Computing the k-error 2-adic complexity of 2<sup>n</sup>-periodic sequence based on genetic algorithm

Abstract

Sequences generated by feedback with carry shift registers (FCSR) have been extensively concerned for their as excellent randomness as the sequences generated by linear feedback shift registers (LFSR). 2-adic complexity is of fundamental importance as measure index on the security of cryptographic sequence. A good random sequence should not only have a high 2-adic complexity but also a few bit changed can not cause a significant decrease of the 2- adic complexity. This requirement leads to the concept of k-error 2-adic complexity. However it is a difficult problem to compute the k-error 2-adic complexity based on the traditional method in algebraic analysis. Considering that it is an optimization problem and the genetic algorithm is good at solving these problems, we investigate the genetic algorithm to compute the k-error 2-adic complexity of 2n-periodic sequences. The experiments show that we can get the approximate values very close to the exact value.