Some Efficient Solutions to Yao's Millionaire Problem

TL;DR

This paper introduces three efficient protocols for Yao's Millionaire Problem, leveraging homomorphic encryption, third-party assistance, and a no-third-party approach, optimizing for communication complexity and input flexibility.

Contribution

The paper presents three novel protocol constructions that improve efficiency and flexibility in solving Yao's Millionaire Problem under different trust assumptions.

Findings

First protocol uses 4 rounds with homomorphic encryption.

Second protocol employs an untrusted third party with linear communication overhead.

Third protocol is a simple no-third-party solution with quadratic communication overhead.

Abstract

We present three simple and efficient protocol constructions to solve Yao's Millionaire Problem when the parties involved are non-colluding and semi-honest. The first construction uses a partially homomorphic Encryption Scheme and is a 4-round scheme using 2 encryptions, 2 homomorphic circuit evaluations (subtraction and XOR) and a single decryption. The second construction uses an untrusted third party and achieves a communication overhead linear in input bit-size with the help of an order preserving function.Moreover, the second construction does not require an apriori input bound and can work on inputs of different bit-sizes. The third construction does not use a third party and, even though, it has a quadratic communication overhead, it is a fairly simple construction.