Public-PEZ Cryptography

Secure multiparty computation (MPC) is a cryptographic technique that enables us to evaluate a predetermined function over players’ private inputs while hiding information about the inputs. MPC can be conducted using a “private PEZ protocol,” that uses PEZ candies and a dispenser. Specifically, in a private PEZ protocol, players first fill a predetermined sequence of candies in a dispenser. Then, each player in turn privately pops out a number of candies, wherein the number depends on their private input (without anybody else knowing how many candies pop out). The next candy to be popped out of the dispenser indicates the output value of the function. Thus, private PEZ protocols are fun and useful. One drawback would be that every player must pop out candies from the dispenser secretly, implying that a private PEZ protocol is vulnerable to dishonest players, for example, a player could peep the candies inside the dispenser. To overcome this drawback, we herein propose MPC protocols that do not need private actions such as secretly popping out candies after the setup (although each player rearranges the candies secretly in a setup phase, any illegal actions can be caught). That is, we construct a computational model of “public-PEZ cryptography,” where any protocol within the model can be publicly executed. Especially, the proposed public-PEZ AND protocol, which uses only five candies and two dispensers, is simple and easy for conducting a secure computation of the AND function.