Recently, Helleseth, Mm, and No described the linear complexity over F-p of Sidel' nikov sequences of length p(m) - 1 for p = 3, 5, and 7. In this correspondence, the result is generalized to all odd primes.
Recently, Helleseth, Mm, and No described the linear complexity over F-p of Sidel' nikov sequences of length p(m) - 1 for p = 3, 5, and 7. In this correspondence, the result is generalized to all odd primes.
complexity measures for sequences of elements of a finite field play an important role in cryptology. We focus first on the linear complexity of periodic sequences. By means of the discrete Fourier transform, we deter...
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complexity measures for sequences of elements of a finite field play an important role in cryptology. We focus first on the linear complexity of periodic sequences. By means of the discrete Fourier transform, we determine the number of periodic sequences S with given prime period length N and linear complexity L-N, 0 (S) = c as well as the expected value of the linear complexity of N-periodic sequences. Cryptographically strong sequences should not only have a large linear complexity. but also the change of a few terms should not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity L-N.k(S) of sequences S with period length N, For some k and c we determine the number of periodic sequences S with given period length N and L-N.k(S) = c. For prime N we establish a lower bound on the expected value of the k-error linear complexity. (C) 2002 Elsevier Science (USA).
A class of binary sequences with period 2p is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over F-q as well as 2-adic complexity are determined using Gauss period a...
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A class of binary sequences with period 2p is constructed using generalized cyclotomic classes, and their linear complexity, minimal polynomial over F-q as well as 2-adic complexity are determined using Gauss period and group ring theory. The results show that the linear complexity of these sequences attains the maximum when p +/- 1 (mod 8) and is equal to p+1 when p +/- 3(mod8) over extension field. Moreover, the 2-adic complexity of these sequences is maximum. According to Berlekamp-Massey(B-M) algorithm and the rational approximation algorithm (RAA), these sequences have quite good cryptographic properties in the aspect of linear complexity and 2-adic complexity.
Generalized cyclotomic sequences have good pseudo-random properties and have been widely used as keystreams in private-key cryptosystems. In this paper, the linear complexity and minimal polynomials of Ding-Helleseth ...
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Generalized cyclotomic sequences have good pseudo-random properties and have been widely used as keystreams in private-key cryptosystems. In this paper, the linear complexity and minimal polynomials of Ding-Helleseth sequences of order 2 have been determined over a finite field GF(l). Results show that these sequences have high linear complexity.
We derive the linear complexity of quaternary sequences of length pq with low autocorrelation over the finite field of four elements and over the finite ring of order 4. Also we examine the linear complexity of the ot...
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We derive the linear complexity of quaternary sequences of length pq with low autocorrelation over the finite field of four elements and over the finite ring of order 4. Also we examine the linear complexity of the other sequences of length pg. (C) 2013 Elsevier B.V. All rights reserved.
Let r be an odd prime, such that r >= 5 and r not equal p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field F(r)m. Let G(x) be the generating polynomial of the considered...
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Let r be an odd prime, such that r >= 5 and r not equal p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field F(r)m. Let G(x) be the generating polynomial of the considered quaternary sequences over F-q[x] with q = r(m). By explicitly computing the number of zeros of the generating polynomial G(x) over F(r)m, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to 1/2(3p - 1) which is more than p, the half of the period 2p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.
In this correspondence, the linear complexity over F-p of Lempel-Cohn-Eastman (LCE) sequences of period p(m) - 1 for an odd prime p is determined. For p = 3, 5, and 7, the exact closed-form expressions for the linear ...
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In this correspondence, the linear complexity over F-p of Lempel-Cohn-Eastman (LCE) sequences of period p(m) - 1 for an odd prime p is determined. For p = 3, 5, and 7, the exact closed-form expressions for the linear complexity over F-p of LCE sequences of period p(m) - 1 are derived. Further, the trace representations for LCE sequences of period p(m) - 1 for p = 3 and 5 are found by computing the values of all Fourier coefficients in F-p for the sequences.
Pseudo-random sequences with high linear complexity play important roles in many domains. We give linear complexity of generalized cyclotomic quaternary sequences with period pq over Z(4) via the weights of its Fourie...
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Pseudo-random sequences with high linear complexity play important roles in many domains. We give linear complexity of generalized cyclotomic quaternary sequences with period pq over Z(4) via the weights of its Fourier spectral sequence. The results show that such sequences have high linear complexity.
Based on the generalized cyclotomy of order two with respect ton = p(1)(e1+1)p(2)(2+1) ... p(t)(et+1), where p(1), p(2), ..., p(t) are pairwise distinct odd primes and e(1), e(2), ..., e(t) are non-negative integers s...
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Based on the generalized cyclotomy of order two with respect ton = p(1)(e1+1)p(2)(2+1) ... p(t)(et+1), where p(1), p(2), ..., p(t) are pairwise distinct odd primes and e(1), e(2), ..., e(t) are non-negative integers satisfying gcd (p(i)(ei) (p(i) - 1), p(j)(ej) (p(j) - 1)) = 2 for all i not equal j, this paper constructs a new family of generalized cyclotomic sequences of order two with length n and investigates their linear complexity. In the view of cascade theory, this paper obtains the linear complexity of a representative sequence.
A unified derivation of the hounds of the linear complexity is given for a sequence obtained from a periodic sequence over GF (q) bl either substituting, inserting, or deleting Ic symbols within one period. The lower ...
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A unified derivation of the hounds of the linear complexity is given for a sequence obtained from a periodic sequence over GF (q) bl either substituting, inserting, or deleting Ic symbols within one period. The lower bounds are useful in case of n < N/k, where N and n are the period and the linear complexity of the sequence. respectively. It is shown that all three different cases can be treated very simply in a unified manner. The bounds are useful enough to show how wide the distribution of the linear complexity becomes as Ic increases, although they are not always tight because their derivations do not use the information about the change values.
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