Hashpõhine

Hashpõhine, or hash-based, is a class of cryptographic constructions that derive security from cryptographic hash functions rather than number-theoretic problems. The core idea is to use properties of hash functions—preimage resistance, second preimage resistance, and collision resistance—to build digital signatures, authentication schemes, and public-key cryptosystems. Because their security is not tied to factoring or discrete logarithms, hash-based systems are regarded as candidates for post-quantum cryptography.

Early and simple methods include Lamport signatures, which provide a one-time signature scheme; Winternitz signatures improve efficiency; and Merkle trees enable many signatures from a single seed by arranging one-time keys into a tree structure. These ideas form the basis for more scalable hash-based schemes while preserving a strong dependence on hash function security.

In modern practice, hash-based signatures such as XMSS (eXtended Merkle Signature Scheme) and XMSSMT (multi-tree) form a family designed for practical use, with mechanisms to manage multiple signatures from a single seed. SPHINCS+ is a prominent stateless hash-based signature scheme that combines several techniques to offer scalable, quantum-resistant signing without maintaining state between signatures in typical deployments.

Security and standards: hash-based signatures are believed resistant to quantum attacks as long as the underlying hash function remains secure; their security relies on hash function properties rather than number-theoretic assumptions. SPHINCS+ has undergone extensive security analysis and is among the leading hash-based algorithms considered for standardization in post-quantum cryptography efforts, such as the NIST process.

Limitations include larger signature sizes and, for some constructions, the need to manage state; SPHINCS+ is designed to be stateless but can be slower and larger than traditional schemes. Nonetheless, hash-based cryptography offers strong, well-understood post-quantum guarantees with a straightforward security basis.