Program requirementsexamen
TeacherVincent Danos
Weekly hours 2 h CM


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.