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1. Private Proof-of-Stake Blockchains using Differentially-Private Stake Distortion

   Wang, Chenghong; Pujol, David; Nayak, Kartik; Machanavajjhala, Ashwin (August 2023, Usenix)

   Safety, liveness, and privacy are three critical properties for any private proof-of-stake (PoS) blockchain. However, prior work (SP'21) has shown that to obtain safety and liveness, a PoS blockchain must, in theory, forgo privacy. In particular, to obtain safety and liveness, PoS blockchains elect parties proportional to their stake, which, in turn, can potentially reveal the stake of a party even if the transaction processing mechanism is private. In this work, we make two key contributions. First, we present the first stake inference attack that can be actually run in practice. Specifically, our attack applies to both deterministic and randomized PoS protocols and has exponentially lesser running time in comparison with the SOTA approach. Second, we use differentially private stake distortion to achieve privacy in PoS blockchains. We formulate certain privacy requirements to achieve transaction and stake privacy, and design two stake distortion mechanisms that any PoS protocol can use. Moreover, we analyze our proposed mechanisms with Ethereum 2.0, a well-known PoS blockchain that is already operating in practice. The results indicate that our mechanisms mitigate stake inference risks and, at the same time, provide reasonable privacy while preserving required safety and liveness properties. 

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2. Private Proof-of-Stake Blockchains using Differentially-Private Stake Distortion

   Wang, Chenghong; Pujol, David; Nayak, Kartik; Machanavajjhala, Ashwin (August 2023, 32nd USENIX Security Symposium (USENIX Security 23))

   Safety, liveness, and privacy are three critical properties for any private proof-of-stake (PoS) blockchain. However, prior work (SP'21) has shown that to obtain safety and liveness, a PoS blockchain must in theory forgo privacy. In particular, to obtain safety and liveness, PoS blockchains elect parties proportional to their stake, which, in turn, can potentially reveal the stake of a party even if the transaction processing mechanism is private. In this work, we make two key contributions. First, we present the first stake inference attack that can be actually run in practice. Specifically, our attack applies to both deterministic and randomized PoS protocols and has exponentially lesser running time in comparison with the SOTA approach. Second, we use differentially private stake distortion to achieve privacy in PoS blockchains. We formulate certain privacy requirements to achieve transaction and stake privacy, and design two stake distortion mechanisms that any PoS protocol can use. Moreover, we analyze our proposed mechanisms with Ethereum 2.0, a well-known PoS blockchain that is already operating in practice. The results indicate that our mechanisms mitigate stake inference risks and, at the same time, provide reasonable privacy while preserving required safety and liveness properties. 

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3. Proof-of-Stake Mining Games with Perfect Randomness

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   Ferreira, Matheus V.; Weinberg, S. Matthew (July 2021, ACM Conference on Economics and Computation)

   null (Ed.)
4. Anonymous Lottery In The Proof-of-Stake Setting

   https://doi.org/10.1109/CSF49147.2020.00030  

   Baldimtsi, Foteini; Madathil, Varun; Scafuro, Alessandra; Zhou, Linfeng (June 2020, 2020 IEEE 33rd Computer Security Foundations Symposium (CSF))
5. Formal Barriers to Longest-Chain Proof-of-Stake Protocols

   Brown-Cohen, Jonah; Narayanan, Arvind; Psomas, Christos-Alexandros; Weinberg, S. Matthew (June 2019, ACM Conference on Economics and Computation)