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41 lines
3.5 KiB
Markdown
41 lines
3.5 KiB
Markdown
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layout: post
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title: CLSAG security proof revisions
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summary: Issues with CLSAG formal security proofs were identified. Monero's implementation of CLSAG is not affected.
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tags: [crypto]
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author: Cypher Stack
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---
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**TL;DR**: A recent review conducted by Cypher Stack identified issues with CLSAG formal security proofs, and proposed fixes.
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These fixes don't affect the Monero implementation of CLSAG, so users are not at risk, and no action needs to be taken.
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The Monero transaction protocol uses [CLSAG](https://eprint.iacr.org/2019/654), a linkable ring signature construction, to authorize transactions.
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The CLSAG preprint and implementation were written by Monero contributing researchers and developers, and improve on an earlier design, [MLSAG](https://eprint.iacr.org/2015/1098).
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The [Zano](https://zano.org/) team recently engaged Cypher Stack, an applied cryptography consultancy, to review [d/v-CLSAG](https://github.com/hyle-team/docs/tree/master/zano/dv-CLSAG-extension), their generalization of CLSAG.
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This generalization is intended to accommodate different types of transactions that the Zano protocol supports, but retains much of the original CLSAG design and security model.
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Because of this, as part of Cypher Stack's review of d/v-CLSAG, aspects of the original CLSAG preprint were reviewed as well.
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Cypher Stack identified two issues with formal security proofs that also apply to CLSAG, and proposed updates to the proofs and protocol description to address them.
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Neither the existing Monero implementation of CLSAG nor the in-progress Zano implementation of d/v-CLSAG is affected by these issues, so users are not at risk and no action needs to be taken.
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Despite no vulnerabilities resulting from the findings, Cypher Stack responsibly disclosed the findings to Monero contributing researchers.
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The review report, which details the findings, is [available](https://github.com/cypherstack/zano-clsag-review/releases/tag/final).
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While it is quite technical in nature, we encourage interested researchers and others to read it.
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The first finding applying to CLSAG concerns an argument in an unforgeability proof that references an earlier signature design, [LSAG](https://eprint.iacr.org/2004/027).
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The argument in LSAG fails to identify an implicit requirement that certain parts of verification equations be nonzero.
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While the argument is somewhat more subtle in CLSAG and d/v-CLSAG, there are several ways it can be addressed.
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Both the Monero and Zano implementations already check that certain values in verification are nonzero, so they are not affected by this finding.
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The other finding that applies to CLSAG deals with another technical aspect of the unforgeability proof relating to how the proof reduces to a certain discrete logarithm hardness problem.
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Essentially, the proof shows that if there existed a way to forge a CLSAG signature, there would be a way to break a cryptographic problem that is widely believed to be infeasible.
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Because of the way certain operations in the proof are performed, the method of analysis does not formally hold.
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The review proposes a modification to the security proof that uses a different, and more standard, hard cryptographic problem instead.
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Making this change doesn't affect the CLSAG protocol or any implementations, but ensures the formal proof is fixed.
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Formal analysis in applied cryptography is challenging and subtle, and it's not uncommon to discover issues in security proofs.
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Cypher Stack hopes these findings, and the proposed proof updates, will be useful to the ecosystem.
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Onward!
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