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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 694–705
Volume 25, No 4, 2018, P. 59-80
UDC 519.8
A. V. Miloserdov
Permutation binomial functions over finite fields
Abstract:
We consider binomial functions over a finite field of order $2^n$. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that $2^{n} - 1$ is prime. Permutation binomial functions are constructed in the case when $n$ is composite and found for $n \le 8$.
Tab. 2, bibliogr. 30.
Keywords: vectorial Boolean function, binomial function, permutation, APN function.
DOI: 10.17377/daio.2018.25.611
Aleksey V. Miloserdov 1
1. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: amiloserdov6@gmail.com
Received 20 February 2018
Revised 4 June 2018
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