Study On Theory And Algorithms For Error Linear Complexity Of Periodic Sequence

With the application of advanced science and technology, cryptography hasbecome a comprehensive and sophisticated technological science. Stream cipher isone of the important branches of modern cryptography, and its security all depends onkeystream sequences. Research on the pseudorandom properties of keystreamsequences is very important in design and analysis of stream ciphers.The linear complexity and the k-error linear complexity have been used asimportant security measures for keystream sequences strength. In the dissertation, wefirst study the k-error linear complexity of several classes of sequences with specialperiod, and then discuss their statistical characteristics. The main results are asfollows:1. By rewrite the W-Z-X algorithm, a new algorithm for computing the k-errorlinear complexity and error vector of binary sequences with period pnis proposed,where p is an odd prime and2is a primitive root modulo p2.2. By rewrite the W-D-X algorithm, a new algorithm for computing the k-errorlinear complexity and error vector of q-ary sequences with period pnis proposed,where p and q are odd prime and q is a primitive root modulo p2.3. A fast algorithm for computing the m-tight error linear complexity of q-arysequences with period pnis proposed, where p and q are odd prime and q is aprimitive root modulo p2.4. Based on the XWLI algorithm, we derived the complete distribution law of the2-error linear complexity of binary sequences with period2n, and counting functionsin some cases are given.5. Based on the XWLI algorithm, we derived the complete distribution law of the3-error linear complexity of binary sequences with period2n, and counting functionsin some cases are given.