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SPHINCS+

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SPHINCS+ is a post quantum digital signature scheme that is based on cryptographic hash functions. As a part of the NIST Post-Quantum Cryptography Standardization process, a version of the scheme was elected by the NIST to be the basis of the Stateless Hash-based Digital Signature Algorithm (SLH-DSA) and was standardized as FIPS 205.[1]

SPHINCS+
General
DesignersJean-Philippe Aumasson, Daniel J. Bernstein, Ward Beullens, Christoph Dobraunig, Maria Eichlseder, Scott Fluhrer, Stefan-Lukas Gazdag, Andreas Hülsing, Panos Kampanakis, Stefan Kölbl, Tanja Lange, Martin M. Lauridsen, Florian Mendel, Ruben Niederhagen, Christian Rechberger, Joost Rijneveld, Peter Schwabe, Bas Westerbaan
First publishedNovember 30, 2017; 8 years ago (2017-11-30)
Derived fromSPHINCS
Detail
Security claims264 signatures before the work needed to forge a signature is less than the required security level
StructureHash-based cryptography

Design

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SPHINCS+ is based on a one-time signature scheme called WOTS+ (a modified version of the Winternitz one-time signature scheme), a few-time signature scheme called FORS (Forest of Random Subsets) and Merkle trees.[2]

When signing, the message is signed with a FORS key. The FORS key is signed with a WOTS+ key that is a leaf of a merkle tree. The root of the tree is then signed with another WOTS+ key that is itself a leaf of another tree. That tree's root is again signed with a WOTS+. The number of layers of trees is a parameter that is specified as part of the algorithm. This "tree of trees" is called a hypertree. The root of the top tree is the public key. The signature consists of the FORS key and its signature, the WOTS+ keys with their signatures and inclusion proofs for the merkle tree and a random value called R that was used to generate the path in the hypertree.[2]

In order to verify a signature, the verifier first verifies the first WOTS+ key's inclusion proof against the public key and then verifies the key's signature of the next root. Then, they check the next WOTS+ key's inclusion proof against the new root. This goes on until the last WOTS+ key is reached, which is then used to verify the FORS key. That key is then used to actually verify the message's signature.[2]

All WOTS+ keys and FORS keys are generated deterministically from the private key. During signing, the signer generates a random bit string called R and hashes it together with the message. Parts of the resulting hash are used to select the path through the hypertree while the rest is signed with the FORS key.[2]

Security

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SPHINCS+ has been called a "conservative" choice by NIST since its security solely relies on the preimage and collision resistance of the underlying hash function.[3][4]

A theoretical forgery attack for specific SHA256 instances has been described that requires a large amount of legitimate signatures and an infeasible amount of computation. It relies on the Merkle–Damgård structure of SHA256[a] and reduces each security claim by 40 bits. The authors of the attack believe that it doesn't "call the general soundness of the SPHINCS+ design into question" and mitigations have been proposed.[2]

History

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SPHINCS+ is based on the SPHINCS scheme, which was presented at EUROCRYPT 2015.[6]

SPHINCS features a larger 1kB public and private key size and a 41kB signature size.[6]

SPHINCS+ was first released in 2017[7] since SPHINCS suffers from a vulnerability called "multi-target attacks in hash-based signatures", which was addressed by a 2016 paper. Furthermore, it doesn't have verifiable index selection (the path through the trees), which enables another kind of multi-target attack. SPHINCS+ was designed to address all these issues and also decrease the key and signature sizes using tree-less WOTS+ key compression, the addition of the R parameter during signing and the replacement of the few-time signature scheme with FORS.[8][9]

SPHINCS+ was standardized as SLH-DSA by NIST in August 2024 in the FIPS 205 standard,[1] making it one of the two NIST standardized post-quantum signature schemes with the other one being ML-DSA.[10][11][12]

Instances

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SLH-DSA specifies the following instances based on the hash function (SHA256 or SHAKE256), the type (f for faster signing time and s for shorter signature) and security level (e.g. 128 means that forging signatures is as hard as breaking AES-128):[1][13]

