Filter generators with variable transition functions over finite fields of characteristic 2

Abstract

Filter generators are a traditional basis for creating synchronous stream ciphers. They are built with the help of linear shift registers (usually over a field of two elements) and nonlinear complexity functions, which are subject to a number of requirements in terms of the generators security against known attacks. Intensive researches of filter generators during the last decades show that meeting these requirements without degrading the performance of the generators is a very difficult task. Despite a large number of publications devoted to the construction of complexity functions with known “good cryptographic properties”, the usage of such functions in practice often becomes unacceptable due to the bulkiness of their constructions, which slows down the functioning of the corresponding generators, especially during software implementation. The way to overcome the noted difficulties by using an additional secret parameter that determines the appearance of the generator transitions’ function is proposed. Such a modification makes it possible to increase the security of generator (compared to traditional filter generators) against known attacks without increasing the length of its initial state. In particular, a specific version of a generator construction with a complexity function, which is determined with the help of substitutions used in the “Kalyna” encryption scheme, is considered. A lower estimate of the output sequences periods of the proposed generators was obtained. A research of their security to known attacks, in particular, Babbage-Golic balancing attack; an attack associated with a small number of terms in the polynomial representation of the complexity function (which negatively affects the value of the equivalent linear complexity of the output sequences of the generator); a natural correlation attack associated with the specifics of the proposed generator construction scheme; algebraic attacks of the Courtois-Mayer type were also conducted. At the end of the article, it is indicated how to choose the components of the proposed generators to ensure their security at a predetermined level.