A novel solution to the millionaire problem

We give an ecient symmetric-key based protocol solving Yao's millionaire problem, with the ad- ditional property of fairness. We assume a semi-honest server assists in comparing values held by two parties. We assume this server only executes the protocol pre- cisely and does not collude with any other participants. We protect the participants against the server getting any information about the numbers or their relationship, by using encryption and hash chains. The protocol has three communication phases; initialisation, computation and announcement, each with distinct algorithms for the parties. Each of the two parties and the server sends two messages during the protocol. We discuss the cor- rectness, security properties and eciency of our scheme. We compare our communication and computational costs against other solutions to the millionaire problem, us- ing an RSA based implementation and using an AES based implementation. The computational cost is gen- erally very low by comparison with other methods, even when we use the less ecient RSA.