Program requirementsexamen
TeacherVincent Danos
Weekly hours 2 h CM
Years Master Logique et Fondements de l'Informatique


This course aims to present the logical and computational foundations of blockchains (communication protocols, game theory), as well as examples of protocols implemented in particular in crypto-currencies and smart-contracts. We will devote a substantial part of the course to the examination of "decentralized finance", i.e. all the existing chain contracts which postpone and in some cases extend financial practices.


  • Communication models and convergence theorems for Nakamoto consensus
  • Games, equilibria, games with commitment and Kakutani-style fixed point theorems.
  • Blockchain protocols: Nakamoto, Tendermint. Economics of equilibria between validators.
  • Economics of Crypto-currencies, tokens.
    • Smart contracts: Swaps- fairness and pricing; double swaps; token pricing. Mixers.


  • Juan A. Garay, Aggelos Kiayias, Nikos Leonoardos: The Bitcoin Backbone Protocol: Analysis and Applications. EUROCRYPT (2) 2015.
  • Ling Ren. Analysis of Nakamoto consensus. Cryptology ePrint Archive, Report 2019/943, 2019.
  • Stefan Dziembowski, Lisa Eckey, and Sebastian Faust. Fairswap : How to fairly exchange digital goods. In Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, CCS ’18.
  • Julien Prat, Vincent Danos, and Stefania Marcassa. Fundamental pricing of utility tokens, 2020. Working paper.
  • Yackolley Amoussou-Guenou and Antonella Del Pozzo and Maria Potop-Butucaru and Sara Tucci-Piergiovanni. Correctness and Fairness of Tendermint-core Blockchains. Cryptology ePrint Archive: Report 2018/574
  • Xi Chen, Christos Papadimitriou, and Tim Roughgarden. An axiomatic approach to block rewards. In Proceedings of the 1st ACM Conference on Advances in Financial Technologies, pages 124–131, 2019.