Primitive transformation shift registers over finite fields
نویسندگان
چکیده
منابع مشابه
Search of Primitive Polynomials over Finite Fields
Let us introduce some notations and definitions: if p denotes a prime integer and n a positive integer, then GF(p”) is the field containing pn elements. a primitive element of GF(p”) is a generator of the cyclic multiplicative group GVP”)*, a manic irreducible polynomial of degree n belonging to GF(p)[X] is called primitive if its roots are primitive elements of GF(p”). These polynomials are in...
متن کاملNilpotent Primitive Linear Groups over Finite Fields
In this paper we investigate the structure of groups as in the title. Our work builds on work of several other authors, namely Konyuh [5], Leedham-Green and Plesken [6], and Zalesskii [10], who have described the abstract isomorphism types of the groups. We obtain more detailed descriptions, in particular explaining how group structure depends on the existence of an abelian primitive subgroup. ...
متن کاملShift Registers Fool Finite Automata
Let x be an m-sequence, a maximal length sequence produced by a linear feedback shift register. We show that the nondeterministic automatic complexity AN (x) is close to maximal: n/2 − AN (x) = O(log 2 n), whereas Hyde has shown AN (y) ≤ n/2 + 1 for all sequences y.
متن کاملAn Equivalence-Preserving Transformation of Shift Registers
The Fibonacci-to-Galois transformation is useful for reducing the propagation delay of feedback shift register-based stream ciphers and hash functions. In this paper, we extend it to handle Galois-to-Galois case as well as feedforward connections. This makes possible transforming Trivium stream cipher and increasing its keystream data rate by 27% without any penalty in area. The presented trans...
متن کاملNormal bases and primitive elements over finite fields
Let q be a prime power, m ≥ 2 an integer and A = ( a b c d ) ∈ GL2(Fq), where A 6= ( 1 1 0 1 ) if q = 2 and m is odd. We prove an extension of the primitive normal basis theorem and its strong version. Namely, we show that, except for an explicit small list of genuine exceptions, for every q, m and A, there exists some primitive x ∈ Fqm such that both x and (ax+b)/(cx+d) produce a normal basis ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2019
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498819501718