A Cryptographer's Conspiracy Santa

Authors Xavier Bultel , Jannik Dreier , Jean-Guillaume Dumas , Pascal Lafourcade

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Author Details

Xavier Bultel
  • LIMOS, University Clermont Auvergne, Campus des Cézeaux, Aubière, France
Jannik Dreier
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Jean-Guillaume Dumas
  • Université Grenoble Alpes, Laboratoire Jean Kuntzmann, UMR CNRS 5224, 700 avenue centrale, IMAG - CS 40700, 38058 Grenoble cedex 9, France
Pascal Lafourcade
  • LIMOS, University Clermont Auvergne, Campus des Cézeaux, Aubière, France

Cite AsGet BibTex

Xavier Bultel, Jannik Dreier, Jean-Guillaume Dumas, and Pascal Lafourcade. A Cryptographer's Conspiracy Santa. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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 each gift among all participants of that 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 learns 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 using envelopes) or, virtually, using a cryptocurrency.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy-preserving protocols
  • Security and privacy → Formal security models
  • Theory of computation → Problems, reductions and completeness
  • Secret Santa
  • Conspiracy Santa
  • Secure Multi-Party Computation
  • Cryptocurrency
  • Physical Cryptography


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