## Cryptology ePrint Archive: Report 2020/1416

Further on the Construction of Feedback Shift Registers with Maximum Strong Linear Complexity

Congwei Zhou and Bin Hu and Jie Guan

Abstract: In this paper, we present the more accurate definition of strong linear complexity of feedback shift registers based on Boolean algebraic than before, and analyze the bound of strong linear complexity by the fixed feedback function. Furthermore, the feedback shift registers with maximum strong linear complexity are constructed, whose feedback functions require the least number of monomials. We also show that the conclusions provide particular ideas and criteria for the design of feedback shift registers.

Category / Keywords: foundations / Feedback shift register&#65292;Strong linear complexity&#65292;Non-singular&#65292;$r -$cycle