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Exploring the solution space: CB-WCA for efficient finite field multiplication in post-quantum cryptography

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Abstract

In the field of post-quantum security, isogeny-based cryptography stands out for its ability to fight quantum attacks. One of the key operations in isogeny-based schemes is finite field multiplication, which plays a crucial role in cryptographic protocols such as key exchange and digital signatures. To ensure practical implementations of these schemes, efficient finite field multiplication is essential. In this research, a novel optimization approach, the Crossover-Boosted Water Cycle Algorithm (CB-WCA), to enhance the efficiency of finite field multiplication in isogeny-based cryptography is proposed. By using both the WCA and a crossover method inspired by genetic algorithms, the CB-WCA effectively explores solution areas, aiming for the best solutions. The formulation of the finite field multiplication optimization problem and an objective function that quantifies the efficiency of the multiplication process based on computational cost is presented and defined. The CB-WCA is then applied to find the optimal set of parameters for finite field multiplication algorithms. Extensive experimental evaluations are conducted, comparing the performance of the CB-WCA-optimized algorithms with traditional optimization methods and other metaheuristic algorithms. Through the findings, it is evident that the CB-WCA stands out for its ability to achieve faster execution times and decrease computational costs. Furthermore, the optimized finite field multiplication algorithms are integrated into isogeny-based cryptographic schemes and evaluate their impact on cryptographic protocol efficiency and security. Real-world implementations showcase the practical applicability of the optimized algorithms in hardware and software environments. To ensure the security of the optimized algorithms, rigorous cryptanalysis is performed to verify their resilience against potential attacks, ensuring they meet the highest standards of security.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, St. Joseph’s College of Engineering, Chennai, Tamil Nadu, India

    Janani Sankaran & Chandrasekar Arumugam

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  1. Janani Sankaran
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  2. Chandrasekar Arumugam
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All authors agreed on the content of the study. JS and CA collected all the data for analysis. JS agreed on the methodology. JS and CA completed the analysis based on agreed steps. Results and conclusions are discussed and written together. The author read and approved the final manuscript.

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Correspondence to Janani Sankaran.

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Sankaran, J., Arumugam, C. Exploring the solution space: CB-WCA for efficient finite field multiplication in post-quantum cryptography. Quantum Inf Process 23, 28 (2024). https://doi.org/10.1007/s11128-023-04232-6

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