کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
395422 665960 2011 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Affine equivalence of cubic homogeneous rotation symmetric functions
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
Affine equivalence of cubic homogeneous rotation symmetric functions
چکیده انگلیسی

Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The simplest case of quadratic rotation symmetric functions which are generated by cyclic permutations of the variables in a single monomial was only settled in 2009. This paper studies the much more complicated cubic case for such functions. A new concept of patterns is introduced, by means of which the structure of the smallest group Gn, whose action on the set of all such cubic functions in n variables gives the affine equivalence classes for these functions under permutation of the variables, is determined. We conjecture that the equivalence classes are the same if all nonsingular affine transformations, not just permutations, are allowed. Our method gives much more information about the equivalence classes; for example, in this paper we give a complete description of the equivalence classes when n is a prime or a power of 3.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Sciences - Volume 181, Issue 22, 15 November 2011, Pages 5067–5083
نویسندگان
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