Digital chaotic sequence generator based on coupled chaotic systems

Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2^128＊2^128 times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array （FPGA） implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4 Mbps indicating that the designed generator can he applied to the real-time video image encryption.

Linear complexity of Ding generalized cyclotomic sequences

Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

FINITE EXTENSIONS OF GENERALIZED BESSEL SEQUENCES TO GENERALIZED FRAMES

The objective of this paper is to investigate the question of modifying a givengeneralized Bessel sequence to yield a generalized frame or a tight generalized frame by finiteextension. Some necessary and sufficient conditions for the finite extensions of generalizedBessel sequences to generalized frames or tight generalized frames are provided, and everyresult is illustrated by the corresponding example.

Linear Complexity of New Generalized Cyclotomic Sequences of Length 2pq

The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity.

Weak generalized self-shrinking generators

The security of certain classes of the generalized self-shrinking sequence （GSS） generators is analyzed. Firstly, it is shown that the security of these GSS generators is equivalent to the security of the GSS generators of the class-1, after which two effective key recovery attacks on the GSS generators of the class-1 are developed to evaluate their security.

SELECTION OF THE LINEAR COMBINING VECTOR G OF THE GENERALIZED SELF-SHRINKING GENERATORS

Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking （GSS） sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomial ofL GSS sequences and the comparison of their degrees, an algorithm for selecting the linear combining vector G is presented, which is simple to understand, to implement and to prove. By using this method, much more than 2^L-l linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

THE HAUSDORFF DIMENSION OF THE SPECTRUM OF A CLASS OF GENERALIZED THUE-MORSE HAMILTONIANS

Letτbe a generalized Thue-Morse substitution on a two-letter alphabet{a,b}:τ(a)=ambm,τ(b)=bmam for the integer m≥2.Letξbe a sequence in{a,b}Z that is generated byτ.We study the one-dimensional Schr?dinger operator Hm,λon l2(Z)with a potential given by v(n)=λVξ(n),whereλ>0 is the coupling and Vξ(n)=1(Vξ(n)=-1)ifξ(n)=a(ξ(n)=b).LetΛ2=2,and for m>2,letΛm=m if m≡0 mod 4;letΛm=m-3 if m≡1 mod 4;letΛm=m-2if m≡2 mod 4;letΛm=m-1 if m≡3 mod 4.We show that the Hausdorff dimension of the spectrumσ(Hm,λ)satisfies that dimHσ(Hm,λ)>logΛm/(log 64m+4).It is interesting to see that dimHσσ(Hm,λ)tends to 1 as m tends to infinity.

Some Notes on Generalized Cyclotomic Sequences of Length pq

We review the constructions of two main kinds of generalized cyclotomic binary sequences with length pq （the product with two distinct primes）. One is the White-generalized cyclotomic sequences, the other is the Ding-Helleseth（DH, for short）-generalized cyclotomic sequences. We present some new pseudo-random properties of DH-generalized cyclotomic sequences using the theory of character sums instead of the theory of cyclotomy, which is a conventional method for investigating generalized cyclotomic sequences.

Examples of entropy generating sequence

We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.

A STRONG LIMIT THEOREM FOR GENERALIZED CANTOR-LIKE RANDOM SEQUENCES

Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.

Design and implementation of the NaI(Tl)/CsI(Na) detectors output signal generator

We designed and implemented a signal generator that can simulate the output of the NaI（Tl）/CsI（Na）detectors＇pre-amplifier onboard the Hard X-ray Modulation Telescope（HXMT）.Using the development of the FPGA（Field Programmable Gate Array）with VHDL language and adding a random constituent,we have finally produced the double exponential random pulse signal generator.The statistical distribution of the signal amplitude is programmable.The occurrence time intervals of the adjacent signals contain negative exponential distribution statistically.

Construction of generalized binary Bent sequences

Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-essary condition is derived to determine whether the sum of the combinations of Gold functions,tr1^(n)(x^(2+1)),1≤i≤n−1,over finite fields 2n F(n be even)in addition to another term tr1^(n/2)(x^(2n/2+1))is a Bent function.Similar to the result presented by Khoo et al.,the condition can be verified by polynominal greatest common divisor(GCD)computation.A similar result also holds in the case n pF(n be even,p be odd prime).Using the constructed Bent functions and Niho type Bent functions given by Dobbertin et al.,many new generalized binary Bent sequences are obtained.