Jean-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 published
November 30, 2017; 7 years ago (2017-11-30)
Derived from
SPHINCS
Detail
Security claims
264 signatures before the work needed to forge a signature is less than the required security level
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
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]
History
SPHINCS+ is based on the SPHINCS scheme, which was presented at EUROCRYPT 2015.[5]
SPHINCS features a larger 1kb public and private key size and a 41kb signature size.[5]
SPHINCS+ was first released in 2017[6] 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.[7][8]
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.[9][10][11]
Instances
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][12]
^Signature forgery should be as hard as a successful key search on AES-128 or a SHA256 collision
^Signature forgery should be as hard as a successful key search on AES-192 or a SHA384 collision
^Signature forgery should be as hard as a successful key search on AES-256
^ abcStateless 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.