NameSecurity levelTypeHash functionPublic key sizePrivate key sizeSignature size
SPHINCS+-SHA2-128s 1[b] small SHA256 32 64 7856
SPHINCS+-SHAKE-128s SHAKE256
SPHINCS+-SHA2-128f fast SHA256 17088
SPHINCS+-SHAKE-128f SHAKE256
SPHINCS+-SHA2-192s 3[c] small SHA256 48 96 16224
SPHINCS+-SHAKE-192s SHAKE256
SPHINCS+-SHA2-192f fast SHA256 35664
SPHINCS+-SHAKE-192f SHAKE256
SPHINCS+-SHA2-256s 5[d] small SHA256 64 128 29792
SPHINCS+-SHAKE-256s SHAKE256
SPHINCS+-SHA2-256f fast SHA256 49856
SPHINCS+-SHAKE-256f SHAKE256

Implementations

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References

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  1. ↑ SHAKE256 instances are unaffected as they rely on the sponge construction[5]
  2. ↑ Signature forgery should be as hard as a successful key search on AES-128 or a SHA256 collision
  3. ↑ Signature forgery should be as hard as a successful key search on AES-192 or a SHA384 collision
  4. ↑ Signature forgery should be as hard as a successful key search on AES-256
  1. 1 2 3 Stateless hash-based digital signature standard (Report). Washington, D.C.: National Institute of Standards and Technology (U.S.). August 13, 2024. doi:10.6028/nist.fips.205.
  2. 1 2 3 4 5 "Breaking Category Five SPHINCS+ with SHA-256". Retrieved May 12, 2025.
  3. ↑ "Recovering the tight security proof of SPHINCS+" (PDF). Retrieved June 29, 2025.
  4. ↑ "A Tight Security Proof for SPHINCS+, Formally Verified". PQShield. January 30, 2025. Retrieved June 30, 2025.
  5. ↑ "Keccak Team". Keccak Team. Retrieved October 24, 2025.
  6. 1 2 "SPHINCS: Introduction". SPHINCS. July 18, 2013. Retrieved June 29, 2025.
  7. ↑ "SPHINCS+ Submission to the NIST post-quantum project" (PDF). Retrieved June 29, 2025.
  8. ↑ "SPHINCS+ – The smaller SPHINCS". Andreas Hülsing. December 4, 2017. Retrieved June 29, 2025.
  9. ↑ "Mitigating Multi-Target Attacks in Hash-based Signatures" (PDF). Retrieved June 29, 2025.
  10. ↑ Valenta, Luke; Gonçalves, Vânia; Westerbaan, Bas; Rosenberg, Michael; Kipp, Kevin; Dincer, Renan; Araya, Felipe Astroza; Galicer, Mari; Meunier, Thibault (August 20, 2024). "NIST's first post-quantum standards". The Cloudflare Blog. Retrieved June 29, 2025.
  11. ↑ "SPHINCS+". Open Quantum Safe. June 10, 2022. Retrieved June 29, 2025.
  12. ↑ Boutin, Chad (August 13, 2024). "NIST Releases First 3 Finalized Post-Quantum Encryption Standards". NIST. Retrieved June 29, 2025.
  13. ↑ "Security (Evaluation Criteria)". CSRC. January 3, 2017. Retrieved June 29, 2025.
  14. ↑ "randombit/botan: Cryptography Toolkit". GitHub. March 6, 2013. Retrieved June 29, 2025.
  15. ↑ "PQC and Lightweight Cryptography Updates". Bouncycastle. January 24, 2025. Retrieved June 29, 2025.
  16. ↑ Hess, Tjaden (August 15, 2024). "We wrote the code, and the code won". The Trail of Bits Blog. Retrieved June 29, 2025.
  17. ↑ "open-quantum-safe/liboqs: C library for prototyping and experimenting with quantum-resistant cryptography". GitHub. August 12, 2016. Retrieved June 29, 2025.
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