For a given hyperelliptic curve C over a finite field with Jacobian J(C), we consider the hyperelliptic analogue of the congruential generator defined by W-n = Wn- 1 + D for n >= 1 and D, W-0 is an element of J(C)....
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For a given hyperelliptic curve C over a finite field with Jacobian J(C), we consider the hyperelliptic analogue of the congruential generator defined by W-n = Wn- 1 + D for n >= 1 and D, W-0 is an element of J(C). We show that curves of genus 2 produce sequences with large linear complexity.
Let be distinct odd primes and let be positive integers. Based on cyclotomic classes proposed by Ding and Helleseth (Finite Fields Appl 4:140-166, 1998), a binary cyclotomic sequence of period is defined and denoted b...
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Let be distinct odd primes and let be positive integers. Based on cyclotomic classes proposed by Ding and Helleseth (Finite Fields Appl 4:140-166, 1998), a binary cyclotomic sequence of period is defined and denoted by . The linear complexity of is determined and is proved to be greater than or equal to . The autocorrelation function of is explicitly computed. Let . We also explicitly compute the crosscorrelation function of and the Legendre sequence with respect to . It is shown that and have two-level or three-level crosscorrelation, and all their two-level crosscorrelation functions are determined.
A unified construction for yielding optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences was proposed by Zeng et al. In this paper, the linear complexity over finite field F-2;F-4 and...
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A unified construction for yielding optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences was proposed by Zeng et al. In this paper, the linear complexity over finite field F-2;F-4 and Galois ring Z(4) of the quaternary sequences are discussed, respectively. The exact values of linear complexity of sequences obtained by Legendre sequence pair, twin-prime sequence pair and Hall's sextic sequence pair are derived.
作者：
Green, DHUniv Manchester
Commun Engn Res Gro Sch Elect & Elect Engn Manchester Lancs England
The linear complexity of m-phase power residue sequences is investigated for the case when m is composite. For each factor of m, the linear complexity and the characteristic polynomial of the shortest linear feedback ...
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The linear complexity of m-phase power residue sequences is investigated for the case when m is composite. For each factor of m, the linear complexity and the characteristic polynomial of the shortest linear feedback shift register that generates this 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 on the categories of the length of the sequence computed modulo of each factor of m, rather than on the category of the length modulo-m itself. For a given length, the highest values of linear complexity results from constructing the sequences using those values of the primitive element which lead to non-zero categories for each factor of m.
Periodic sequences over finite fields have been used as key streams in private-key cryptosystems since the 1950s. Such periodic sequences should have a series of cryptographic properties in order to resist many attack...
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Periodic sequences over finite fields have been used as key streams in private-key cryptosystems since the 1950s. Such periodic sequences should have a series of cryptographic properties in order to resist many attack methods. The binary generalized cyclotomic periodic sequences, constructed by the cyclotomic classes over finite fields, have good pseudo-random properties and correlation properties. In this paper, the linear complexity and minimal polynomials of some generalized cyclotomic sequences over GF(q) have been determined where g = p(m) and p is an odd prime. Results show that these sequences have high linear complexity over GF(q) for a large part of odd prime power q, which means they can resist the linear attack method. (C) 2015 Elsevier Inc. All rights reserved.
The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2p(m+1)q(n+1). Furthermore, we e...
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The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2p(m+1)q(n+1). Furthermore, we establish the formula of the linear complexity of proposed sequences. The results reveal that such sequences with period 2p(m+1)q(n+1) have a good balance property and high linear complexity.
作者：
Green, DHChoi, JUMIST
Dept Elect Engn & Elect Digital Commun Res Grp Manchester M60 1QD Lancs England
Legendre sequences are a well-known class of binary sequences, which possess good periodic and aperiodic autocorrelation functions. They are also known to exhibit high linear complexity, which makes them significant f...
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Legendre sequences are a well-known class of binary sequences, which possess good periodic and aperiodic autocorrelation functions. They are also known to exhibit high linear complexity, which makes them significant for cryptographic applications. Jacobi and modified Jacobi sequences are constructed by combining two appropriate Legendre sequences and they also have good correlation properties. This class also contains the Twin Prime sequences as a special case. The authors report the results of subjecting a wide range of modified Jacobi sequences to the Berlekamp-Massey algorithm in order to establish their linear complexities. The results obtained confirm that some members of this class also have high linear complexity. The findings display sufficient structure to enable the general form of the linear complexity and the corresponding generator polynomials to be conjectured.
Pseudorandom sequences with large linear complexity have been widely applied in electronic countermeasures, mobile communication and cryptography. linear complexity is considered as a primary security criterion to mea...
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Pseudorandom sequences with large linear complexity have been widely applied in electronic countermeasures, mobile communication and cryptography. linear complexity is considered as a primary security criterion to measure the unpredictability of pseudorandom sequences. This paper presents the linear complexity and minimal polynomial of a new family of binary sequences derived from polynomial quotients modulo an odd prime p in general case. The results indicate that the sequences have high linear complexity, which means they can resist the linear attack against pseudo-noise or stream ciphers. Moreover, we generalize the result to the polynomial quotients modulo a power of p in general case. Finally, we design a Gpqs stream cipher generator based on the generalized binary pseudorandom sequences to implement the sequences in hardware.
A family of quaternary sequences over Z(4) is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defi...
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A family of quaternary sequences over Z(4) is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the sequences, which is in fact connected with the discrete Fourier transform of the sequences. The results show that the sequences possess large linear complexity and are "good" sequences from the viewpoint of cryptography.
In this correspondence, the linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are determined. Our results show that these sequences also have high linear complexity.
In this correspondence, the linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are determined. Our results show that these sequences also have high linear complexity.
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