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Solving ECDLP via List Decoding

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Provable Security (ProvSec 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11821))

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Abstract

We provide a new approach to the elliptic curve discrete logarithm problem (ECDLP). First, we construct Elliptic Codes (EC codes) from the ECDLP. Then we propose an algorithm of finding the minimum weight codewords for algebraic geometry codes, especially for the elliptic code, via list decoding. Finally, with the minimum weight codewords, we show how to solve ECDLP. This work may provide a potential approach to speeding up the computation of ECDLP.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61672550 and 61672346) and the National Key R&D Program of China(2017YFB0802503).

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Authors and Affiliations

  1. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Fangguo Zhang

  2. Guangdong Key Laboratory of Information Security, Guangzhou, 510006, China

    Fangguo Zhang

  3. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shengli Liu

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  1. Fangguo Zhang
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  2. Shengli Liu
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Correspondence to Fangguo Zhang .

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Editors and Affiliations

  1. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

  2. The University of Hong Kong, Pok Fu Lam, Hong Kong

    Tsz Hon Yuen

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Zhang, F., Liu, S. (2019). Solving ECDLP via List Decoding. In: Steinfeld, R., Yuen, T. (eds) Provable Security. ProvSec 2019. Lecture Notes in Computer Science(), vol 11821. Springer, Cham. https://doi.org/10.1007/978-3-030-31919-9_13

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  • DOI: https://doi.org/10.1007/978-3-030-31919-9_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31918-2

  • Online ISBN: 978-3-030-31919-9

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