- MQOM relies on the MPC-in-the-Head paradigm which was introduced by:
Yuval Ishai, Eyal Kushilevitz, Rafail Ostrovsky, and Amit Sahai. Zero-knowledge from secure multiparty computation (STOC 2007).
- MQOM uses commitments based on GGM trees as suggested by
Jonathan Katz, Vladimir Kolesnikov, and Xiao Wang. Improved non-interactive zero knowledge with applications to post-quantum signatures (CCS 2018).
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MQOM v1 (round-1 submission)
- MQOM v1 relies on a specific MPC protocol inspired from and improving previous works
— Carsten Baum, Cyprien Delpech de Saint Guilhem, Daniel Kales, Emmanuela Orsini, Peter Scholl, and Greg Zaverucha. Banquet: Short and Fast Signatures from AES (PKC 2021).
— Thibauld Feneuil. Building MPCitH-based Signatures from MQ, MinRank, and Rank SD (ACNS 2024).
- MQOM v1 uses the hypercube technique introduced by
Carlos Aguilar Melchor, Nicolas Gama, James Howe, Andreas Hülsing, David Joseph, and Dongze Yue. The Return of the SDitH (EUROCRYPT 2023).
- The first-round submitters of MQOM to NIST are
Thibauld Feneuil and Matthieu Rivain.
- The design of MQOM v1 has been further published in
Ryad Benadjila, Thibauld Feneuil, and Matthieu Rivain. MQ on my Mind: Post-Quantum Signatures from the Non-Structured Multivariate Quadratic Problem (EuroS&P 2024).
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MQOM v2 (round-2 submission)
- MQOM v2 relies on the Threshold-Computation-in-the-Head (TCitH) framework proposed in
Thibauld Feneuil and Matthieu Rivain. Threshold Computation in the Head: Improved Framework for Post-Quantum Signatures and Zero-Knowledge Arguments (ePrint 2023/1573)
- The TCitH framework can be interpreted as a variant of the VOLE-in-the-Head framework proposed in
Carsten Baum, Lennart Braun, Cyprien Delpech de Saint Guilhem, Michael Klooß, Emmanuela Orsini, Lawrence Roy, and Peter Scholl. Publicly Verifiable Zero-Knowledge and Post-Quantum Signatures From VOLE-in-the-Head (CRYPTO 2023).
- MQOM v2 uses correlated half GGM trees as proposed in
— Xiaojie Guo, Kang Yang, Xiao Wang, Wenhao Zhang, Xiang Xie, Jiang Zhang, and Zheli Liu. Half-tree: halving the cost of tree expansion in COT and DPF (EUROCRYPT 2023).
— Janik Huth, and Antoine Joux. MPC in the head using the subfield bilinear collision problem (EUROCRYPT 2023).
— Seongkwang Kim, Byeonghak Lee, Mincheol Son. Relaxed Vector Commitment for Shorter Signatures (EUROCRYPT 2025).
- The second-round submitters of MQOM to NIST are
Ryad Benadjila, Charles Bouillaguet, Thibauld Feneuil, and Matthieu Rivain.