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SPHINCS+

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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 Westerbaa
First publishedNovember 30, 2017; 7 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

SPHINCS+, also known officially as SLH-DSA,[1] is a post-quantum signature scheme selected by the NIST for the FIPS 205 standard of the post-quantum standardisation process.

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+'s security solely relies on the preimage and collision resistance of the underlying hash function.[3]

History

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SPHINCS+ is based on the SPHINCS scheme, which was presented at EUROCRYPT 2015.[4]

SPHINCS features a larger 1kb public and private key size and a 41kb signature size.[4]

SPHINCS+ was first released in 2017[5] 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.[6][7]

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.[8][9][10]

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][11]

Name Security level Type Hash function Public key size Private key size Signature size
SPHINCS+-SHA2-128s 1[a] small SHA256 32 64 7856
SPHINCS+-SHAKE-128s SHAKE256
SPHINCS+-SHA2-128f fast SHA256 17088
SPHINCS+-SHAKE-128f SHAKE256
SPHINCS+-SHA2-192s 3[b] small SHA256 48 96 16224
SPHINCS+-SHAKE-192s SHAKE256
SPHINCS+-SHA2-192f fast SHA256 35664
SPHINCS+-SHAKE-192f SHAKE256
SPHINCS+-SHA2-256s 5[c] 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. ^ Signature forgery should be as hard as a successful key search on AES-128 or a SHA256 collision
  2. ^ Signature forgery should be as hard as a successful key search on AES-192 or a SHA384 collision
  3. ^ Signature forgery should be as hard as a successful key search on AES-256
  1. ^ a b c 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. ^ a b c d "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 b "SPHINCS: Introduction". SPHINCS. July 18, 2013. Retrieved June 29, 2025.
  5. ^ "SPHINCS+ Submission to the NIST post-quantum project" (PDF). Retrieved June 29, 2025.
  6. ^ "SPHINCS+ – The smaller SPHINCS". Andreas Hülsing. December 4, 2017. Retrieved June 29, 2025.
  7. ^ "Mitigating Multi-Target Attacks in Hash-based Signatures" (PDF). Retrieved June 29, 2025.
  8. ^ 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.
  9. ^ "SPHINCS+". Open Quantum Safe. June 10, 2022. Retrieved June 29, 2025.
  10. ^ Boutin, Chad (August 13, 2024). "NIST Releases First 3 Finalized Post-Quantum Encryption Standards". NIST. Retrieved June 29, 2025.
  11. ^ "Security (Evaluation Criteria)". CSRC. January 3, 2017. Retrieved June 29, 2025.
  12. ^ "randombit/botan: Cryptography Toolkit". GitHub. March 6, 2013. Retrieved June 29, 2025.
  13. ^ "PQC and Lightweight Cryptography Updates". Bouncycastle. January 24, 2025. Retrieved June 29, 2025.
  14. ^ Hess, Tjaden (August 15, 2024). "We wrote the code, and the code won". The Trail of Bits Blog. Retrieved June 29, 2025.
  15. ^ "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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