Shor’s algorithm breaks our existing public key cryptography digital signature methods. In order to replace these, NIST has standardised ML-DSA (Dilithium) with FIPS 204, SLH-DSA (SPHINCS+) with FIPS 205 and FN-DSA (FALCON) with FIPS 206. ML-DSA and FN-DSA use lattice methods, while SLH-DSA uses a hash-based signature method. Recently, NIST has announced Round 2 Additional Digital Signature Candidates [here]:
Multivariate Signatures (4): MAYO, QR-UOV, SNOVA, and UOV (Unbalanced Oil and Vinegar).
MPC-in-the-Head Signatures (5): MIRA/MiRitH (MinRank in the Head), MQOM (MQ on my Mind), PERK, RYDE, and SDitH (Syndrome Decoding in the Head).
Lattice-based Signatures (1): HAWK.
Code-based Signatures (2): CROSS (Codes and Restricted Objects Signature), and LESS (Linear Equivalence).
Symmetric-based Signatures (1): FAEST.
Isogeny Signatures (1): SQIsign.
Overall, Bob will create a keypair, and then sign a hash of a message with his private key and where Alice will verify this with his public key:
Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. Based in Edinburgh. Old World Breaker. New World Creator. Building trust.
