A Cryptographer's Conspiracy Santa

Xavier Bultel (1) , Jannik Dreier (2) , Jean-Guillaume Dumas (3) , Pascal Lafourcade (1)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
2 PESTO - Proof techniques for security protocols
3 CASYS - Calculs Algébriques et Systèmes Dynamiques

In Conspiracy Santa, a variant of Secret Santa, a group of people offer each other Christmas gifts, where each member of the group receives a gift from the other members of the group. To that end, the members of the group form conspiracies, to decide on appropriate gifts, and usually divide the cost of the gift among all participants of the conspiracy. This requires to settle the shared expenses per conspiracy, so Conspiracy Santa can actually be seen as an aggregation of several shared expenses problems. First, we show that the problem of finding a minimal number of transaction when settling shared expenses is NP-complete. Still, there exists good greedy approximations. Second, we present a greedy distributed secure solution to Conspiracy Santa. This solution allows a group of people to share the expenses for the gifts in such a way that no participant will learn the price of his gift, but at the same time notably reduces the number of transactions with respect to a naive aggregation. Furthermore, our solution does not require a trusted third party, and can either be implemented physically (the participants are in the same room and exchange money) or, virtually, using a cryptocurrency.

Mots clés: Secret Santa; Conspiracy Santa; Secure Multi-Party Computation; Cryptocurrency; Physical Cryptography

Domaines: Cryptographie et sécurité [cs.CR]; Complexité [cs.CC]

Xavier Bultel, Jannik Dreier, Jean-Guillaume Dumas, Pascal Lafourcade. A Cryptographer's Conspiracy Santa. FUN 2018 - 9th International Conference on Fun with Algorithms, Jun 2018, La Maddalena, Italy. pp.13:1--13:13, ⟨10.4230/LIPIcs.FUN.2018.13⟩. ⟨hal-01777997v2⟩