Coin Transfer Unlinkability Under the Counterparty Adversary Model


  • Takeshi Miyamae Fujitsu Limited
  • Kanta Matsuura The University of Tokyo



Unlinkability is a crucial property of cryptocurrencies that protects users from deanonymization attacks. However, currently, even anonymous cryptocurrencies do not necessarily attain unlinkability under specific conditions. For example, Mimblewimble, which is considered to attain coin unlinkability using its transaction kernel offset technique, is vulnerable under the assumption that privacy adversaries can send their coins to or receive coins from the challengers. This paper first illustrates the privacy issue in Mimblewimble that could allow two colluded adversaries to merge a person’s two independent chunks of personally identifiable information (PII) into a single PII. To analyze the privacy issue, we formulate unlinkability between two sets of objects and a privacy adversary model in cryptocurrencies called the counterparty adversary model. On these theoretical bases, we define an abstract model of blockchain-based cryptocurrency transaction protocols called the coin transfer system, and unlinkability over it called coin transfer unlinkability (CT-unlinkability). Furthermore, we introduce zero-knowledgeness for the coin transfer systems to propose a method to easily prove the CT-unlinkability of cryptocurrency transaction protocols. Finally, we prove that Zerocash is CT-unlinkable by using our proving method to demonstrate its effectiveness.


Amarasinghe, N., Boyen, X., Mckague, M. “A Survey of Anonymity of Cryptocurrencies.” In Australasian Computer Science Week Multiconference (ACSW). 1 1–10 (2019)

Androulaki, E., Karame, G. O., Roeschlin, M., Scherer, T., Capkun, S. “Evaluating User Privacy in Bitcoin.” In 17th International Conference, Financial Cryptography and Data Security (FC). LNCS 7859 34–51 (2013)

Backes, M., Kate, A., Manoharan, P., Meiser, S., Mohammadi, E. “AnoA: A Framework for Analyzing Anonymous Communication Protocols.” In 26th IEEE Computer Security Foundations Symposium (CSF). 1 163–178 (2013)

Beam community. “Beam: The Scalable Confidential Cryptocurrency.” (2020) (accessed 22 July 2022)

Ben-Sasson, E., Chiesa, A., Tromer, E., Virza, M. “Succinct Non-Interactive Zero Knowledge for a von Neumann Architecture.” In 23rd USENIX Security Symposium. 1 781–796 (2014)

Ben-sasson, E., et al. “Zerocash: Decentralized Anonymous Payments from Bitcoin.” In 35th IEEE Sympo- sium on Security and Privacy (S&P). 1 459–474 (2014)

Bonneau, J., Miller, A., Clark, J., Narayanan, A., Kroll, J. A., Felten, E. W. “SoK: Research Perspectives and Challenges for Bitcoin and Cryptocurrencies.” In 36th IEEE Symposium on Security and Privacy (S&P). 1 104–121 (2015)

Goldreich, O. Foundations of Cryptography: Volume 1, Basic Tools. Cambridge: Cambridge University Press (2001).

Grin community. “Introduction to Mimblewimble and Grin.” (2017) (accessed 22 July 2022)

Groth, J. “On the Size of Pairing-Based Non-interactive Arguments.” In 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT). LNCS 9666 305–326 (2016)

Jedusor, T. E. “Mimblewimble.” (2016) (accessed 19 August 2022)

Maxwell, G. “Confidential Transactions.” (2015) (accessed 22 July 2022)

Nakamoto, S. “Bitcoin: A Peer-to-Peer Electronic Cash System.” (2008) (accessed 22 July 2022)

National Institute of Standards and Technology (NIST). “Guide to Protecting the Confidentiality of Personally Identifiable Information (PII).” (2010) (accessed 22 July 2022)

Parno, B., Howell, J., Gentry, C., Raykova, M. “Pinocchio: Nearly Practical Verifiable Computation.” In 34th IEEE Symposium on Security and Privacy (S&P). 1 238–252 (2013)

Pfitzmann, A., Hansen, M. “A Terminology for Talking About pPrivacy by Data Minimization: Anonymity, Unlinkability, Undetectability, Unobservability, Pseudonymity, and Identity Management.” (2010) (accessed 22 July 2022)

Poelstra, A. “Mimblewimble.” (2016) (accessed 22 July 2022)

Ruffing, T., Moreno-Sanchez, P. “ValueShuffle: Mixing Confidential Transactions for Comprehensive Transaction Privacy in Bitcoin.” 133–154 (2017)

Silveira, A., Betarte, G., Cristia, M., Luna, C. “A Formal Analysis of the Mimblewimble Cryptocurrency Protocol.” Sensors 21.17 5951 (2021)

Zcash community “Zcash github.” (2019) (accessed 22 July 2022)


Additional Files


2022-08-29 — Updated on 2022-08-31


How to Cite

Miyamae, T., & Matsuura, K. (2022). Coin Transfer Unlinkability Under the Counterparty Adversary Model. Ledger, 7. (Original work published August 29, 2022)



Research Articles