کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8895698 1630353 2018 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Nilpotent linearized polynomials over finite fields and applications
ترجمه فارسی عنوان
چندجملهای خطی چندگانه بر روی زمینه های محدود و برنامه های
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
Let q be a prime power and Fqn be the finite field with qn elements, where n>1. We introduce the class of the linearized polynomials L(X) over Fqn such thatL(t)(X):=L∘L∘⋯∘L︸ttimes(X)≡0(modXqn−X) for some t≥2, called nilpotent linearized polynomials (NLP's). We discuss the existence and construction of NLP's and, as an application, we show how to obtain permutations of Fqn from these polynomials. For some of those permutations, we can explicitly give the compositional inverse map and the cycle decomposition. This paper also contains a method for constructing involutions over binary fields with no fixed points, which are useful in block ciphers.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 50, March 2018, Pages 279-292
نویسندگان
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