9,949 research outputs found
Linear Complexity and Autocorrelation of two Classes of New Interleaved Sequences of Period
The autocorrelation and the linear complexity of a key stream sequence in a
stream cipher are important cryptographic properties. Many sequences with these
good properties have interleaved structure, three classes of binary sequences
of period with optimal autocorrelation values have been constructed by
Tang and Gong based on interleaving certain kinds of sequences of period .
In this paper, we use the interleaving technique to construct a binary sequence
with the optimal autocorrelation of period , then we calculate its
autocorrelation values and its distribution, and give a lower bound of linear
complexity. Results show that these sequences have low autocorrelation and the
linear complexity satisfies the requirements of cryptography
New Binary Sequences with Optimal Autocorrelation Magnitude
New binary sequences of period � � for even � � are found. These sequences can be described by a � interleaved structure. The new sequences are almost balanced and have four-valued autocorrelation, i.e., � � � ��, which is optimal with respect to autocorrelation magnitude. Complete autocorrelation distribution and exact linear complexity of the sequences are mathematically derived. From the simple implementation with a small number of shift registers and a connector, the sequences have a benefit of obtaining large linear complexity
A New Method to Compute the 2-adic Complexity of Binary Sequences
In this paper, a new method is presented to compute the 2-adic complexity of
pseudo-random sequences. With this method, the 2-adic complexities of all the
known sequences with ideal 2-level autocorrelation are uniformly determined.
Results show that their 2-adic complexities equal their periods. In other
words, their 2-adic complexities attain the maximum. Moreover, 2-adic
complexities of two classes of optimal autocorrelation sequences with period
, namely Legendre sequences and Ding-Helleseth-Lam sequences,
are investigated. Besides, this method also can be used to compute the linear
complexity of binary sequences regarded as sequences over other finite fields.Comment: 16 page
The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude
Recently, a class of binary sequences with optimal autocorrelation magnitude
has been presented by Su et al. based on interleaving technique and
Ding-Helleseth-Lam sequences (Des. Codes Cryptogr.,
https://doi.org/10.1007/s10623-017-0398-5). And its linear complexity has been
proved to be large enough to resist the B-M Algorighm (BMA) by Fan (Des. Codes
Cryptogr., https://doi.org/10.1007/s10623-018-0456-7). In this paper, we study
the 2-adic complexity of this class of binary sequences. Our result shows that
the 2-adic complexity of this class of sequence is no less than one half of its
period, i.e., its 2-adic complexity is large enough to resist the Rational
Aproximation Algorithm (RAA).Comment: 9page
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
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
Secure CDMA Sequences
Single sequences like Legendre have high linear complexity. Known CDMA
families of sequences all have low complexities. We present a new method of
constructing CDMA sequence sets with the complexity of the Legendre from new
frequency hop patterns, and compare them with known sequences. These are the
first families whose normalized linear complexities do not asymptote to 0,
verified for lengths up to 6x108. The new constructions in array format are
also useful in watermarking images. We present a conjecture regarding the
recursion polynomials. We also have a method to reverse the process, and from
small Kasami/No-Kumar sequences we obtain a new family of 2n doubly periodic
(2n+1)x(2n-1) frequency hop patterns with correlation 2.Comment: 10 pages, 8 figure
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
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
On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences
We determine the 2-adic complexity of the Ding-Helleseth-Martinsen (DHM)
binary sequences by using cyclotomic numbers of order four, "Gauss periods" and
"quadratic Gauss sum" on finite field and valued in
where is a prime number and is
the period of the DHM sequences.Comment: 16 page
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