Majority Function Investigation of Cryptografical Features

Abstract

Majority function is nonlinear Boolean function, which belongs to threshold functions class. This function has features like nonlinearity, simple design which enables its using in constructing stream ciphers. Most known Ruppel`s scheme is used in A5/1 which enables LFSR control with majority scheme. In this article we investigate LFRS majority synchronization by using mathematical model. Constructed 12 segments stream cipher which registers are three, four and five segments length. Statistical analysis of this cipher showed that 76 % of all sequences are 89 bits sequence. Constructed recursive eleven bits sequence truth table. Constructed generating function matrix or ones and zeros. Determined that generating function doesn’t belongs to Bent functions class so it is not nonlinear. Functions matrix has 1959 elements so exists 21959 functions which generate that sequence. Il. 4, bibl. 5 (in Lithuanian; summaries in Lithuanian, English, Russian).