Ring Confidential Transactions
This article introduces a method of hiding transaction amounts in the strongly decentralized anonymous cryptocurrency Monero. Similar to Bitcoin, Monero is a cryptocurrency which is distributed through a proof-of-work “mining” process having no central party or trusted setup. The original Monero protocol was based on CryptoNote, which uses ring signatures and one-time keys to hide the destination and origin of transactions. Recently the technique of using a commitment scheme to hide the amount of a transaction has been discussed and implemented by Bitcoin Core developer Gregory Maxwell. In this article, a new type of ring signature, A Multilayered Linkable Spontaneous Anonymous Group signature is described which allows one to include a Pedersen Commitment in a ring signature. This construction results in a digital currency with hidden amounts, origins and destinations of transactions with reasonable efficiency and verifiable, trustless coin generation. The author would like to note that early drafts of this were publicized in the Monero Community and on the #bitcoin-wizards IRC channel. Blockchain hashed drafts are available showing that this work was started in Summer 2015, and completed in early October 2015. An eprint is also available at http://eprint.iacr.org/2015/1098.
Abe, M., Ohkubo, M., Suzuki K. “1-out-of-n signatures from a variety of keys.” Advances in Cryptology?Asiacrypt 2002 415-432 (2002)
Back, A. “Bitcoins with homomorphic value (validatable but encrypted).” Bitcointalk (accessed 1 May 2015) https://bitcointalk.org/ index.php?topic=305791.0, 2013.
Back, A. “Ring signature efficiency.” Bitcointalk (accessed 1 May 2015) https://bitcointalk.org/index.php?topic=972541 msg10619684#msg10619684
Ben Sasson, E., et al. “Zerocash: Decen- tralized anonymous payments from bitcoin.” In IEEE, 2014 IEEE Symposium on Security and Privacy, 459–474 (2014).
Bernstein, D.J., Duif, N., Lange, T., Schwabe, P., Yang, B.-Y. “High-speed high-security signatures.” Journal of Cryptographic Engineering 2.2 77–89 (2012).
Bissias, G., Ozisik, A. P., Levine, B. N., Liberatore. M. “Sybil-resistant mixing for bitcoin.” In ACM, Proceedings of the 13th Workshop on Privacy in the Electronic Society, 149–158 (2014)
Duffield, E. and Hagan, K. “Darkcoin: Peertopeer cryptocurrency with anonymous blockchain transactions and an improved proof of work system.” (2014)
Fromknecht, C. “One-time zero sum ring signature.” Github (2016) https://github.com/cfromknecht/ OZcoin/raw/master/whitepaper/zerosum.pdf
Fujisaki, E., Suzuki, K. “Traceable ring signature.” In Public Key Cryptography–PKC 2007. Springer 181– 200 (2007)
Liu, J.K., Wei, V. K., Wong, D. S. “Linkable spontaneous anonymous group signature for ad hoc groups.” In Information Security and Privacy. Springer 325–335 (2004)
Mackenzie, A., Noether, S., M. C. Team. “Improving obfuscation in the cryptonote protocol.” (2015) https: //lab.getmonero.org/pubs/MRL-0004.pdf
Maxwell, G. “Coinjoin: Bitcoin privacy for the real world, august 2013.” Bitcointalk (accessed 1 July 2015) https: //bitcointalk.org/index.php?topic=279249.0
Maxwell, G. “Confidential Transactions.” (accessed 1 June 2015) https://people.xiph.org/~greg/confidential_values. txt
Maxwell, G., Poelstra, A. “Borromean ring signatures.” (accessed 12 December 2016) https://github.com/Blockstream/borromean_paper/raw/master/borromean_draft_0.01_34241bb.pdf
Nakamoto, S. “Bitcoin: A peer-to-peer electronic cash system.”(2008).
Noether, S. “Mininero.” (2015) https://github.com/ShenNoether/MiniNero
Noether, S. “Ringct demo in c++.” (2016) https://github.com/ShenNoether/RingCT
Noether, S. “Ringct demo in python.” (2016) https://github.com/ShenNoether/RingCT-Python
Noether, S., Mackenzie, A., M. C. Team. “Ring multisignature.” (2016). https://shnoe.wordpress.com/2016/03/ 22/ring-multisignature/
Rivest, R. L., Shamir, A., Tauman, Y.. “How to leak a secret.” In Advances in Cryptology???ASIACRYPT 2001. Springer 552–565 (2001).
van Saberhagen, N. “Cryptonote v 2. 0.” (2013) https://cryptonote.org/whitepaper.pdf
Copyright (c) 2016 Shen Noether, Adam Mackenzie
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- The Author retains copyright in the Work, where the term “Work” shall include all digital objects that may result in subsequent electronic publication or distribution.
- Upon acceptance of the Work, the author shall grant to the Publisher the right of first publication of the Work.
- The Author shall grant to the Publisher and its agents the nonexclusive perpetual right and license to publish, archive, and make accessible the Work in whole or in part in all forms of media now or hereafter known under a Creative Commons Attribution 4.0 International License or its equivalent, which, for the avoidance of doubt, allows others to copy, distribute, and transmit the Work under the following conditions:
- Attribution—other users must attribute the Work in the manner specified by the author as indicated on the journal Web site;
- The Author is able to enter into separate, additional contractual arrangements for the nonexclusive distribution of the journal's published version of the Work (e.g., post it to an institutional repository or publish it in a book), as long as there is provided in the document an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post online a prepublication manuscript (but not the Publisher’s final formatted PDF version of the Work) in institutional repositories or on their Websites prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work. Any such posting made before acceptance and publication of the Work shall be updated upon publication to include a reference to the Publisher-assigned DOI (Digital Object Identifier) and a link to the online abstract for the final published Work in the Journal.
- Upon Publisher’s request, the Author agrees to furnish promptly to Publisher, at the Author’s own expense, written evidence of the permissions, licenses, and consents for use of third-party material included within the Work, except as determined by Publisher to be covered by the principles of Fair Use.
- The Author represents and warrants that:
- the Work is the Author’s original work;
- the Author has not transferred, and will not transfer, exclusive rights in the Work to any third party;
- the Work is not pending review or under consideration by another publisher;
- the Work has not previously been published;
- the Work contains no misrepresentation or infringement of the Work or property of other authors or third parties; and
- the Work contains no libel, invasion of privacy, or other unlawful matter.
- The Author agrees to indemnify and hold Publisher harmless from Author’s breach of the representations and warranties contained in Paragraph 6 above, as well as any claim or proceeding relating to Publisher’s use and publication of any content contained in the Work, including third-party content.
- The Author agrees to digitally sign the Publisher’s final formatted PDF version of the Work.
Revised 7/16/2018. Revision Description: Removed outdated link.