The XMSS (eXtended Merkle Signature Scheme) and SPHINCS hash-based signature schemes were introduced in 20, respectively. Leslie Lamport invented hash-based signatures in 1979. NIST standardized stateful hash-based cryptography based on the eXtended Merkle Signature Scheme (XMSS) and Leighton–Micali Signatures (LMS), which are applicable in different circumstances, in 2020, but noted that the requirement to maintain state when using them makes them more difficult to implement in a way that avoids misuse. In 2022, NIST announced SPHINCS+ as one of three algorithms to be standardized for digital signatures. The US National Institute of Standards and Technology (NIST), specified that algorithms in its post-quantum cryptography competition support a minimum of 2 64 signatures safely. One consideration with hash-based signature schemes is that they can only sign a limited number of messages securely, because of their use of one-time signature schemes. In this hierarchical data structure, a hash function and concatenation are used repeatedly to compute tree nodes. A Merkle tree structure is used to this end. Since a one-time signature scheme key can only sign a single message securely, it is practical to combine many such keys within a single, larger structure. Hash-based signature schemes combine a one-time signature scheme, such as a Lamport signature, with a Merkle tree structure. So far, hash-based cryptography is used to construct digital signatures schemes such as the Merkle signature scheme, zero knowledge and computationally integrity proofs, such as the zk-STARK proof system and range proofs over issued credentials via the HashWires protocol. It is of interest as a type of post-quantum cryptography. Hash-based cryptography is the generic term for constructions of cryptographic primitives based on the security of hash functions.
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