In this paper, we present a generic construction of r-ary sequences with period pq(2) based on the Euler quotient modulo pq, where p and q are odd primes satisfying that p divides q - 1 and r is any prime less than q....
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In this paper, we present a generic construction of r-ary sequences with period pq(2) based on the Euler quotient modulo pq, where p and q are odd primes satisfying that p divides q - 1 and r is any prime less than q. The minimal polynomial and the linear complexity of the proposed sequences are determined in most cases under the assumption that r(q-1)not equivalent to 1 (mod q(2)). The result shows that each of the sequences has large linear complexity.
For an odd prime p and positive integers r,d such that 0r,a generic construction of dary sequence based on Euler quotients is presented in this *** with the known construction,in which the support set of the sequence ...
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For an odd prime p and positive integers r,d such that 0r,a generic construction of dary sequence based on Euler quotients is presented in this *** with the known construction,in which the support set of the sequence is fixed and d is usually required to be a prime,the support set of the proposed sequence is flexible and d could be any positive integer less then prin our ***,the linear complexity of the proposed sequence over prime field GF（q）with the assumption of qp-1■ mod p2is *** algorithm of computing the linear complexity of the sequence is also *** results indicate that,with some constrains on the support set,the new sequences possess large linear complexities.
Binary sequences with large linear complexity have been found many applications in communication *** determine the linear complexity of a family of p;-periodic binary sequences derived from polynomial quotients modulo...
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Binary sequences with large linear complexity have been found many applications in communication *** determine the linear complexity of a family of p;-periodic binary sequences derived from polynomial quotients modulo an odd prime *** show that these sequences have high linear complexity,which means they can resist the linear attack method.
In this correspondence, we obtain the linear complexity and minimal polynomials of binary Whiteman generalized cyclotomic sequences of order 2(k), where k > 1. Our result shows that all of these sequences possess l...
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In this correspondence, we obtain the linear complexity and minimal polynomials of binary Whiteman generalized cyclotomic sequences of order 2(k), where k > 1. Our result shows that all of these sequences possess large linear complexity. (C) 2008 Elsevier Inc. All rights reserved.
We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq and calculate the discrete Fourier...
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We define a family of quaternary sequences over the residue class ring modulo 4 of length pq, a product of two distinct odd primes, using the generalized cyclotomic classes modulo pq 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.
Periodic sequences, used as keys in cryptosystems, plays an important role in cryptography. Such periodic sequences should possess high linear complexity to resist B-M algorithm. Sequences constructed by cyclotomic co...
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Periodic sequences, used as keys in cryptosystems, plays an important role in cryptography. Such periodic sequences should possess high linear complexity to resist B-M algorithm. Sequences constructed by cyclotomic cosets have been widely studied in the past few years. In this paper, the linear complexity of n-periodic cyclotomic sequences of order 2 and 4 over F-p has been calculated, where n and p are two distinct odd primes. The conclusions reveal that the presented sequences have high linear complexity in many cases, which indicates that the sequences can resist the linear attack.
In this paper, binary sequences based on the generalized cyclotomy are studied. We define two generalized cyclotomic sequences of length 2p (m) , one sequence (called the classical one) is defined using the classical ...
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In this paper, binary sequences based on the generalized cyclotomy are studied. We define two generalized cyclotomic sequences of length 2p (m) , one sequence (called the classical one) is defined using the classical method, the other one (called the modified one) is defined in a slightly modified manner. The linear complexity of the two proposed sequences of length 2p (m) is determined with two different approaches. The results show that the two proposed sequences have high linear complexity.
Let p = ef + 1 be an odd prime, where e = 0 (mod 4). A family of balanced quaternary sequences is defined by using the classical cyclotomic classes of order e with respect to p in this paper. We derive the formulas fo...
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Let p = ef + 1 be an odd prime, where e = 0 (mod 4). A family of balanced quaternary sequences is defined by using the classical cyclotomic classes of order e with respect to p in this paper. We derive the formulas for their linear complexity and trace representation over Z(4) by computing the discrete Fourier transform of these sequences. As an application, the linear complexity and trace representation over Z(4) are given for two types of specific sequences with low autocorrelation derived from the cyclotomic classes of order 4 and 8, respectively. Furthermore, we also determine the exact linear complexity and minimal polynomial for each sequence of the second type over the finite field F-4.
We obtain new lower bounds on the linear complexity of several consecutive values of the discrete logarithm modulo a prime p. These bounds generalize and improve several previous results.
We obtain new lower bounds on the linear complexity of several consecutive values of the discrete logarithm modulo a prime p. These bounds generalize and improve several previous results.
作者：
Green, DHUniv Manchester
Sch Elect & Elect Engn Commun Engn Res Grp Manchester Lancs England
The linear complexity of m-phase related prime sequences is investigated for the case when m is composite. For each relatively prime factor p(i)(k) of m, the linear complexity and the characteristic polynomial of the ...
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The linear complexity of m-phase related prime sequences is investigated for the case when m is composite. For each relatively prime factor p(i)(k) of m, the linear complexity and the characteristic polynomial of the shortest linear feedback shift register that generates the P(i)(k-)phase version of the sequence can be deduced and these results can then be combined using the Chinese remainder theorem to derive the m-phase values. These values are shown to depend r on the categories of the sequence length computed modulo each factor of m, rather than on the category of the length modulo m itself, and that these values depend on the primitive roots employed. For a given length, the highest values of linear complexity result from constructing the sequences using those values of primitive elements that lead to non-zero categories for each factor of m.
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