On the Minimal Polynomial of the Product of Linear Recurring Sequences

Authors:
R. Göttfert;H. Niederreiter
Affiliations:
Institute for Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria;Institute for Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria
Venue:
Finite Fields and Their Applications
Year:
1995

Citing 7
Cited 7

Introduction to finite fields and their applications

Introduction to finite fields and their applications
On functions of linear shift register sequences

Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
Products of linear recurring sequences with maximum complexity

IEEE Transactions on Information Theory
A generalization of a congruential property of Lucas

American Mathematical Monthly
On the linear complexity of products of shift-register sequences

EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Sequences with almost perfect linear complexity profile

EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
On the linear complexity of functions of periodic GF(q) sequences

IEEE Transactions on Information Theory

Root Counting, the DFT and the Linear Complexity of Nonlinear Filtering

Designs, Codes and Cryptography
Correlation-Immune and Resilient Functions Over a FiniteAlphabet and Their Applications in Cryptography

Designs, Codes and Cryptography
Improved Bounds on the Linear Complexity of Keystreams Obtained by Filter Generators

Information Security and Cryptology
Sequences of period 2N–2

SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Lower bounds on sequence complexity via generalised vandermonde determinants

SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Efficient Linear Feedback Shift Registers with Maximal Period

Finite Fields and Their Applications
A Remark on the Minimal Polynomial of the Product of Linear Recurring Sequences

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The determination of the minimal polynomial, and thus of the linear complexity, of the product of two linear recurring sequences is a basic problem in the theory of stream ciphers in cryptology. We establish results on the minimal polynomial of such a product which yield, in particular, a general lower bound on the linear complexity of the product sequence. The problem is mainly of interest for finite fields, but our methods work for arbitrary fields.