Penalties must cover future losses to stop blockchain collusion
When One Leak Pays Forever: Context Binding and the Price of Deterring Collusion
Computer Science and Game TheoryCryptography and Security
Summary
The paper studies a problem where a group in charge of unlocking blockchain data can cheat once and keep profiting multiple times afterward. The authors model this as a game and show that to stop such cheating, penalties must be large enough to cover all future gains from the first dishonest act. They also find that splitting the authority's key for shorter time periods reduces the needed penalty to prevent cheating. Their analysis could help design better blockchain and voting systems to resist collusion.
What this means in practice
- •For blockchain developers: Set penalty sizes in blockchain decryption committees to effectively prevent members from selling decryption rights and profiting repeatedly.
- •For federated learning engineers: Design secure shared key schemes to deter collusion and data leakage over repeated uses of a joint decryption capability.
Tested on one dataset.
Authors
Tingyi Lin, Shawn Yu, Ruoran Lai, Huanxi Zhang
Abstract
A coalition that deviates once can profit many times when what it sells keeps working. In a threshold-encrypted mempool, a leading defense against maximal extractable value (MEV), a quorum of the decryption committee that sells its decryption capability to a front-runner exposes every later block that the capability still decrypts. We ask how large a penalty, such as slashable stake, deters this kind of collusion. In our repeated game, a single leak by any coalition in a monotone family of authorized coalitions (for example, any $k$ of the $n$ committee members) unlocks a set of future rounds, costs a one-time penalty, and ends the coalition's participation. We show that every dynamic deviation reduces to choosing a leak time, so deterrence holds if and only if each coalition's penalty covers the largest discounted value that a single leak reaches. Without discounting, over $T$ rounds of unit value full reuse needs a penalty of $T$ while binding each leak to its own round needs $1$, so no penalty that is constant in the horizon deters unbounded reuse; a reuse window of $w$ rounds costs at most $w$ times the largest per-round value. The cheapest profile of per-party stakes that deters every coalition solves a covering linear program. For blockchain design, per-epoch keys cut the required stake from the value of a key's lifetime to the value of one epoch; we calibrate the gap on Ethereum front-running data and place Ferveo and Shutter in the model. The analysis extends to sealed-bid auctions, multi-authority voting, and federated learning under a shared key.