On The Critical Error Linear Complexity Spectrum Of Periodic Sequences

Stream cipher is a basic symmetric cryptography of the modern cryptology. It is vastly deployed in the high security areas, such as diplomatic and military fields.Sequence cipher security should be unpredictable and stable. The most important measure indexes for unpredictable of Stream cipher is the linear complexity L?s?, k error linear complexity L_k ?s? is an indicator to measure the stability of the sequence. The critical error linear complexity spectrum ?CELCS? is composed of ordered key points ?k, L_k ?s??, and the k error Linear complexity decrease only on the critical point.In this thesis, the critical errors linear complexity Spectrum is discussed which include the distribution of the 2ⁿ-periodic binary sequences with more than one descent points on k error linear complexity and how to construct the 2ⁿ-periodic binary sequences with giving the CELCS. The main results are as follows:1. Studying 2ⁿ-periodic binary sequences that the first descent point is k= 4 and the second descent point is k'=6 on k error linear complexity, providing the distribution of the sequences with k error linear complexity. The constraint relationship between linear complexity L?s? and the first descent point linear complexity L₄?s? is discussed. The possible value of L₆?s? is established. Moreover, the number of sequence is calculated with given L?s?, L₄?s? and L₆?s?.2. Studying the 2ⁿ periodic binary sequences with 4-error linear complexity L₄?s?, and obtain the counting Formula. Based on the result 1, The possible value of 4-error linear complexity on each critical point is established. And the perfect counting process of the sequence with given L₄?s? is provided.3. Constructing the 2ⁿ periodic binary sequences with giving k error linear complexity. Discussing the 2ⁿ-periodic binary sequences that the first descent point is k= 2, the second descent point is k'= 6 of k error linear complexity and WH?s?n??=10. The relationship between parameters of descent point ?critical point? linear complexity is provided. And the steps are given under each relationship of parameters.