215 research outputs found
Corrigendum to New Generalized Cyclotomic Binary Sequences of Period
New generalized cyclotomic binary sequences of period are proposed in
this paper, where is an odd prime. The sequences are almost balanced and
their linear complexity is determined. The result shows that the proposed
sequences have very large linear complexity if is a non-Wieferich prime.Comment: In the appended corrigendum, we pointed out that the proof of Lemma 6
in the paper only holds for and gave a proof for any when
is a non-Wieferich prim
Some New Balanced and Almost Balanced Quaternary Sequences with Low Autocorrelation
Quaternary sequences of both even and odd period having low autocorrelation
are studied. We construct new families of balanced quaternary sequences of odd
period and low autocorrelation using cyclotomic classes of order eight, as well
as investigate the linear complexity of some known quaternary sequences of odd
period. We discuss a construction given by Chung et al. in "New Quaternary
Sequences with Even Period and Three-Valued Autocorrelation" [IEICE Trans.
Fundamentals Vol. E93-A, No. 1 (2010)] first by pointing out a slight
modification (thereby obtaining new families of balanced and almost balanced
quaternary sequences of even period and low autocorrelation), then by showing
that, in certain cases, this slight modification greatly simplifies the
construction given by Shen et al. in "New Families of Balanced Quaternary
Sequences of Even Period with Three-level Optimal Autocorrelation" [IEEE Comm.
Letters DOI10.1109/LCOMM.2017.26611750 (2017)]. We investigate the linear
complexity of these sequences as well
A lower bound on the 2-adic complexity of modified Jacobi sequence
Let be distinct primes satisfying and let
, , be Whiteman's generalized cyclotomic classes with
. In this paper, we give the values of Gauss
periods based on the generalized cyclotomic sets
and
. As an application, we
determine a lower bound on the 2-adic complexity of modified Jacobi sequence.
Our result shows that the 2-adic complexity of modified Jacobi sequence is at
least with period . This indicates that the 2-adic complexity
of modified Jacobi sequence is large enough to resist the attack of the
rational approximation algorithm (RAA) for feedback with carry shift registers
(FCSRs).Comment: 13 pages. arXiv admin note: text overlap with arXiv:1702.00822,
arXiv:1701.0376
Linear complexity and trace representation of quaternary sequences over based on generalized cyclotomic classes modulo
We define a family of quaternary sequences over the residue class ring modulo
of length , a product of two distinct odd primes, using the generalized
cyclotomic classes modulo and calculate the discrete Fourier transform
(DFT) of the sequences. The DFT helps us to determine the exact values of
linear complexity and the trace representation of the sequences.Comment: 16 page
Linear complexity of generalized cyclotomic sequences of period
In this paper, we construct two generalized cyclotomic binary sequences of
period based on the generalized cyclotomy and compute their linear
complexity, showing that they are of high linear complexity when
A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period
Let be an odd prime, a positive integer and a primitive root of
. Suppose
, , is
the generalized cyclotomic classes with . In this
paper, we prove that Gauss periods based on and are both equal to 0
for . As an application, we determine a lower bound on the 2-adic
complexity of a class of Ding-Helleseth generalized cyclotomic sequences of
period . The result shows that the 2-adic complexity is at least
, which is larger than , where is the
period of the sequence.Comment: 1
Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences
Pseudorandom number generators are required to generate pseudorandom numbers
which have good statistical properties as well as unpredictability in
cryptography. An m-sequence is a linear feedback shift register sequence with
maximal period over a finite field. M-sequences have good statistical
properties, however we must nonlinearize m-sequences for cryptographic
purposes. A geometric sequence is a sequence given by applying a nonlinear
feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a
geometric sequence whose nonlinear feedforward function is given by the
Legendre symbol, and showed the period, periodic autocorrelation and linear
complexity of the sequence. Furthermore, Nogami et al. proposed a
generalization of the sequence, and showed the period and periodic
autocorrelation. In this paper, we first investigate linear complexity of the
geometric sequences. In the case that the Chan--Games formula which describes
linear complexity of geometric sequences does not hold, we show the new formula
by considering the sequence of complement numbers, Hasse derivative and
cyclotomic classes. Under some conditions, we can ensure that the geometric
sequences have a large linear complexity from the results on linear complexity
of Sidel'nikov sequences. The geometric sequences have a long period and large
linear complexity under some conditions, however they do not have the balance
property. In order to construct sequences that have the balance property, we
propose interleaved sequences of the geometric sequence and its complement.
Furthermore, we show the periodic autocorrelation and linear complexity of the
proposed sequences. The proposed sequences have the balance property, and have
a large linear complexity if the geometric sequences have a large one.Comment: 20 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1709.0516
On the Use of Cellular Automata in Symmetric Cryptography
In this work, pseudorandom sequence generators based on finite fields have
been analyzed from the point of view of their cryptographic application. In
fact, a class of nonlinear sequence generators has been modelled in terms of
linear cellular automata. The algorithm that converts the given generator into
a linear model based on automata is very simple and is based on the
concatenation of a basic structure. Once the generator has been linearized, a
cryptanalytic attack that exploits the weaknesses of such a model has been
developed. Linear cellular structures easily model sequence generators with
application in stream cipher cryptography.Comment: 25 pages, 0 figure
Cellular Automata in Stream Ciphers
A wide family of nonlinear sequence generators, the so-called
clock-controlled shrinking generators, has been analyzed and identified with a
subset of linear cellular automata. The algorithm that converts the given
generator into a linear model based on automata is very simple and can be
applied in a range of practical interest. Due to the linearity of these
automata as well as the characteristics of this class of generators, a
cryptanalytic approach can be proposed. Linear cellular structures easily model
keystream generators with application in stream cipher cryptography.Comment: 26 pages, 1 figur
Autocorrelation and Linear Complexity of Quaternary Sequences of Period 2p Based on Cyclotomic Classes of Order Four
We examine the linear complexity and the autocorrelation properties of new
quaternary cyclotomic sequences of period 2p. The sequences are constructed via
the cyclotomic classes of order four
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