# Involutions over the Galois field ${\mathbb F}_{2^{n}}$

Abstract : An involution is a permutation such that its inverse is itself (i.e., cycle length less than 2). Due to this property involutions have been used in many applications including cryptography and coding theory. In this paper we provide a systematic study of involutions that are defined over finite field of characteristic 2. We characterize the involution property of several classes of polynomials and propose several constructions. Further we study the number of fixed points of involutions which is a pertinent question related to permutations with short cycle. In this paper we mostly have used combinatorial techniques.
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Journal articles
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https://hal.inria.fr/hal-01272943
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Submitted on : Thursday, February 11, 2016 - 3:44:36 PM
Last modification on : Tuesday, October 19, 2021 - 10:54:35 AM

### Citation

Pascale Charpin, Sihem Mesnager, Sumanta Sarkar. Involutions over the Galois field ${\mathbb F}_{2^{n}}$. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2016, 62 (4), ⟨10.1109/TIT.2016.2526022⟩. ⟨hal-01272943⟩

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