Error Linear Complexity Measures of Binary Multisequences

In complexity measures for sequences over finite fields, such as the linear complexity and the k – error linear complexity is of great relevance to cryptology, in particular, to the area of stream ciphers. There are basically two types of requirements for suitability of a keystream generated by a stream cipher. One of the requirements is the keystream sequence must pass various statistical tests for randomness. This is to make it difficult to capture any information about the plaintext by an attacker from any possible statistical deficiencies in the keystream. The second is that it should be very hard to predict the entire keystream from the knowledge of a part of it. For this purpose, one is interested to know how hard a sequence might be to predict. This requirement leads to the study of several complexity measures for sequences. The most significant complexity measure is the linear complexity: length of the shortest linear recurrence relation satisfied by the sequence and ABSTRACT