بخشی از مقاله (انگلیسی)
Bitcoin is one of the best-known cryptocurrencies, which captivated researchers with its innovative blockchain structure. Examinations of this public blockchain resulted in many proposals for improvement in terms of anonymity and privacy. Generally used methods for improvement include mixing protocols, ring signatures, zero-knowledge proofs, homomorphic commitments, and off-chain storage systems. To the best of our knowledge, in the literature, there is no study examining Bitcoin in terms of differential privacy, which is a privacy notion coming up with some mechanisms that enable running useful statistical queries without identifying any personal information. In this paper, we provide a theoretical examination of differential privacy in Bitcoin. Our motivation arises from the idea that the Bitcoin public blockchain structure can benefit from differential privacy mechanisms for improved privacy, both making anonymization and privacy breaches by direct queries impossible, and preserving the checkability of the integrity of the blockchain. We first examine the current Bitcoin implementation for four query functions using the differential privacy formulation. Then, we present the feasibility of the utilization of two differential privacy mechanisms in Bitcoin; the noise addition to the transaction amounts and the user graph perturbation. We show that these mechanisms decrease the fraction of the cases violating differential privacy, therefore they can be used for improving anonymity and privacy in Bitcoin. Moreover, we showcase the noise addition to transaction amounts by using IBM Differential Privacy Library. We compare four differential privacy mechanisms for varying privacy parameter values and determine the feasible mechanisms and the parameters.
Bitcoin and its blockchain structure proposed in 2008  caused a new era to be opened in digital cash systems with the concept of proof of work and conversion of mining power into money. Since then, although, many blockchain-based digital currencies came out, Bitcoin still remains at the top of the market with $1,171,005,836,167 market capitalization  as of November 2021. Since Bitcoin has a public blockchain and transactions are explicitly visible, activities of the users can be tracked and linked, and the user identities can be revealed by linking one of the transactions to off-network information as surveyed in  and . For instance, with the knowledge that someone shopped online for 0.000381 BTC from a well-known e-commerce site, Bitcoin addresses that made a 0.000381 BTC valued shopping can be found by querying the Bitcoin address of the site and the transaction amounts equal to 0.000381 from the blockchain. Consequently, room for research came up for anonymity and privacy improvement in Bitcoin, and many academic papers have been published –. In these studies, generally used methods for anonymity and privacy improvement include mixing protocols, ring signatures, zero-knowledge proof, homomorphic commitments, and off-chain storage systems. Some of these studies are implemented, for example, Monero  using ring signatures, and Zcash  using zero-knowledge proofs are two of the prominent cryptocurrencies.
In this study, we present an examination of Bitcoin in terms of differential privacy. Our motivation arises from the fact that differential privacy approaches can be used for improving the privacy of the public Bitcoin blockchain. The differential privacy methods offer the prevention of anonymization and privacy breaches by direct queries and the preservation of checkability of the integrity of the blockchain. We first examine the current Bitcoin implementation using the differential privacy formulation. Then, we examine the application of noise addition to transaction amounts and user graph perturbation as differential privacy mechanisms. Furthermore, we demonstrate an empirical study for practical utilization of the noise addition approach and compare four differential privacy mechanisms according to mean absolute error for varying ε and δ values. In addition, we introduce a new metric called mean ranking offset and use it for the comparison, as well. In Section VII, we summarize our observations. It is observed that the noise addition and the graph perturbation mechanisms decrease the fraction of the cases violating differential privacy, therefore they can be used for improving anonymity and privacy in Bitcoin. The noise addition method decreases the fraction of the cases violating differential privacy by half for the three query functions, whereas the graph perturbation method decreases the fraction of the cases violating differential privacy by half for all of the four query functions considered.