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On the security of DLCSP over \(GL_n(\mathbb {F}_q[S_r])\)

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Abstract

Discrete logarithm problem (DLP) and Conjugacy search problem (CSP) are two important tools for designing public key protocols. However DLP is used over commutative as well as non-commutative platforms but CSP is used only over non-commutative platforms. To harden the security of cryptosystems using DLP and CSP as base problems, various authors have combined these two problems to form a new problem called Discrete logarithm with conjugacy search problem (DLCSP). It has been used to design key exchange protocols and signature schemes over the general linear group with entries from group ring, that is, \(GL_n(\mathbb {F}_q[S_r])\). In this paper, we show that, if someone can solve DLP in polynomial time over some finite extension of \(\mathbb {F}_q\), then DLCSP over \(GL_n(\mathbb {F}_q[S_r])\) can also be solved in polynomial time with non-negligible probability.

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Acknowledgements

The research of first author is supported by University Grants Commission(UGC), reference number-1100 (DEC-2016). The third author is grateful for the support from the SERB-MATRICS scheme (MTR/2020/000508) of the Department of Science and Technology, Government of India.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Atul Pandey

  2. SAG, Metcalfe House, DRDO Complex, Delhi, 110054, India

    Indivar Gupta

  3. Zakir Husain Delhi College, University of Delhi, Jawaharlal Nehru Marg, Delhi, 110002, India

    Dhiraj Kumar Singh

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  1. Atul Pandey
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  2. Indivar Gupta
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  3. Dhiraj Kumar Singh
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Correspondence to Atul Pandey.

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Pandey, A., Gupta, I. & Singh, D.K. On the security of DLCSP over \(GL_n(\mathbb {F}_q[S_r])\). AAECC 34, 619–628 (2023). https://doi.org/10.1007/s00200-021-00523-6

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  • DOI: https://doi.org/10.1007/s00200-021-00523-6

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