SPHINCS+ A stateless hash-based signature scheme

SPHINCS+ is a post-quantum cryptosystem (PQC) and should still be secure even if it proves feasible for an attacker to build a quantum computer. Its security against both classical and post-quantum attacks depends solely on the properties of a cryptographic hash function.

In June 2022, SPHINCS+ was chosen by NIST as one of the first four quantum-resistant cryptographic signature algorithms in NIST's post-quantum cryptography standardization project.

SPHINCS+ builds on the seminal works by Lamport, Diffie, Winternitz, and Merkle.

In this paper we look first at the building blocks on which SPHINCS+ is made. Then we describe the algorithms used and work through an actual example, taken from the round 3 submission to NIST by the SPHINCS+ team in 2020. We find it is often easier to work through an actual example rather than decipher abtract descriptions.

Contents

Properties of a cryptographic hash function
Lamport one-time signature (OTS)
Winternitz improvement (WOTS)
Winternitz parameter
Adding a checksum to WOTS
Merkle Tree
Basic Merkle Signature Scheme
Few Time Signature (FTS) HORS
Forest of Random Subsets (FORS)
WOTS+
SPHINCS+ Example
PK.Root Calculation
References

First let's look at the properties of a cryptographic hash function.

References

• [SPHINCSPLUS] Andreas Hülsing, SPHINCS+, accessed 14 February 2023, <https://sphincs.org/>

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This page first published 14 February 2023. Last updated 9 September 2025.