Optimal Strategic Mining Against Cryptographic Self-Selection in Proof-of-Stake

Matheus V.X. Ferreira, Ye Lin Sally Hahn, S. Matthew Weinberg, Catherine Yu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations


Cryptographic Self-Selection is a subroutine used to select a leader for modern proof-of-stake consensus protocols. In cryptographic self-selection, each round r has a seed Qr. In round r, each account owner is asked to digitally sign Qr, hash their digital signature to produce a credential, and then broadcast this credential to the entire network. A publicly-known function scores each credential in a manner so that the distribution of the lowest scoring credential is identical to the distribution of stake owned by each account. The user who broadcasts the lowest-scoring credential is the leader for round r, and their credential becomes the seed Qr+1. Such protocols leave open the possibility of manipulation: a user who owns multiple accounts that each produce low-scoring credentials in round r can selectively choose which ones to broadcast in order to influence the seed for round r+1. Indeed, the user can pre-compute their credentials for round r+1 for each potential seed, and broadcast only the credential (among those with low enough score to be leader) that produces the most favorable seed. We consider an adversary who wishes to maximize the expected fraction of rounds in which an account they own is the leader. We show such an adversary always benefits from deviating from the intended protocol, regardless of the fraction of the stake controlled. We characterize the optimal strategy; first by proving the existence of optimal positive recurrent strategies whenever the adversary owns last than 3-5/2 ∼38% of the stake. Then, we provide a Markov Decision Process formulation to compute the optimal strategy.

Original languageEnglish (US)
Title of host publicationEC 2022 - Proceedings of the 23rd ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Number of pages26
ISBN (Electronic)9781450391504
StatePublished - Jul 12 2022
Event23rd ACM Conference on Economics and Computation, EC 2022 - Boulder, United States
Duration: Jul 11 2022Jul 15 2022

Publication series

NameEC 2022 - Proceedings of the 23rd ACM Conference on Economics and Computation


Conference23rd ACM Conference on Economics and Computation, EC 2022
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Economics and Econometrics
  • Computational Mathematics
  • Statistics and Probability


  • blockchain
  • cryptocurrency
  • leader election
  • proof-of-stake
  • strategic mining


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