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Analysis of Stability for Periodic Sequences

Author: YangMingHui
Tutor: ZhuShiXin
School: Hefei University of Technology
Course: Applied Mathematics
Keywords: Periodic sequence Linear complexity k - error linear complexity Stream cipher k - error sequence
CLC: TN918
Type: Master's thesis
Year: 2010
Downloads: 41
Quote: 0
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Abstract


Stream ciphers have very important applications in the field of cryptography , communications and computer , and how to evaluate the pseudo-random sequence is an important problem in the stream ciphers . With the deepening of the pseudo-random sequence , particularly in the late sixties , Berlekamp-Massey linear feedback shift register sequence BM algorithm makes linear complexity measure an important indicator of the strength of the stream cipher systems . The linear complexity of the sequence a is defined as the number of stages to produce the sequence a shortest linear shift register (LFSR) , referred to as LC (a). The known sequence of a continuous 2 LC (a) bits, using the BM algorithm can recover the entire sequence a . Therefore, a combat strength key sequence must have a high linear complexity , high linear complexity and can not guarantee the sequence has a strong anti- attack strength . For example : the binary sequence a = (000010000100001) equal to the period of linear complexity , namely the linear complexity degree , but when each cycle it last a bit changed to 0:00 linear complexity instantly becomes 0. To this end, it is proposed another measure an important indicator of the sequence of pseudo- randomness : k - error linear complexity . Sequence of a security not only have a high linear complexity and k - error linear complexity , there should be fewer of the smaller values ??of k , k - error sequence . First, k - error linear complexity well reflect the characteristics of the stability of the sequence using Chan-Games algorithm get linear complexity degree 2 n - 2m 2n - periodic binary sequences k - wrong the specific form of linear complexity , and gives an example to illustrate the specific form of this result is important to further investigate the security of the stream cipher key sequence . Next, the security strength of the error sequence of how much the key sequence a great relationship , k = 4,5, papers also determine the linear complexity of 2 n - 2m 2n - periodic binary sequences k - the error count of the sequence of M k (a) all possible values.

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