Linear Complexity and Autocorrelation of two Classes of New Interleaved Sequences of Period $2N$
This work addresses cryptographic security for stream ciphers by providing new sequences with proven properties, but it is incremental as it builds on prior interleaving methods.
The paper constructs binary sequences of period 2N with optimal autocorrelation using an interleaving technique, showing they have low autocorrelation and linear complexity meeting cryptographic standards.
The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of period $4N$ with optimal autocorrelation values have been constructed by Tang and Gong based on interleaving certain kinds of sequences of period $N$. In this paper, we use the interleaving technique to construct a binary sequence with the optimal autocorrelation of period $2N$, then we calculate its autocorrelation values and its distribution, and give a lower bound of linear complexity. Results show that these sequences have low autocorrelation and the linear complexity satisfies the requirements of cryptography.