Abstract
This paper considers the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of order 2 and period pq, where p and q are distinct odd primes with gcd(p - 1, q - 1) = 2, p - q - 3 (mod 4). These sequences have been proved to possess good linear complexity. Our results show that the 2-adic complexity of these sequences is at least pq - q - 1. Then it is large enough to resist the attack of the rational approximation algorithm.
Highlights
Key streams of stream cipher systems are assumed by pseudorandom sequences
The 2-adic complexity is an important security measure for a pseudo-random sequence as a key stream. It refers to the minimum length of the feedback with carry shift register that generates this pseudo-random sequence, that is, the minimum number of registers required therein
Xiong et al raised a method of determining the 2-adic complexity of binary sequences by circulant matrices [7]. They showed that Legendre sequences and DHL sequences with optimal autocorrelation and two other classes of sequences with interleaved structures have maximal the 2-adic complexity [7], [8]
Summary
Key streams of stream cipher systems are assumed by pseudorandom sequences. The 2-adic complexity is an important security measure for a pseudo-random sequence as a key stream. Xiong et al raised a method of determining the 2-adic complexity of binary sequences by circulant matrices [7]. Using this method, they showed that Legendre sequences and DHL sequences with optimal autocorrelation and two other classes of sequences with interleaved structures have maximal the 2-adic complexity [7], [8]. Xiao modified these generalized cyclotomic sequences of order two of length pq and proved that they have high linear complexity [2].
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