CoinMagic: A Differential Privacy Framework for Ring Signature Schemes
This work addresses privacy risks for users in blockchain systems like Monero by enhancing anonymity against deanonymization attacks, though it is incremental as it builds on existing ring signature methods.
The paper tackles the vulnerability of ring signature schemes in privacy-preserving blockchains to chain-reaction analysis by proposing a differential privacy framework called ε-coin-indistinguishability to ensure similar distributions for mixins, and it develops approximation algorithms to solve the NP-hard mixin selection problem, demonstrating efficiency and effectiveness through experiments on real and synthetic datasets.
By allowing users to obscure their transactions via including "mixins" (chaff coins), ring signature schemes have been widely used to protect a sender's identity of a transaction in privacy-preserving blockchain systems, like Monero and Bytecoin. However, recent works point out that the existing ring signature scheme is vulnerable to the "chain-reaction" analysis (i.e., the spent coin in a given ring signature can be deduced through elimination). Especially, when the diversity of mixins is low, the spent coin will have a high risk to be detected. To overcome the weakness, the ring signature should be consisted of a set of mixins with high diversity and produce observations having "similar" distributions for any two coins. In this paper, we propose a notion, namely $ε$-coin-indistinguishability ($ε$-CI), to formally define the "similar" distribution guaranteed through a differential privacy scheme. Then, we formally define the CI-aware mixins selection problem with disjoint-superset constraint (CIA-MS-DS), which aims to find a mixin set that has maximal diversity and satisfies the constraints of $ε$-CI and the budget. In CIA-MS-DS, each ring signature is either disjoint with or the superset of its preceding ring signatures. We prove that CIA-MS-DS is NP-hard and thus intractable. To solve the CIA-MS-DS problem, we propose two approximation algorithms, namely the Progressive Algorithm and the Game Theoretic Algorithm, with theoretic guarantees. Through extensive experiments on both real data sets and synthetic data sets, we demonstrate the efficiency and the effectiveness of our approaches.