Getting CROSS with Post Quantum Cryptography

NIST is currently assessing a number of methods for PQC digital signatures, and which would add to Dilithium, FALCON and SPHINCS+. These are:

• Code-based Signatures (5): CROSS (Codes and Restricted Objects Signature), Enhanced pqsigRM, FuLeeca, LESS (Linear Equivalence), MEDS (Matrix Equivalence Digital Signature).
• Multivariate Signatures (10): 3WISE, DME-Sign, HPPC (Hidden Product of Polynomial Composition), MAYO, PROV (PRovable unbalanced Oil and Vinegar), QR-UOV, SNOVA, TUOV (Triangular Unbalanced Oil and Vinegar), UOV (Unbalanced Oil and Vinegar), and VOX.
• MPC-in-the-Head Signatures (7): Biscuit, MIRA, MiRitH (MinRank in the Head), MQOM (MQ on my Mind), PERK, RYDE, and SDitH (Syndrome Decoding in the Head).
• Lattice-based Signatures (6): EagleSign, EHTv3 and EHTv4, HAETAE, HAWK, HuFu (Hash-and-Sign Signatures From Powerful Gadgets), and SQUIRRELS ( Square Unstructured Integer Euclidean Lattice Signature).
• Symmetric-based Signatures (4): AIMer, Ascon-Sign, FAEST, and SPHINCS-alpha.
• Other Signatures (4): ALTEQ, eMLE-Sig 2.0 (Embedded Multilayer Equations with Heavy Layer Randomization), KAZ-SIGN (Kriptografi Atasi Zarah), Preon, and Xifrat1-Sign.
• Isogeny Signatures (1): SQIsign.