Research Article Open Access

A Secure Key Authentication Scheme Based on the Hardness of Solving Elliptic Curve Discrete Logarithm Problem

Izzmier Izzuddin Zulkepli1 and Eddie Shahril Ismail1
  • 1 Universiti Kebangsaan Malaysia, Malaysia
Journal of Computer Science
Volume 16 No. 5, 2020, 583-590

DOI: https://doi.org/10.3844/jcssp.2020.583.590

Submitted On: 24 January 2020 Published On: 15 May 2020

How to Cite: Zulkepli, I. I. & Ismail, E. S. (2020). A Secure Key Authentication Scheme Based on the Hardness of Solving Elliptic Curve Discrete Logarithm Problem. Journal of Computer Science, 16(5), 583-590. https://doi.org/10.3844/jcssp.2020.583.590

Abstract

A key authentication scheme is a scheme that protects a user’s public key from modification and counterfeiting by an adversary. The new development and improvement of key authentication schemes should be made continuously so that the systems are safe and practical to be used. To the best of our knowledge, there is no key authentication using the elliptic curve so far. Thus, in this paper, we propose the first secure elliptic curve-based key authentication scheme with its security, relying on the difficulty of solving the elliptic curve discrete logarithm problem. We show that the proposed scheme is secure against various defined cryptographic attacks such as public keyword modification and keyword guessing attacks. Next, we analyze the computational time complexity of the algorithms by computing the number of modular operations needed in these algorithms together with asymptotical analysis of running time using O(g(n)) notation. It turns out that our scheme requires the least amount of time complexity of 203.36Tmul + Th for user registration phase, 58.12Tmul for key authentication phase, and offers less running time compared to some existing key authentication schemes.

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Keywords

  • Cryptography
  • Key Authentication Scheme
  • Elliptic Curve
  • Elliptic Curve Discrete Logarithm Problem