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DOI: 10.4230/LIPIcs.AFT.2023.16

Pay Less for Your Privacy: Towards Cost-Effective On-Chain Mixers

Authors: Zhipeng Wang, Marko Cirkovic, Duc V. Le, William Knottenbelt, and Christian Cachin

Published in: LIPIcs, Volume 282, 5th Conference on Advances in Financial Technologies (AFT 2023)

Abstract

On-chain mixers, such as Tornado Cash (TC), have become a popular privacy solution for many non-privacy-preserving blockchain users. These mixers enable users to deposit a fixed amount of coins and withdraw them to another address, while effectively reducing the linkability between these addresses and securely obscuring their transaction history. However, the high cost of interacting with existing on-chain mixer smart contracts prohibits standard users from using the mixer, mainly due to the use of computationally expensive cryptographic primitives. For instance, the deposit cost of TC on Ethereum is approximately 1.1M gas (i.e., 66 USD in June 2023), which is 53× higher than issuing a base transfer transaction. In this work, we introduce the Merkle Pyramid Builder approach, to incrementally build the Merkle tree in an on-chain mixer and update the tree per batch of deposits, which can therefore decrease the overall cost of using the mixer. Our evaluation results highlight the effectiveness of this approach, showcasing a significant reduction of up to 7× in the amortized cost of depositing compared to state-of-the-art on-chain mixers. Importantly, these improvements are achieved without compromising users' privacy. Furthermore, we propose the utilization of verifiable computations to shift the responsibility of Merkle tree updates from on-chain smart contracts to off-chain clients, which can further reduce deposit costs. Additionally, our analysis demonstrates that our designs ensure fairness by distributing Merkle tree update costs among clients over time.

Cite as

Zhipeng Wang, Marko Cirkovic, Duc V. Le, William Knottenbelt, and Christian Cachin. Pay Less for Your Privacy: Towards Cost-Effective On-Chain Mixers. In 5th Conference on Advances in Financial Technologies (AFT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 282, pp. 16:1-16:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wang_et_al:LIPIcs.AFT.2023.16,
  author =	{Wang, Zhipeng and Cirkovic, Marko and Le, Duc V. and Knottenbelt, William and Cachin, Christian},
  title =	{{Pay Less for Your Privacy: Towards Cost-Effective On-Chain Mixers}},
  booktitle =	{5th Conference on Advances in Financial Technologies (AFT 2023)},
  pages =	{16:1--16:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-303-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{282},
  editor =	{Bonneau, Joseph and Weinberg, S. Matthew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2023.16},
  URN =		{urn:nbn:de:0030-drops-192050},
  doi =		{10.4230/LIPIcs.AFT.2023.16},
  annote =	{Keywords: Privacy, Blockchain, Mixers, Merkle Tree}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2022.19

Modeling Resources in Permissionless Longest-Chain Total-Order Broadcast

Authors: Sarah Azouvi, Christian Cachin, Duc V. Le, Marko Vukolić, and Luca Zanolini

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract

Blockchain protocols implement total-order broadcast in a permissionless setting, where processes can freely join and leave. In such a setting, to safeguard against Sybil attacks, correct processes rely on cryptographic proofs tied to a particular type of resource to make them eligible to order transactions. For example, in the case of Proof-of-Work (PoW), this resource is computation, and the proof is a solution to a computationally hard puzzle. Conversely, in Proof-of-Stake (PoS), the resource corresponds to the number of coins that every process in the system owns, and a secure lottery selects a process for participation proportionally to its coin holdings. Although many resource-based blockchain protocols are formally proven secure in the literature, the existing security proofs fail to demonstrate why particular types of resources cause the blockchain protocols to be vulnerable to distinct classes of attacks. For instance, PoS systems are more vulnerable to long-range attacks, where an adversary corrupts past processes to re-write the history, than PoW and Proof-of-Storage systems. Proof-of-Storage-based and PoS-based protocols are both more susceptible to private double-spending attacks than PoW-based protocols; in this case, an adversary mines its chain in secret without sharing its blocks with the rest of the processes until the end of the attack. In this paper, we formally characterize the properties of resources through an abstraction called resource allocator and give a framework for understanding longest-chain consensus protocols based on different underlying resources. In addition, we use this resource allocator to demonstrate security trade-offs between various resources focusing on well-known attacks (e.g., the long-range attack and nothing-at-stake attacks).

Cite as

Sarah Azouvi, Christian Cachin, Duc V. Le, Marko Vukolić, and Luca Zanolini. Modeling Resources in Permissionless Longest-Chain Total-Order Broadcast. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{azouvi_et_al:LIPIcs.OPODIS.2022.19,
  author =	{Azouvi, Sarah and Cachin, Christian and Le, Duc V. and Vukoli\'{c}, Marko and Zanolini, Luca},
  title =	{{Modeling Resources in Permissionless Longest-Chain Total-Order Broadcast}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{19:1--19:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.19},
  URN =		{urn:nbn:de:0030-drops-176398},
  doi =		{10.4230/LIPIcs.OPODIS.2022.19},
  annote =	{Keywords: blockchain, consensus, resource, broadcast}
}

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Documents authored by Le, Duc V.

Pay Less for Your Privacy: Towards Cost-Effective On-Chain Mixers

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Modeling Resources in Permissionless Longest-Chain Total-Order Broadcast

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