Counting Functions and Expected Values for the k-Error Linear Complexity

Authors:
Wilfried Meidl;Harald Niederreiter
Affiliations:
Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010, Vienna, Austriaf1wilfried.meidl@oeaw.ac.atf1;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543
Venue:
Finite Fields and Their Applications
Year:
2002

Citing 3
Cited 10

Analysis of the Berlekamp-Massey linear feedback shift-register synthesis algorithm

IBM Journal of Research and Development
Shift-register synthesis and BCH decoding

IEEE Transactions on Information Theory
An algorithm for the k-error linear complexity of binary sequences with period 2n

IEEE Transactions on Information Theory

The expectation and variance of the joint linear complexity of random periodic multisequences

Journal of Complexity
Error linear complexity measures for multisequences

Journal of Complexity
Expected Π-Adic Security Measures of Sequences

SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Characterization of 2n-periodic binary sequences with fixed 2-error or 3-error linear complexity

Designs, Codes and Cryptography
The expectation and variance of the joint linear complexity of random periodic multisequences

Journal of Complexity
On the k-operation linear complexity of periodic sequences

INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Expected π-adic security measures of sequences

IEEE Transactions on Information Theory
Asymptotic analysis on the normalized k-error linear complexity of binary sequences

Designs, Codes and Cryptography
The characterization of 2n-periodic binary sequences with fixed 1-error linear complexity

SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Counting functions and expected values for the lattice profile at n

Finite Fields and Their Applications

Quantified Score

Hi-index	0.06

Visualization

Abstract

In cryptology, complexity measures for sequences of elements of a finite field, such as the linear complexity, play an important role. Cryptographically strong sequences or finite strings must not only have a large linear complexity, but also the change of a few terms must not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity L"n","k(S) of a string S with terms in a finite field F"q and length n. In this article, bounds for the number of strings S of length n with k-error linear complexity L"n","k(S)=c or L"n","k(S)@?c for a given c are established. Under certain conditions on n, k, and c, exact formulas are also determined. On the basis of these results we derive bounds for the expected value of L"n","k(S) for random strings S of length n.