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On Fair Ordering and Differential Privacy

Shir Cohen, Neel Basu, Soumya Basu, Lorenzo Alvisi

TL;DR

This paper tackles fair transaction ordering in blockchain SMR, addressing how to prevent bias arising from irrelevant features. It extends prior $\epsilon$-Ordering Equality to a more flexible $k\epsilon$-Ordering Equality and reveals a surprising link to Differential Privacy, showing that DP mechanisms can enforce fair ordering when requests are scored by a relevance-driven signal plus noise. The key contributions include a generalized fairness definition, a formal DP-based bridge to ordering guarantees, and practical blockchain applications that mitigate MEV, front-running, and bribery. The work provides a principled framework for designing fair distributed protocols using established DP techniques, with implications for both theory and blockchain system design.

Abstract

In blockchain systems, fair transaction ordering is crucial for a trusted and regulation-compliant economic ecosystem. Unlike traditional State Machine Replication (SMR) systems, which focus solely on liveness and safety, blockchain systems also require a fairness property. This paper examines these properties and aims to eliminate algorithmic bias in transaction ordering services. We build on the notion of equal opportunity. We characterize transactions in terms of relevant and irrelevant features, requiring that the order be determined solely by the relevant ones. Specifically, transactions with identical relevant features should have an equal chance of being ordered before one another. We extend this framework to define a property where the greater the distance in relevant features between transactions, the higher the probability of prioritizing one over the other. We reveal a surprising link between equal opportunity in SMR and Differential Privacy (DP), showing that any DP mechanism can be used to ensure fairness in SMR. This connection not only enhances our understanding of the interplay between privacy and fairness in distributed computing but also opens up new opportunities for designing fair distributed protocols using well-established DP techniques.

On Fair Ordering and Differential Privacy

TL;DR

This paper tackles fair transaction ordering in blockchain SMR, addressing how to prevent bias arising from irrelevant features. It extends prior -Ordering Equality to a more flexible -Ordering Equality and reveals a surprising link to Differential Privacy, showing that DP mechanisms can enforce fair ordering when requests are scored by a relevance-driven signal plus noise. The key contributions include a generalized fairness definition, a formal DP-based bridge to ordering guarantees, and practical blockchain applications that mitigate MEV, front-running, and bribery. The work provides a principled framework for designing fair distributed protocols using established DP techniques, with implications for both theory and blockchain system design.

Abstract

In blockchain systems, fair transaction ordering is crucial for a trusted and regulation-compliant economic ecosystem. Unlike traditional State Machine Replication (SMR) systems, which focus solely on liveness and safety, blockchain systems also require a fairness property. This paper examines these properties and aims to eliminate algorithmic bias in transaction ordering services. We build on the notion of equal opportunity. We characterize transactions in terms of relevant and irrelevant features, requiring that the order be determined solely by the relevant ones. Specifically, transactions with identical relevant features should have an equal chance of being ordered before one another. We extend this framework to define a property where the greater the distance in relevant features between transactions, the higher the probability of prioritizing one over the other. We reveal a surprising link between equal opportunity in SMR and Differential Privacy (DP), showing that any DP mechanism can be used to ensure fairness in SMR. This connection not only enhances our understanding of the interplay between privacy and fairness in distributed computing but also opens up new opportunities for designing fair distributed protocols using well-established DP techniques.
Paper Structure (13 sections, 2 theorems, 9 equations)

This paper contains 13 sections, 2 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Model
  3. Fair Ordering
  4. Background: Differential Privacy
  5. Bridging Fairness and Privacy
  6. $\epsilon$-Ordering Equality and Differential Privacy
  7. $k\epsilon$-Ordering Equality and Group Privacy
  8. Practical Considerations
  9. Application for Blockchains
  10. Miner Fees and Bribery
  11. Time of Transaction Issuance.
  12. Related Work
  13. Conclusion

Key Result

theorem thmcountertheorem

Let score be a function that, for a given request $r$, returns the value $r.\text{relev} + r.\eta$, and let $\mathcal{D}$ be an additive-noise DP mechanism. If an algorithm $\mathcal{A}$ orders requests based on score, and $\mathcal{D}$ is applied to $\mathcal{A}$ with sensitivity $\Delta = \lambda$

Theorems & Definitions (8)

  • definition thmcounterdefinition: $\epsilon$-Ordering Equality
  • definition thmcounterdefinition: $\epsilon$-Ordering Equality -- revised
  • definition thmcounterdefinition: $\epsilon$-Differential Privacy
  • definition thmcounterdefinition
  • theorem thmcountertheorem
  • proof
  • definition thmcounterdefinition: $k\epsilon$-Ordering Equality
  • theorem thmcountertheorem