Study On The Stability Measure Indexes Of Stream Ciphers

This dissertation mainly research on the important stability measure indexes of str-eam ciphers-linear complexity, weight complexity, linear complexity profile andk -error linear complexity profile. The author obtains main results as follows:I.The characters of linear complexity profile of periodic sequences are investigat-ed. The relation between the continued fraction expansion of rational function and its 1-inear complexity profile is established. The expression of linear complexity profite is gi-~~en and a condition estimating the randomness of a sequence is presented. By the linearcomplexity profile, the bound of sphere complexity is proposed. A formula to record thenumber of sequences with given linear complexity profile is presented.2.The bound of weight complexity of binary sequences with period 2q is prop-osed. The linear complexity of 2~ periodic sequence obtained from one-symbol substi-tution within one period is presented.3.A relationship between linear complexity and k -error linear complexity of2" qperiodic sequence is investigated, an explicit formula of minerror( S AY) is given,whereN 2q.