What question did this study set out to answer?

This research aims to introduce and analyze the Ladhe hash-based signature scheme's security.

April 26, 2026Open Access

The Ladhe Decomposition Problem: A Candidate Post-Quantum Hardness Assumption on Additive Prime Structure, with an Identification Scheme

Key Points

This research aims to introduce and analyze the Ladhe hash-based signature scheme's security.
Developed a hash-based signature scheme with distinct primes forming a public prime.
Utilized Merkle aggregation to extend from one-time to many-time signature variants.
Performed formal security analysis in the random oracle model.
Demonstrated that security relies on the preimage resistance of SHA-256.
Achieved compact signatures without Merkle paths in one-time scenarios.
Provided a public cryptanalysis challenge to assess the scheme's robustness.

Abstract

We introduce Ladhe, a hash-based signature scheme whose private key is an ascending tuple of distinct primes summing to a public prime P. The public key is the hash of an indexed-pair compression of these primes. We present a one-time variant and describe its extension to a many-time scheme via standard Merkle aggregation. Security reduces to preimage resistance of the underlying hash function (SHA-256 in our reference), the same foundation as SPHINCS+. The arithmetic structure of the private key enables compact signatures (the primes themselves, no Merkle path in the one-time case) and structural verification (a fixed number of primality tests plus one hash evaluation). We give the full construction, formal security analysis in the random oracle model, an IANA-registered al- gorithm identifier (Private Enterprise Number 65644, registered April 2026), a reference Python implementation, and a public cryptanalysis challenge. Efficient KeyGen at crypto- graphic parameter sizes remains open.

Perguntar à IA

Bookmark

View Full Paper