Two classes of optimal quaternary sequences have been constructed by applying the sign alternation transform and Gray mapping to Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, a...
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Two classes of optimal quaternary sequences have been constructed by applying the sign alternation transform and Gray mapping to Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, a new method for investigating the linear complexity over finite field is proposed, and the exact values of the linear complexity over finite field F-4 and Galois ring Z(4) of the quaternary sequences are determined. The results show that their linear complexity are quite good.
A construction of a family of generalized polyphase cyciotomic sequences of length pq is presented in terms of the generalized cyciotomic classes modulo *** linear complexity and corresponding minimal polynomials are ...
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A construction of a family of generalized polyphase cyciotomic sequences of length pq is presented in terms of the generalized cyciotomic classes modulo *** linear complexity and corresponding minimal polynomials are deduced. Some upper bounds on periodic and aperiodic autocorrelation values of resulting sequences are also estimated by using certain exponential sums.
Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternar...
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Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternary sequences have large linear complexity to resist Reeds and Sloane algorithm attack effectively.
We first introduce a family of binary pq(2)-periodic sequences based on the Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q - 1. The minimal polynomials and linear complexities are...
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We first introduce a family of binary pq(2)-periodic sequences based on the Euler quotients modulo pq, where p and q are two distinct odd primes and p divides q - 1. The minimal polynomials and linear complexities are determined for the proposed sequences provided that 2(q-1) not equivalent to 1 mod q(2). The results show that the proposed sequences have high linear complexities.
In this paper, we construct two generalized cyclotomic binary sequences of period 2p(m) based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when m &g...
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In this paper, we construct two generalized cyclotomic binary sequences of period 2p(m) based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when m >= 2.
During the last two decades, many kinds of periodic sequences with good pseudorandom properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and se...
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During the last two decades, many kinds of periodic sequences with good pseudorandom properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and secure communications. Among them are a family DH-GCS(d) of generalized cyclotomic sequences on the basis of Ding and Helleseth's generalized cyclotomy, of length pq and order d=gcd(p-1,q-1) for distinct odd primes p and q. The linear complexity (or linear span), as a valuable measure of unpredictability, is precisely determined for DH-GCS(8) in this paper. Our approach is based on Edemskiy and Antonova's computation method with the help of explicit expressions of Gaussian classical cyclotomic numbers of order 8. Our result for d = 8 is compatible with Yan's low bound (pq - 1)/2 on the linear complexity for any order d, which is high enough to resist attacks of the Berlekamp-Massey algorithm. Finally, we include SageMath codes to illustrate the validity of our result by examples.
Four kinds of sequences generated by single cycle triangular function （T-function） are investigated to check the possibility for a single cycle T-function to be a cryptographic component in stream ciphers. Based on ...
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Four kinds of sequences generated by single cycle triangular function （T-function） are investigated to check the possibility for a single cycle T-function to be a cryptographic component in stream ciphers. Based on the special properties of single cycle T-function and an algorithm due to Wei, linear complexities of these four kinds of sequence are all acquired. The results show that single cycle T-function sequences have high linear complexity. Therefore, T-function satisfies the essential requirements being a basic component of stream cipher.
linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popu...
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linear complexity is a much used metric of the security of any binary sequence with application in communication systems and cryptography. In this work, we propose a method of computing the linear complexity of a popular family of cryptographic sequences, the so-called generalized sequences. Such a family is generated by means of the irregular decimation of a single Pseudo Noise sequence (PN-sequence). The computation method is based on the comparison of the PN-sequence with shifted versions of itself. The concept of linear recurrence relationship and the rows of the Sierpinski triangle play a leading part in this computation.
Sequences with high linear complexity play a fundamental part in cryptography. In this study, the authors construct general forms of Whiteman's generalised cyclotomic quaternary sequences with period 2p(m+1)q(n+1)...
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Sequences with high linear complexity play a fundamental part in cryptography. In this study, the authors construct general forms of Whiteman's generalised cyclotomic quaternary sequences with period 2p(m+1)q(n+1) of order two over o?"1/2(4) and give the linear complexity of the proposed sequences. The conclusions reveal that such sequences have good balance property and high linear complexity.
作者：
Du, XiaoniChen, ZhixiongHu, LeiPutian Univ
Dept Math Putian 351100 Fujian Peoples R China Chinese Acad Sci
State Key Lab Informat Secur Grad Sch Beijing 100049 Peoples R China NW Normal Univ
Coll Math & Informat Sci Lanzhou 730070 Gansu Peoples R China Xidian Univ
State Key Lab Integrated Serv Networks Xian 710071 Shaanxi Peoples R China
We extend the definition of binary threshold sequences from Fermat quotients to Euler quotients modulo p(r) with odd prime p and r >= 1. Under the condition of 2(p-1) not equivalent to 1 (mod p(2)), we present exac...
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We extend the definition of binary threshold sequences from Fermat quotients to Euler quotients modulo p(r) with odd prime p and r >= 1. Under the condition of 2(p-1) not equivalent to 1 (mod p(2)), we present exact values of the linear complexity by defining cyclotomic classes modulo p(n) for all 1 <= n <= r. The linear complexity is very close to the period and is of desired value for cryptographic purpose. We also present a lower bound on the linear complexity for the case of 2(p-1) equivalent to 1 (mod p(2)). (C) 2012 Elsevier B.V. All rights reserved.
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