[FEATURE REQUEST] Add HORS (Hash to Obtain Random Subset) few-time signature scheme #7634

What would you like to Propose?

I would like to add an educational implementation of HORS (Hash to Obtain Random Subset), a hash-based few-time signature scheme (Reyzin & Reyzin, 2002), to the ciphers package.

HORS is the predecessor of FORS, the few-time signature used inside SLH-DSA/SPHINCS+ (FIPS 205). Together with the existing Lamport, Winternitz (WOTS) and Merkle Signature Scheme implementations, it would cover all the core building blocks of SPHINCS+.

Issue details

Algorithm: HORS (Reyzin & Reyzin, "Better than BiBa", ACISP 2002)

Problem statement: One-time signatures such as Lamport and WOTS become insecure after a single use. HORS is a few-time signature: one key pair can sign a small number of messages, with security decreasing gradually as more secret values are revealed. Signing and verification only require k hash evaluations.

How it works:

• Key generation: generate t = 2^τ random secret values; the public key is their hashes, pk[i] = H(sk[i]).
• Signing: hash the message and split the digest into k chunks of τ bits. Each chunk is interpreted as an index, and the signature consists of the secret values at those k indices.
• Verification: derive the same indices from the message and check that the hash of each revealed value matches the public key at that index.

Proposed API (com.thealgorithms.ciphers.HorsSignature):

• HorsSignature() with t = 1024, k = 16 (parameters suggested in the paper) / HorsSignature(int t, int k)
• byte[][] getPublicKey()
• byte[][] sign(byte[] message)
• static boolean verify(byte[] message, byte[][] signature, byte[][] publicKey)

Scope:

• SHA-256 via java.security.MessageDigest; no external dependencies
• JUnit 5 tests: valid signatures, signing multiple messages with one key, deterministic signing, tampered message/signature, wrong public key, known-vector tests for index derivation, parameterized (t, k), input validation and immutability
• Only two new files (implementation + test)

Additional Information

This is a follow-up to the existing hash-based signatures in the repository (Lamport, Winternitz OTS and the Merkle Signature Scheme) and is intended for educational purposes only. The Javadoc will explain the few-time security degradation and how FORS in SLH-DSA improves on HORS.

References:

• Reyzin & Reyzin, "Better than BiBa: Short One-time Signatures with Fast Signing and Verifying": https://eprint.iacr.org/2002/014
• https://en.wikipedia.org/wiki/Hash-based_cryptography
• FIPS 205 (SLH-DSA): https://csrc.nist.gov/pubs/fips/205/final