Investigation and Application of Differential Privacy in Bitcoin

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.