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Digital Signature Schemes Based on Group Ring

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Abstract

In this paper, we propose three digital signature schemes based on the algebraic structure of group ring. The first scheme is a deterministic signature scheme, the second scheme is a probabilistic signature scheme whereas the third scheme is an uplifting of the NTRU signature scheme in group ring. We carefully discuss the security of these schemes by studying the hardness of the associated hard problems. We show that our schemes, with parameters of small size, provide the security equivalent to the security provided by the current secure implementations of discrete logarithm problem (e.g. 128 bits). We also discuss some examples to see the practicality of our schemes. This paper is the first advancement in the field of group ring based digital signatures.

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Authors and Affiliations

  1. Defence Research and Development Organization, New Delhi, India

    Sunil Kumar, Gaurav Mittal & Sandeep Kumar

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Gaurav Mittal

Authors
  1. Sunil Kumar
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  2. Gaurav Mittal
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  3. Sandeep Kumar
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Correspondence to Gaurav Mittal.

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Kumar, S., Mittal, G. & Kumar, S. Digital Signature Schemes Based on Group Ring. SN COMPUT. SCI. 3, 398 (2022). https://doi.org/10.1007/s42979-022-01286-8

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