The expected value of the joint linear complexity of periodic multisequences
Journal of Complexity
Remarks on the k-error linear complexity of pn-periodic sequences
Designs, Codes and Cryptography
On the counting function of the lattice profile of periodic sequences
Journal of Complexity
Expected Π-Adic Security Measures of Sequences
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Generalized Joint Linear Complexity of Linear Recurring Multisequences
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
New results on periodic sequences with large k-error linear complexity
IEEE Transactions on Information Theory
Multisequences with large linear and k-error linear complexity from Hermitian function fields
IEEE Transactions on Information Theory
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
Linear filtering of nonlinear shift-register sequences
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
On the 2-adic complexity and the k-error 2-adic complexity of periodic binary sequences
SETA'04 Proceedings of the Third international conference on Sequences and Their Applications
The probabilistic theory of the joint linear complexity of multisequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
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
On the expected value of the joint 2-adic complexity of periodic binary multisequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Improved results on periodic multisequences with large error linear complexity
Finite Fields and Their Applications
Quadratic functions with prescribed spectra
Designs, Codes and Cryptography
| Hi-index | 755.02 |
Rueppel (1986) conjectured that periodic binary sequences have expected linear complexity close to the period length N. In this paper, we determine the expected value of the linear complexity of N-periodic sequences explicitly and confirm Rueppel's conjecture for arbitrary finite fields. Cryptographically strong sequences should not only have a large linear complexity, but also the change of a few terms should not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity of N-periodic sequences. We present a method to establish a lower bound on the expected k-error linear complexity of N-periodic sequences based on the knowledge of the counting function 𝒩N,0(c), i.e., the number of N-periodic sequences with given linear complexity c. For some cases, we give explicit formulas for that lower bound and we also determine 𝒩N,0(c)