Multi Party Computation Motivated by the Birthday Problem

Suppose there are n people in a classroom and we want to decide if there are two of them who were born on the same day of the year. The well-known birthday paradox is concerned with the probability of this event and is discussed in many textbooks on probability. In this paper we focus on cryptographic aspects of the problem: how can we decide if there is a collision of birthdays without the participants disclosing their respective date of birth. We propose several procedures for solving this generally in a privacy-preserving way and compare them according to their computational and communication complexity.