Abstract
In this paper, we study the differential \(\delta \)-uniform property of two position swapped Exponential Welch Costas (EWC) permutations on \({\mathbb {Z}}_{p-1}\) and construct permutations with \(\delta = 4, 6\) for different values of p. We calculate the number of swapped EWC permutations with differential uniformity 6 for primes of the form \(4d+3\). For primes of the form \(4d+1\), we obtain a lower bound on the number of swapped EWC permutations with differential uniformity 4.
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Acknowledgements
The authors thank the learned referees and the editor for their valuable comments and suggestions, which improved the presentation of the paper. Prof. R. K. Sharma is the ConsenSys Blockchain Chair Professor at IIT Delhi. He is grateful to ConsenSys AG for that privilege.
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Sharma, R.K., Mishra, P.R. & Kumar, Y. A new class of differential 4-uniform permutations from exponential permutation. AAECC 34, 897–912 (2023). https://doi.org/10.1007/s00200-021-00528-1
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DOI: https://doi.org/10.1007/s00200-021-00528-1