have are three saucepans with Borscht soup and some kinds of ingredients. Interestingly, by secretly putting ingredients in the saucepans depending on their inputs, they can find only the AND value from the taste of the cooked Borscht. Because cooking for secure computations is not so convenient, let us regard ingredients and saucepans (with Borscht soup) as balls and bags, respectively, which are easy to handle and also familiar tools for learning Probability in high school. Then, our problem is generalized as: Can we realize secure multiparty computations (MPCs) with balls and bags? There are techniques to realize MPCs with everyday objects, such as physical cards, coins, and a PEZ dispenser. We encode the input bits with such objects and securely compute some predetermined function using them. In this paper, we present a novel technique based on the physical properties of balls and bags. That is, our challenges are how to utilize an interesting feature that the balls become disordered immediately after they are put into a bag, namely they are "automatically shuffled." We give the first framework of MPCs using balls and bags (namely, ball-based cryptography), and propose secure AND computation and general MPCs. Our protocols are realizations of usable security which helps people with understanding the principles of MPCs as well as solving social problems in daily life.