[2608.09699] Full-Key Recovery and Forgery from One MQOM v2.1 Signature

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Computer Science > Cryptography and Security

arXiv:2608.09699 (cs)

[Submitted on 10 Aug 2026]

Title:Full-Key Recovery and Forgery from One MQOM v2.1 Signature

Authors:José Luis Delgado<br>View a PDF of the paper titled Full-Key Recovery and Forgery from One MQOM v2.1 Signature, by Jos\'e Luis Delgado

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Abstract:We give a full-key-recovery attack on MQOM v2.1, a Round-3 candidate in the NIST additional-signature process, that recovers the complete signing key from one accepted signature and uses it to sign a fresh message. If $\delta=\operatorname{FirstBits}_{\lambda}(x)$ is the prefix of the witness $x$, the sibling path determines a public value $A$ such that tree parity gives $s=\delta\oplus A$. Substitution into the hidden-leaf commitment yields $$\mathsf{Enc}_K(\delta\oplus A)=T\oplus\mathsf{LinOrtho}(\delta)$$ with public values $K$ and $T$. The correction in the same signature expands a solution into a complete witness, while the public MQ relation identifies those yielding valid signing keys; serializing such a witness gives the secret key, enabling a fresh-message signature accepted by the reference verifier.

We evaluate this equation over the specified AES/Rijndael circuits using retained circuit state along a Gray traversal. Complete-domain scans for Categories I and V cost $2^{142.335112}$ and $2^{271.794162}$ Boolean gates. Category-III scans cover $1/2+2^{-20}$ and $0.580004770183$ of the domain at costs of $2^{206.774558}$ and $2^{206.988685}$ gates. All four totals are below the NIST security benchmarks. Reduced-domain runs against the reference implementation recover the byte-exact witness and key in all three categories and produce a fresh-message forgery accepted by the reference verifier. Independently generated source-syntax circuits evaluate the fixed ciphers over the stated domains and translated L3 prefixes, while an exact ideal-cipher factorial-moment bound controls additional equation preimages passed to public-key validation. Every value in the equation is fixed by the accepted transcript, so salt-bound global-root expansion changes its public constants without removing the one-signature recovery channel.

Subjects:

Cryptography and Security (cs.CR)

Cite as:<br>arXiv:2608.09699 [cs.CR]

(or<br>arXiv:2608.09699v1 [cs.CR] for this version)

https://doi.org/10.48550/arXiv.2608.09699

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: José Luis Delgado [view email]<br>[v1]<br>Mon, 10 Aug 2026 15:04:50 UTC (51 KB)

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