Mixing Property Tester: A General Framework for Evaluating the Mixing Properties of Initialization of Stream Ciphers

In this paper, a general framework for evaluating the mixing properties of initialization of stream ciphers, called Mixing Property Tester-MPT, is exploited and formalized. Based on this general framework, we propose a concrete and efficient algorithm, which can compute the maximum number of initialization rounds of a given stream cipher such that any internal state bit or generated keystream bit does not achieve full mixing properties. Our algorithm has linear time complexity and needs a negligible amount of memory. As illustrations, we apply our algorithm to ZUC-128, ZUC-256 and Trivium stream ciphers. The results show that though ZUC-256 has a much larger initial input size than ZUC-128, its mixing properties are almost as good as ZUC-128. As for Trivium, the tap positions of keystream output function are not chosen optimally with respect to this tester and we provide some better selections of tap positions. As a general cryptanalytic tool, MPT can help to give the designers more insights to choose the initialization functions and the required number of initialization rounds.