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, Volume 101, Issue 1, pp 439–451 | Cite as

A Method of Generating 8 × 8 Substitution Boxes Based on Elliptic Curves

  • Umar Hayat
  • Naveed Ahmed Azam
  • Muhammad Asif


Elliptic curve cryptography provides better security and is more efficient as compared to other public key cryptosystems with identical key size. In this article, we present a new method for the construction of substitution boxes(S-boxes) based on points on elliptic curve over prime field. The resistance of the newly generated S-box against common attacks such as linear, differential and algebraic attacks is analyzed by calculating their non-linearity, linear approximation, strict avalanche, bit independence, differential approximation and algebraic complexity. The experimental results are further compared with some of the prevailing S-boxes presented in Shi et al. (Int Conf Inf Netw Appl 2:689–693, 1997), Jakimoski and Kocarev (IEEE Trans Circuits Syst I 48:163–170, 2001), Guoping et al. (Chaos, Solitons Fractals 23:413–419, 2005), Guo (Chaos, Solitons Fractals 36:1028–1036, 2008), Kim and Phan (Cryptologia 33: 246–270, 2009), Neural et al. (2010 sixth international conference on natural computation (ICNC 2010), 2010), Hussain et al. (Neural Comput Appl., 2012). Comparison reveals that the proposed algorithm generates cryptographically strong S-boxes as compared to some of the other exiting techniques.


Elliptic curve Substitution box Non-linearity Differential approximation probability Algebraic complexity 


Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Umar Hayat
    • 1
  • Naveed Ahmed Azam
    • 2
    • 3
  • Muhammad Asif
    • 1
  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan
  3. 3.Faculty of Engineering SciencesGIK InstituteTopiPakistan

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