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Improved algorithms in parallel evaluation of large cryptographic S-boxes

Khadem, B ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1080/17445760.2020.1760863
  3. Publisher: Taylor and Francis Ltd , 2020
  4. Abstract:
  5. Nowadays computational complexity of fast Walsh Hadamard transform and non-linearity for Boolean functions and large cryptographic substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear and differential attacks. Time and memory complexities of the best existing algorithm for computing fast Walsh Hadamard transform and non-linearity for (Formula presented.) substitution boxes is (Formula presented.). This paper proposes three new innovation in acceleration methods that improve the computation time for paralleled Walsh matrix up to 68 folds and the evaluation time for non-linearity degree up to 1021 folds. These methods include defining and accessing Walsh matrix transpose and combining an important part of evaluation process of non-linearity in the computation algorithm of Walsh matrix. The validity of the proposed algorithms is verified by means of simulation and experiments.The overall analysis of resource consumption of proposed algorithms is compared with previous ones. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Computational complexity ; Fast Walsh Hadamard transform ; Implementation ; Non-linearity ; Parallelisation ; S-boxes ; Boolean functions ; Cryptography ; Matrix algebra ; Acceleration method ; Computation algorithm ; Differential attacks ; Encryption schemes ; Fast Walsh-Hadamard transforms ; Parallel evaluation ; Resource consumption ; Substitution boxes ; Hadamard transforms
  8. Source: International Journal of Parallel, Emergent and Distributed Systems ; Volume 35, Issue 4 , 2020 , Pages 461-472
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/17445760.2020.1760863?journalCode=gpaa20