Abstract
Combining with the research on the linear complexity of explicit nonlinear generators of pseudorandom sequences, we study the stability on linear complexity of two classes of explicit inversive generators and two classes of explicit nonlinear generators. We present some lower bounds in theory on the k-error linear complexity of these explicit generators, which further improve the cryptographic properties of the corresponding number generators and provide very useful information when they are applied to cryptography.
Similar content being viewed by others
References
Cusick T W, Ding C, Renvall A. Stream Ciphers and Number Theory[M]. Amsterdam: Elsevier, 1998.
Stamp M, Martin C. An Algorithm for the k-Error Linear Complexity of Binary Sequences with Period 2n [J]. IEEE Transactions on Information Theory, 1993, 39(4): 1398–1401.
Shparlinski I E. Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness[ M]. Basel: Birkhäuser Verlag, 2003.
Gutierrez J, Shparlinski I E, Winterhof A. On the Linear and Nonlinear Complexity Profile of Nonlinear Pseudorandom Number Generators[J]. IEEE Transactions on Information Theory, 2003, 49(1): 60–64.
Niederreiter H, Winterhof A. Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers[J]. Applicable Algebra in Engineering, Communication and Computing, 2002, 13(4): 319–326.
Niederreiter H, Shparlinski I E. On the Distribution of Pseudorandom Numbers and Vectors Generated by Inversive Methods[J]. Applicable Algebra in Engineering, Communication and Computing, 2000, 10(3): 189–202.
Niederreiter H, Shparlinski I E. On the Distribution of Inversive Congruential Pseudorandom Numbers in Parts of the Period[J]. Math Comp, 2000, 70(236): 1569–1574.
Zhao Yaodong, Qi Wenfeng. On Cryptanalysis of the Inversive Generator[J]. J Wuhan Univ (Nat Sci Ed), 2007, 53(3): 279–282(Ch).
Niederreiter H, Winterhof A. On the Distribution of Compound Inversive Congruential Pseudorandom Numbers[J]. Monatsh Math, 2001, 132(1): 35–48.
Niederreiter H, Winterhof A. On the Distribution of Some New Explicit Nonlinear Congruential Pseudorandom Numbers[C]// Proceedings of SETA 2004 (LNCS 3486). Heidelberg: Springer-Verlag, 2005: 266–274.
Winterhof A. On the Distribution of Some New Explicit Inversive Pseudorandom Numbers and Vectors[C]//Proceedings of Monte Carlo and Quasi-Monte Carlo Methods 2004. Heidelberg: Springer-Verlag, 2006: 487–499.
Meidl W, Winterhof A. On the Linear Complexity Profile of Some New Explicit Inversive Pseudorandom Numbers[J]. Journal of Complexity, 2004, 20(2–3): 350–355.
Niederreiter H, Winterhof A. Incomplete Exponential Sums over Finite Fields and Their Applications to New Inversive Pseudorandom Number Generators[J]. Acta Arith, 2000, 93: 387–399.
Meidl W, Winterhof A. On the Linear Complexity Profile of Explicit Nonlinear Pseudorandom Numbers[J]. Information Processing Letters, 2003, 85(1): 13–18.
Blahut R E. Theory and Practice of Error Control Codes[M]. Reading, Massachusetts Addison-Wesley, 1983.
Chen Z X. Finite Binary Sequences Constructed by Explicit Inversive Methods[J]. Finite Fields and Their Applications, 2008, 14(3): 579–592.
Niederreiter H, Rivat J. On the Correlation of Pseudorandom Numbers Generated by Inversive Methods[J]. Monatsh Math, 2008, 153(3): 251–264.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Supported by the Natural Science Foundation of Fujian Province (2007F3086), the Funds of the Education Department of Fujian Province ( JA07164) and the Open Funds of Key Laboratory of Fujian Province University Network Security and Cryptology (07B005)
Rights and permissions
About this article
Cite this article
Chen, Z., Wu, C. On k-error linear complexity of some explicit nonlinear pseudorandom sequences. Wuhan Univ. J. Nat. Sci. 13, 577–581 (2008). https://doi.org/10.1007/s11859-008-0513-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11859-008-0513-6