Journals Information
Mathematics and Statistics Vol. 13(5), pp. 312 - 319
DOI: 10.13189/ms.2025.130506
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Binary Huff Curves over Non-Local Rings: The Yak Protocol and Blockchain
EL MEHDI Badre 1,*, SAMIR Kourtite 2, SLIMANE Sidouna 3, M鈥橦ammed Ziane 2, ABDELALI Lahrech 1
1 Laboratory of Economic and Social Studies and Research, Moulay Ismail University, FSJES, Meknes, Morocco
2 Mohammed First University, FSO, Oujda, Morocco
3 Laboratory of Research in Management, Marketing, International Logistics and Finance, Sidi Mohamed Ben Abdellah University, EST, Fez, Morocco
ABSTRACT
Motivated by the growing need for secure and efficient cryptographic solutions in blockchain technology, this study explores the cryptographic potential of binary Huff curves defined over the non-local ring 
, introducing novel group structures for advanced blockchain applications. The research aims to enhance the security and efficiency of cryptographic primitives by leveraging the algebraic properties of these curves, particularly for resource-constrained devices in blockchain ecosystems. We establish a bijection between the Huff curve 
and the product 
, enabling an efficient group law that increases the complexity of the discrete logarithm problem (DLP). Methodologically, we define arithmetic operations in 
, prove the bijection, and derive addition formulas for the curve. These results are applied to adapt the Yak key exchange protocol, enhancing its resistance to DLP-based attacks through the non-local ring's structure. Principal findings demonstrate that achieves approximately 
group order, doubling the DLP security to 
-bit compared to /2-bit for standard curves over 
, with computational efficiency suitable for Internet of Things (IoT) devices. The study contributes to cryptography by proposing a robust framework for blockchain transaction security and secure data management, notably in multi-party computation and zero-knowledge proofs. Key conclusions highlight the curves' potential to secure blockchain validators and IoT nodes, as exemplified in supply chain applications. Novel aspects include the non-local ring's algebraic constraints and the Yak protocol's adaptation for blockchain. Limitations include the need for practical implementation and benchmarking against curves like secp256k1. Practical implications involve improved transaction security and data privacy in blockchain, while social implications include enabling secure, decentralized systems for healthcare and supply chain tracking. Future research should validate performance in real-world blockchain environments and assess resistance to side-channel attacks.
KEYWORDS
Binary Huff Curves, Finite Rings, Non-Local Rings, Cryptography, Yak Protocol, Blockchain Technology, Data Management
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] EL MEHDI Badre , SAMIR Kourtite , SLIMANE Sidouna , M鈥橦ammed Ziane , ABDELALI Lahrech , "Binary Huff Curves over Non-Local Rings: The Yak Protocol and Blockchain," Mathematics and Statistics, Vol. 13, No. 5, pp. 312 - 319, 2025. DOI: 10.13189/ms.2025.130506.
(b). APA Format:
EL MEHDI Badre , SAMIR Kourtite , SLIMANE Sidouna , M鈥橦ammed Ziane , ABDELALI Lahrech (2025). Binary Huff Curves over Non-Local Rings: The Yak Protocol and Blockchain. Mathematics and Statistics, 13(5), 312 - 319. DOI: 10.13189/ms.2025.130506.