Linear complexity of quaternary sequences over Z4 based on Ding-Helleseth generalized cyclotomic classes
This work addresses the need for secure sequences in cryptography, but it is incremental as it builds on existing cyclotomic methods.
The paper tackled the problem of constructing secure cryptographic sequences by defining a family of quaternary sequences over Z4 using Ding-Helleseth generalized cyclotomic classes modulo pq for odd primes p and q, and it determined their linear complexity, showing they possess large linear complexity, making them suitable for cryptography.
A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the sequences, which is in fact connected with the discrete Fourier transform of the sequences. The results show that the sequences possess large linear complexity and are good sequences from the viewpoint of cryptography.