Quantum-Resilient Cryptographic Primitives: An Innovative Modular Hash Learning Algorithm to Enhanced Security in the Quantum Era

Abstract

In the era of rapid advancements in quantum computing, classical cryptographic primitives are facing unprecedented security challenges. Shor's algorithm, a powerful quantum tool, poses a significant threat to existing hash functions, raising concerns about data integrity and confidentiality. In response to these emerging threats, the paper introduces a novel Quantum-Resistant Hash Algorithm (QRHA) named the 'Modular Hash Learning Algorithm (MHLA).' MHLA has been meticulously designed with a strong focus on fundamental principles of quantum resistance and incorporates advanced mathematical and algorithmic techniques to enhance its security. This paper presents a comprehensive examination of MHLA's resistance to both classical and quantum attacks, with a particular emphasis on Shor's algorithm. Our research demonstrates that MHLA offers improved security in the context of the quantum era, ensuring data confidentiality and integrity. Moreover, MHLA boasts an efficient algorithmic complexity with a time complexity of $O(m \cdot n \cdot k)$ for the matrix-vector product. This research contributes to the ongoing efforts to fortify cryptographic systems against the evolving landscape of quantum computing.