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 wellknown 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 privacypreserving way and compare them according to their computational and communication complexity