The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are tw...The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd（p-1, q-1） = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.展开更多
Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two clas...Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.展开更多
Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = ...Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed.展开更多
Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-...Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-periodic sequences respectively,where N is an odd primeand 2 is a primitive root modulo N. The results show that there are a large percentage of sequenceswith both the linear complexity and the k-enor linear complexity not less than N, quite close totheir maximum possible values.展开更多
Complexity measures for keystream multisequences over Z/(N) play a crucial role in designing good stream cipher systems. This correspondence shows a general upper bound on k-error joint N-adic complexity of periodic m...Complexity measures for keystream multisequences over Z/(N) play a crucial role in designing good stream cipher systems. This correspondence shows a general upper bound on k-error joint N-adic complexity of periodic multisequences over Z/(N), and establishes the existence of periodic N-adic multisequences over Z/(N) which simultaneously possess maximal joint N-adic complexity and large k-error joint N-adic complexity. Under some conditions the overwhelming majority of all T-periodic N-adic multisequences over Z/(N) with maximal joint N-adic complexity logN(NT- 1)have a k-error joint N-adic complexity close to logN(NT- 1).展开更多
Complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, pr...Complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, presented by Venkateswarlu A, to computer the k-error joint linear complexity of a binary periodic multisequence. In this paper, the aim is mainly to complement the theoretical derivation and proof of the existing algorithm. Moreover, our algorithm reduces computation.展开更多
Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of ...Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-error linear complexity.展开更多
基金Supported by the National Natural Science Foun-dation of China (60373092)
文摘The k-error linear complexity and the linear complexity of the keystream of a stream cipher are two important standards to scale the randomness of the key stream. For a pq^n-periodic binary sequences where p, q are two odd primes satisfying that 2 is a primitive root module p and q^2 and gcd（p-1, q-1） = 2, we analyze the relationship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity.
基金the Natural Science Foundation of Fujian Province (2007F3086)the Funds of the Education Department of Fujian Prov-ince (JA07164)the Open Funds of Key Laboratory of Fujian Province University Network Security and Cryptology (07B005)
文摘Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generatol＇s, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.
基金the National Natural Science Foundation of China (No.60373092).
文摘Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed.
文摘Using the fact that the factorization of x^N — 1 over GF(2) is especiallyexplicit, we completely establish the distributions and the expected values of the lineal complexityand the k-error linear complexity of the N-periodic sequences respectively,where N is an odd primeand 2 is a primitive root modulo N. The results show that there are a large percentage of sequenceswith both the linear complexity and the k-enor linear complexity not less than N, quite close totheir maximum possible values.
基金supported by the National Natural Science Foundation of China under Grant Nos.61271271 and 61370089100 Talents Program of Chinese Academy of Sciencethe Fundamental Research Funds for the Central Universities under Grant No.2012HGBZ0622
文摘Complexity measures for keystream multisequences over Z/(N) play a crucial role in designing good stream cipher systems. This correspondence shows a general upper bound on k-error joint N-adic complexity of periodic multisequences over Z/(N), and establishes the existence of periodic N-adic multisequences over Z/(N) which simultaneously possess maximal joint N-adic complexity and large k-error joint N-adic complexity. Under some conditions the overwhelming majority of all T-periodic N-adic multisequences over Z/(N) with maximal joint N-adic complexity logN(NT- 1)have a k-error joint N-adic complexity close to logN(NT- 1).
基金supported by the National Natural Science Foundation of China (61370089)the Fundamental Research Funds for the Central Universities (2012HGBZ0622)
文摘Complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, presented by Venkateswarlu A, to computer the k-error joint linear complexity of a binary periodic multisequence. In this paper, the aim is mainly to complement the theoretical derivation and proof of the existing algorithm. Moreover, our algorithm reduces computation.
基金supported by the National Natural Science Foundation of China under Grant Nos.61070178, 61100200,and 60833008
文摘Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-error linear complexity.
