Stateless Hash-Based Signature

A stateless hash-based signature is a form of post-quantum cryptography designed to be secure against attacks from both classical and quantum computers. Unlike traditional schemes like ECDSA or RSA, its security is based on the one-way property and collision resistance of a hash function (e.g., SHA-256), not the hardness of problems like integer factorization or discrete logarithms. This makes it a leading candidate for quantum-resistant digital signatures in blockchain and secure communication protocols.

The "stateless" property is critical: the signer does not need to track which one-time signature keys have been used, eliminating complex state management and synchronization issues present in earlier stateful HBS schemes like XMSS. Stateless schemes, such as SPHINCS+, achieve this by using a few-time signature (FTS) layer and a vast hyper-tree structure, where each leaf is a one-time key. A signature includes a path through this tree and a proof, allowing verification without the signer remembering past signatures.

In practice, stateless HBS schemes trade some efficiency for robustness and simplicity. They typically produce larger signatures and require more computational resources for signing and verification compared to classical algorithms. However, their provable security and resistance to side-channel attacks make them invaluable for long-term cryptographic applications, such as securing blockchain smart contracts, software updates, and foundational internet infrastructure against future quantum adversaries.

A stateless hash-based signature (HBS) scheme is a digital signature construction designed to be secure against attacks from both classical and quantum computers. Its core innovation is the generation of a massive set of one-time private keys from a single, compact seed using a hash function, eliminating the need for the signer to track which keys have been used. This stateless property is critical for reliability and scalability in distributed systems, as it prevents signature failure due to lost state synchronization.

The most prominent construction is the Extended Merkle Signature Scheme (XMSS) and its multi-tree variant XMSS^MT. The signer first generates a Merkle tree of one-time verification keys, where the root of this tree becomes the single, long-term public key. Each leaf is derived from a unique Winternitz One-Time Signature (WOTS+) key pair, itself generated from a pseudorandom function seeded by a master secret. To sign, the signer uses a leaf's private key and provides the corresponding authentication path—a set of hashes—to prove the leaf's membership in the Merkle tree.

Verification involves checking the one-time signature against the leaf's public key and then recomputing the Merkle root using the provided authentication path to match the signer's published root. While highly secure, these schemes produce larger signatures and keys compared to ECDSA or EdDSA, and they have a finite cap on the number of signatures that can be issued, defined by the height of the Merkle tree. They are standardized by bodies like NIST and the IETF for use in a post-quantum cryptographic future.