Authors: Kamil Begny & Samuel Laferriere

The goal of this blog post is to be the first accessible introductory exposition to the very difficult ideas behind decentralized block production, or decentralized FIFO transaction processing. We do so through the lens of a recent paper, Themis, which forms one of the two core technologies of Chainlink’s Fair Sequencing Service, the other being threshold encryption. We have not been able to find any blog posts on the subject and thus hope to help disseminate the ideas, with ultimate desire to see them implemented in some blockchains and/or oracle networks.

Table of Content

• Introduction
• Time-based Order Fairness: from send-order-fairness to batch-order-fairness
• Themis Fundamental Concepts
  • Intuition behind $\gamma$
  • Thresholds, thresholds everywhere
    • Edge Thresholds: strong vs weak
      • consequent-tx-fairness
    • Transaction Thresholds and Types: Blank, Shaded, Solid
    • Byzantine Threshold: n > 4f
  • Condorcet Cycles
    • Batching as a solution
    • Batch unspooling for inter-block condorcet cycles
    • Weak condorcet cycles: makes themis too conservative
    • Stronger fairness guarantees within SCCs
• Toy model: 2-Transactions Order Fairness
• Vectors of attacks for f
• Themis-simplified
• Conclusion
• References
• Appendices
  • A: Different models to help visualize orderings
  • B: Generalized Threshold
  • C: byzantine vs rationality assumptions

Lexicon

• TBOF: Time-based Order Fairness
• SOF: Send Order Fairness
• ROF: Received Order Fairness
• BOF: Batch Order Fairness
• nTOF: n-Transactions Order Fairness
• CTF: Consequent Transaction Fairness

Introduction