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SPHINCS+
Post-quantum digital signature scheme From Wikipedia, the free encyclopedia
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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.
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Design
Summarize
Perspective
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]
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Security
SPHINCS+'s security solely relies on the preimage and collision resistance of the underlying hash function.[3]
History
SPHINCS+ is based on the SPHINCS scheme, which was prsented 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 paramater 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
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]
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Implementations
- Botan[12]
- Bouncy Castle[13]
- RustCrypto, written by Trail of Bits[14]
- Open Quantum Safe[15]
External links
References
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