KHA-256: A Next-Generation Cryptographic Hash Function Based on Keçeci Numbers and Mathematical Constants

KHA-256: A Next-Generation Cryptographic Hash Function Based on Keçeci Numbers and Mathematical Constants Mehmet Keçeci ORCID: https://orcid.org/0000-0001-9937-9839 Received: 01.04.2026 Abstract: KHA-256 (Keçeci Hash Algorithm-256) is a novel cryptographic hash function that departs from conventional bit-level constructions by leveraging mathematical constants (e.g., π, e, φ) and the multidimensional algebraic structures of Keçeci Numbers—encompassing real, complex, quaternion, octonion, and neutrosophic representations. Entropy is derived from the non-repeating decimal expansions of transcendental constants, whilst high-dimensional nonlinear mixing layers ensure cryptographic robustness. Empirical evaluations confirm security properties comparable to SHA-256, including an average avalanche effect of 50.5%, zero collision incidence in extensive trials, and statistically uniform output distributions. Crucially, the algorithm prioritises mathematical diversity and theoretical resilience over raw computational speed—a deliberate design choice aligned with post-quantum security considerations. Released under the open-source AGPL-3.0 licence, KHA-256 is intended for high-assurance applications such as cryptographic modules, data integrity verification, and digital signatures. This work proposes a new design paradigm for hash functions, demonstrating that foundational cryptographic primitives can be enriched through deep mathematical structures, thereby opening avenues for innovation in post-classical cryptography. The current implementation provides a foundational prototype; formal security proofs, performance optimisations, and adaptive mixing layers are intentionally deferred to subsequent development phases. Although the use of neutrosophic algebra in isolation may raise cryptographic concerns, KHA-256 mitigates this risk through a multi-type selection framework drawn from 22 distinct Keçeci Number families; structural weaknesses in any single algebraic system are thus neutralised by synergistic interaction across dimensions, enhancing both robustness and entropy diversity. Keywords: Keçeci Numbers, KHA-256, Mathematical constants, Cryptographic hash function, Avalanche effect, Multidimensional algebra, Post-Quantum Resistance, Quantum-resistant hash, Deterministic complexity, Open-source cryptography, Niche Cryptography.