Linear transformation shift registers

Dewar, Michael; Panario, Daniel

doi:10.1109/tit.2003.814487

Cited by 12 publications

(12 citation statements)

References 2 publications

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“…So the study of irreducible TSRs is helpful to find primitive TSRs. Dewar and Panario studied irreducible TSRs for even characteristic fields in [3] and odd characteristic fields in [4] respectively. Hasan et al…”

Section: Conjecture 1 For Positive Integers M and N The Number Of Prmentioning

confidence: 99%

On the number of irreducible linear transformation shift registers

Jiang

Yang

2016

Des. Codes Cryptogr.

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We deal with the problem of counting the number of irreducible linear transformation shift registers (TSRs) over a finite field. In a recent paper, Ram reduced this problem to calculate the cardinality of some set of irreducible polynomials and got explicit formulae for the number of irreducible TSRs of order two. We find a bijection between Ram's set to another set of irreducible polynomials which is easier to count, and then give a conjecture about the number of irreducible TSRs of any order. We also get explicit formulae for the number of irreducible TSRs of order three.

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Section: Conjecture 1 For Positive Integers M and N The Number Of Prmentioning

confidence: 99%

On the number of irreducible linear transformation shift registers

Jiang

Yang

2016

Des. Codes Cryptogr.

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“…LFSR Figure 1 and Figure 2 show a typical internal and external XOR LFSR, respectively [6]. n denotes the length of the LFSR.…”

Section: IImentioning

confidence: 99%

A Reversible LFSR Pseudo-Random Sequences Generator

Hu¹

2015

Proceedings of the International Conference on Computer Information Systems and Industrial Applications

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“…We refer to the papers of Dewar and Panario [5,6] for subsequent developments on TSRs. It turns out that the TSRs have very good cryptographic properties when the corresponding characteristic polynomial is primitive.…”

Section: Introductionmentioning

confidence: 99%

Enumeration of linear transformation shift registers

Ram

2014

Des. Codes Cryptogr.

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Abstract. We consider the problem of counting the number of linear transformation shift registers (TSRs) of a given order over a finite field. We derive explicit formulae for the number of irreducible TSRs of order two. An interesting connection between TSRs and self-reciprocal polynomials is outlined. We use this connection and our results on TSRs to deduce a theorem of Carlitz on the number of self-reciprocal irreducible monic polynomials of a given degree over a finite field. IntroductionA linear feedback shift register (LFSR) is a mechanism for generating a sequence in a finite field. LFSRs have a plethora of practical applications and are frequently used in generating pseudorandom numbers, fast digital counters and stream ciphers. A generalization of LFSR called word-oriented feedback shift register (σ-LFSR) was considered by Zeng, Han and He [20]. For LFSRs as well as σ-LFSRs, those that are primitive (i.e., for which the corresponding infinite sequence is of maximal possible period) are of particular interest. The following conjecture was proposed in the binary case in [20] and was extended to the q-ary case in [8]:Conjecture 1.1. For positive integers m and n, the number of primitive σ-LFSRs of order n over F q m is given byThe notion of σ-LFSR is essentially equivalent to that of a splitting subspace previously defined by Niederreiter [16]: Given positive integers m, n and α ∈ F q mn , an m-dimensional F q -linear subspace of F q mn is said to be α-splitting if

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Linear transformation shift registers

Cited by 12 publications

References 2 publications

On the number of irreducible linear transformation shift registers

On the number of irreducible linear transformation shift registers

A Reversible LFSR Pseudo-Random Sequences Generator

Enumeration of linear transformation shift registers

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