Efficient generation of quadratic cyclotomic classes for shortest quadratic decompositions of polynomials
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Nikova et al. investigated the decomposition problem of power permutations over finite fields F-2n in (Cryptogr. Commun. 11:379-384, 2019). In particular, they provided an algorithm to give a decomposition of a power permutation into quadratic power permutations. Their algorithm has a precomputation step that finds all cyclotomic classes of F-2n and then use the quadratic ones. In this paper, we provide an efficient and systematic method to generate the representatives of quadratic cyclotomic classes and hence reduce the complexity of the precomputation step drastically. We then apply our method to extend their results on shortest quadratic decompositions of x(2n-2) from 3 <= n <= 16 to 3 <= n <= 24 and correct a typo (for n = 11). We also give two explicit formulas for the time complexity of the adaptive search to understand its efficiency with respect to the parameters.
Açıklama
Anahtar Kelimeler
Boolean functions, S-boxes, Power permutations
Kaynak
Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences
WoS Q Değeri
Q2
Scopus Q Değeri
Q1
Cilt
13
Sayı
5
