On the quadratic spans of periodic sequences
CRYPTO '89 Proceedings on Advances in cryptology
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
Designs, Codes and Cryptography
Elliptic Curve Pseudorandom Sequence Generators
SAC '99 Proceedings of the 6th Annual International Workshop on Selected Areas in Cryptography
Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
The Filter-Combiner Model for Memoryless Synchronous Stream Ciphers
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Generalization of Siegenthaler Inequality and Schnorr-Vaudenay Multipermutations
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Ciphertext Only Reconstruction of Stream Ciphers Based on Combination Generators
FSE '00 Proceedings of the 7th International Workshop on Fast Software Encryption
On the existence of secure feedback registers
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Pseudorandom sequences and stream ciphers
Algorithms and theory of computation handbook
Clock-controlled FCSR sequence with large linear complexity
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
On boolean functions with generalized cryptographic properties
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
On the Minimal Polynomial of the Product of Linear Recurring Sequences
Finite Fields and Their Applications
Hi-index | 754.84 |
Conditions are derived which guarantee that products of linear recurring sequences attain maximum linear complexity. It is shown that the product of any number of maximum-length GF(q)sequences has maximum linear complexity, provided only the degrees of the corresponding minimal polynomials are distinct and greater than two. It is also shown that if the roots of any number of (not necessarily irreducible) minimal polynomials are simple and lie in extension fields of pairwise relatively prime degrees, then the product of the corresponding GF(q)sequences attains maximum linear complexity, provided only that no two roots of any minimal polynomial are linearly dependent over the groundfield GF(q)(which is automatically satisfied whenq = 2). The results obtained for products are extended to arbitrary linear combinations of product sequences.