Linear complexity of second order PN_sequences addition with single order PN_sequence in nonlinear filter generator

Abstract

A method of analyzing the root presence test for Nonlinear Filter Generator is presented. We have proved that the Key’s upper bound on linear complexity hold for 2nd order product sequence with addition of single order sequence and also for a non-zero linear combination of such sequences under some conditions. Some of these sequences are balanced sequences and satisfy statistical randomness property than the Key's and Groth's sequences. The analysis can also be extended to Word-Oriented Nonlinearly Filtered Primitive Transformation Shift Registers.

Keywords:

• Linear complexity
• nonlinear filter generator
• traces function
• root and conjugate root of a polynomial
• 2^nd order product sequences