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Article

Three Authentication Schemes Based on Finite Fields and Galois Rings

This version is not peer-reviewed.

Submitted:

25 January 2021

Posted:

26 January 2021

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Abstract
We give three new systematic authentication schemes, two using Gray map, finite fields and Galois rings, and one using only Galois rings. In the first scheme, we increase the size and simplify the scheme’s source space in [9]. In the second scheme, we reduce the key space of the first scheme. Finally, by not considering Gray map, used in the previous schemes, we give a third scheme on Galois rings, which generalizes the scheme over finite fields given in [8]. The introduced schemes obtain optimal impersonation and substitution probabilities.
Keywords: 
Authentication Schemwes; Galois Rings; Gray map
Subject: 
Computer Science and Mathematics  -   Algebra and Number Theory
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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