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Recent Advances in the Index Calculus Method for Solving the ECDLP

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Proceedings of International Conference on Paradigms of Communication, Computing and Data Analytics (PCCDA 2023)

Part of the book series: Algorithms for Intelligent Systems ((AIS))

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Abstract

Elliptic curve cryptography (ECC) is a well-developed and widely used type of public key encryption that outperforms older cryptographic systems such as RSA. Because of its ability to provide improved security while using smaller key sizes, ECC has recently gained popularity. The computation of the private scalar integer that is used as a private key to generate the public key is the most important determinant of ECC security. The elliptic curve discrete logarithm problem (ECDLP) serves as the foundation for the complexity of ECC. The index calculus approach is one of the most effective strategies for solving ECDLP. In the recent years, significant progress has been made in theoretically and functionally improving the efficiency of the index calculus approach for ECDLP. This research looks at the recent advances in the algorithm and its complexity, new methodologies and methods for improving its efficiency, the current state of the art in this field, as well as outstanding research challenges that require further investigation. The goal of this paper is to provide an overview of the recent developments in this critical area of cryptography research. We compare and contrast cutting-edge algorithms and strategies designed to improve the method's efficiency.

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Authors and Affiliations

  1. Amity University, Haryana, Gurugram, India

    Aayush Jindal, Aman Jatain & Shalini Bhaskar Bajaj

Authors
  1. Aayush Jindal
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  2. Aman Jatain
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  3. Shalini Bhaskar Bajaj
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Correspondence to Aayush Jindal .

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Editors and Affiliations

  1. Department of Mathematics, Dr. B. R. Ambedkar National Institute Technology, Jalandhar, India

    Anupam Yadav

  2. Department of Electronics and Communication Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, India

    Satyasai Jagannath Nanda

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore

    Meng-Hiot Lim

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Jindal, A., Jatain, A., Bajaj, S.B. (2023). Recent Advances in the Index Calculus Method for Solving the ECDLP. In: Yadav, A., Nanda, S.J., Lim, MH. (eds) Proceedings of International Conference on Paradigms of Communication, Computing and Data Analytics. PCCDA 2023. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-99-4626-6_23

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