Generalized joint linear complexity of linear recurring multisequences

The joint linear complexity of multisequences is an important security measure for vectorized stream cipher systems. Extensive research has been carried out on the joint linear complexity of $N$-periodic multisequences using tools from Discrete Fourier transform. Each $N$-periodic multisequence can be identified with a single $N$-periodic sequence over an appropriate extension field. It has been demonstrated that the linear complexity of this sequence, the so called generalized joint linear complexity of the multisequence, may be considerably smaller than the joint linear complexity, which is not desirable for vectorized stream ciphers. Recently new methods have been developed and results of greater generality on the joint linear complexity of multisequences consisting of linear recurring sequences have been obtained. In this paper, using these new methods, we investigate the relations between the generalized joint linear complexity and the joint linear complexity of multisequences consisting of linear recurring sequences

Error linear complexity measures for multisequences

Complexity measures for sequences over finite fields, such as the linear complexity and the k-error linear complexity, play an important role in cryptology. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multisequences. We introduce various options for error linear complexity measures for multisequences. For finite multisequences as well as for periodic multisequences with prime period, we present formulas for the number of multisequences with given error linear complexity for several cases, and we present lower bounds for the expected error linear complexity