SPHINCS

SPHINCS stands for Stateless Practical Hash-Based Signatures. It is a family of post-quantum digital signature schemes that rely on cryptographic hash functions rather than traditional number-theoretic problems. A key feature is statelessness: unlike other hash-based schemes that require keeping state about used keys, SPHINCS derives signing material in a way that does not require maintaining a signing state between invocations.

SPHINCS uses a layered Merkle-tree construction called a hypertree. Leaves of the hypertree are one-time signatures, typically WOTS+. A separate component called FORS (Forest of Random Subsets) signs short digests, providing a way to sign many messages with a small amount of private material. A complete SPHINCS signature includes a FORS signature, a set of WOTS+ signatures along the hypertree paths, and the authentication data needed to verify the internal nodes. The public key is the root of the top-level tree.

Key generation produces seeds for the hypertree layers; private constants are derived deterministically from these seeds. The public key is the top root. To sign, the message is hashed to a digest, FORS signs the digest, and the remaining layers provide the authentication information to link the signature to the root. Verification reconstructs the root from the signature and checks it against the public key.

SPHINCS+ is a refined version with adjustable parameter sets to trade security, speed, and signature size. Its security rests on standard hash-function assumptions. It was developed in the context of the NIST post-quantum cryptography process and remains a central example of hash-based, stateless signatures. Signatures are relatively large and signing can be slower than traditional schemes, but verification is efficient and quantum-resistant.