Computing the k-error N-adic complexity of a sequence of period pn

Authors:
Lihua Dong;Yupu Hu;Yong Zeng
Affiliations:
The Key Lab. of Computer Networks and Information Security, the Ministry of Education, Xidian University, Xi'an, ShaanXi Province, P.R. China;The Key Lab. of Computer Networks and Information Security, the Ministry of Education, Xidian University, Xi'an, ShaanXi Province, P.R. China;The Key Lab. of Computer Networks and Information Security, the Ministry of Education, Xidian University, Xi'an, ShaanXi Province, P.R. China
Venue:
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Year:
2006

Citing 11
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Abstract

Cryptographically strong sequences should have a large N-adic complexity to thwart the known feedback with carry shift register (FCSR) synthesis algorithms. At the same time the change of a few terms should not cause a significant decrease of the N-adic complexity. This requirement leads to the concept of the k-error N-adic complexity. In this paper, an algorithm for upper bounding the k-error N-adic complexity of the sequence with period T=pn, and p is just a prime, is proposed by extending the 2-adic complexity synthesis algorithm of Wilfried Meidl, and the Stamp-Martin algorithm. This algorithm is the first concrete construction of the algorithm for calculating the k-error N-adic complexity. Using the algorithm proposed, the upper bound of the k-error N-adic complexity can be obtained in n steps.