In this paper, we generalize the results about the k-error linear complexity of binary sequences derived from Euler quotients modulo pr(-1) on the q-ary sequences. We also continue the study of q-ary sequences derived...
详细信息
In this paper, we generalize the results about the k-error linear complexity of binary sequences derived from Euler quotients modulo pr(-1) on the q-ary sequences. We also continue the study of q-ary sequences derived from Euler quotients modulo 2p started by R. Mohammed et al. (LNCS, 11634, 2019) and investigate the k-error linear complexity of sequences derived from Euler quotients with a period 2p(r). In particular, we generalize the results of Wu et al. (IEEE Access, 8, 2020) about k-error the binary sequences derived by Euler quotients modulo 2p on the same sequences with a period 2p(r).
Pseudorandom sequences play an important role in communication and stream ciphers. In recent years, the method of generating pseudorandom sequences based on arithmetical functions has attracted increasing attention. k...
详细信息
Pseudorandom sequences play an important role in communication and stream ciphers. In recent years, the method of generating pseudorandom sequences based on arithmetical functions has attracted increasing attention. k-error linear complexity is an important index to evaluate the stability of a sequence. Recently, J. Zhang and C. Zhao introduced binary sequences derived from Euler quotients modulo 2p (where p > 3 is an odd prime). In this paper, the k-error linear complexity of such sequences over F-2 was considered with the condition that 2 is a primitive root modulo p(2). Certain decimal sequences were used to determine the values of k-error linear complexity for all k > 0. The results showed that such sequences have good stability in terms of cryptography.
We study the k-error linear complexity of subsequences of the d-ary Sidel'nikov sequences over the prime field F-d. A general lower bound for the k-error linear complexity is given. For several special periods, we...
详细信息
We study the k-error linear complexity of subsequences of the d-ary Sidel'nikov sequences over the prime field F-d. A general lower bound for the k-error linear complexity is given. For several special periods, we show that these sequences have large k-error linear complexity.
The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linearcomplexity. After computing the k-error linear complexity of a sequence, those bits that cause the linear ...
详细信息
The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linearcomplexity. After computing the k-error linear complexity of a sequence, those bits that cause the linearcomplexity reduced also need to be determined. For binary sequences with period 2p(n), where p is an odd prime and 2 is a primitive root modulo p(2), we present an algorithm which computes the minimum number k such that the k-error linear complexity is not greater than a given constant c. The corresponding error sequence is also obtained.
Due to good pseudorandom properties, generalized cyclotomic sequences have been widely used in simulation, radar systems, cryptography, and so on. In this paper, we consider the k-error linear complexity of Zeng-Cai-T...
详细信息
ISBN:
(纸本)9789811330957;9789811330940
Due to good pseudorandom properties, generalized cyclotomic sequences have been widely used in simulation, radar systems, cryptography, and so on. In this paper, we consider the k-error linear complexity of Zeng-Cai-Tang-Yang generalized cyclotomic binary sequences of period p(2), proposed in the recent paper "New generalized cyclotomic binary sequences of period p(2)", by Z. Xiao et al., who calculated the linearcomplexity of the sequence (Designs, Codes and Cryptography, 2018, 86(7): 1483-1497). More exactly, we determine the values of k-error linear complexity over F-2 for f = 2 and almost k > 0 in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.
The linearcomplexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2(n), a new to...
详细信息
The linearcomplexity and k-error linear complexity of a sequence have been used as important measures for keystream strength. In order to study k-error linear complexity of binary sequences with period 2(n), a new tool called cube theory is developed. In this paper, we first give a general decomposition approach to decompose a binary sequence with period 2(n) into some disjoint cubes. Second, a counting formula for m-cubes with the same linearcomplexity is derived, which is equivalent to the counting formula for k-error vectors. The counting formula of 2(n)-periodic binary sequences which can be decomposed into more than one cube is also investigated, which extends an important result by Etzion et al.. Finally, we study 2(n)-periodic binary sequences with the given k-error linear complexity profile. Consequently, the complete counting formula of 2(n)-periodic binary sequences with given k-error linear complexity profile of descent points 2, 4 and 6 is derived. The periodic sequences having the prescribed k-error linear complexity profile with descent points 1, 3, 5 and 7 are also briefly discussed.
The linearcomplexity and k-error linear complexity of sequences are important measures of the strength of key-streams generated by stream ciphers. Fu et al. studied the distribution of 2(n)-periodic binary sequences ...
详细信息
ISBN:
(数字)9783319491516
ISBN:
(纸本)9783319491516;9783319491509
The linearcomplexity and k-error linear complexity of sequences are important measures of the strength of key-streams generated by stream ciphers. Fu et al. studied the distribution of 2(n)-periodic binary sequences with 1-errorlinearcomplexity in their SETA 2006 paper. Recently, people have strenuously promoted the solving of this problem from k = 2 to k = 4 step by step. Unfortunately, it still remains difficult to obtain the solutions for larger k. In this paper, we propose a new sieve method to solve this problem. We first define an equivalence relationship on error sequences and build a relation between the number of sequences with given k-error linear complexity and the number of pair-wise non-equivalent error sequences. We introduce the concept of cube fragment and build specific equivalence relation based on the concept of the cube classes to figure out the number of pair-wise non-equivalent error sequences. By establishing counting functions for several base cases and building recurrence relations for different cases of k and L, it is easy to manually get the complete counting function when k is not too large. And an efficient algorithm can be derived from this method to solve the problem using a computer when k is large.
The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from...
详细信息
The k-error linear complexity is an important cryptographic measure of pseudorandom sequences in stream ciphers. In this paper, we investigate the k-error linear complexity of p2-periodic binary sequences defined from the polynomial quotients modulo p, which are the generalizations of the well-studied Fermat ***, first we determine exact values of the k-error linear complexity over the finite field F2 for these binary sequences under the assumption of 2 being a primitive root modulo p2, and then we determine their k-error linear complexity over the finite field Fp. Theoretical results obtained indicate that such sequences possess‘good’ errorlinearcomplexity.
In this paper, a constructive approach for determining CELCS(critical errorlinearcomplexity spectrum) for the kerrorlinearcomplexity distribution of 2~n-periodic binary sequences is developed via the sieve metho...
详细信息
ISBN:
(纸本)9781510830981
In this paper, a constructive approach for determining CELCS(critical errorlinearcomplexity spectrum) for the kerrorlinearcomplexity distribution of 2~n-periodic binary sequences is developed via the sieve method and Games-Chan algorithm. Accordingly, the second descent point(critical point) distribution of the k-error linear complexity for 2~n-periodic binary sequences is characterized. As a by product, it is proved that the maximum k-error linear complexity is 2~n-(2) over all 2~n-periodic binary sequences, where 2<=k < 2 and l < n. With these results, some work by Niu et al. are proved to be incorrect.
The linearcomplexity and the -errorlinearcomplexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method o...
详细信息
The linearcomplexity and the -errorlinearcomplexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, we investigate the -errorlinearcomplexity distribution of -periodic binary sequences in this paper based on Games-Chan algorithm. First, for , the complete counting functions for the -errorlinearcomplexity of -periodic binary sequences (with linearcomplexity less than ) are characterized. Second, for , the complete counting functions for the -errorlinearcomplexity of -periodic binary sequences with linearcomplexity are presented. Third, as a consequence of these results, the counting functions for the number of -periodic binary sequences with the -errorlinearcomplexity for and are obtained.
暂无评论