Some properties of a nonlinear combiner function: Linear complexity, mutual information, and correlation immunity

• Published in: Electronics & communications in Japan. Part 3, Fundamental electronic science Vol. 86; no. 3; pp. 44 - 56
• Main Authors: Shiraishi, Yoshiaki, Morii, Masakatu, Uyematsu, Tomohiko, Sakaniwa, Kohichi
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.03.2003
• Subjects: correlation immunity; linear complexity; linear feedback shift register; mutual information; nonlinear random number generator; pseudo-random numbers
• ISSN: 1042-0967; 1520-6440
• DOI: 10.1002/ecjc.1139

Pseudo‐random number generators are used in spectrum‐spread communications and stream encryption, which is a shared‐key encryption scheme. In particular, the nonlinearly coupled pseudo‐random number generator (NLCRG), in which the outputs from multiple linear feedback shift registers (LFSRs) are nonlinearly coupled, is becoming increasingly important in practical applications because of its structural simplicity. However, even with the NLCRG, its properties, and especially the properties of its output system, are not yet fully understood. Previously, Moriyasu, Morii, and Kasahara proposed a dynamic random number generator (DRG), which is a subclass of NLCRGs, and attempted to analyze its output sequences. The present work provides a further analysis of the DRG; it also positions the DRG in the class of NLCRGs, and discusses the general properties of the NLCRG, such as linear complexity and mutual information. The paper also presents a simple method for constructing a nonlinear circuit with correlation immunity by using a DRG. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 44–56, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1139