| The stream cipher algorithm is an important class of symmetric encryption algorithms using in secure communications, the cryptanalysis and design of Stream ciphers is one of the hot academic research problems. In this dissertation, we focus on some nonlinear primitives in stream ciphers. We make a survey and research of cryptanalysis of some non-linear cryptographic primitives and the impact on the overall security of stream cipher algorithms. In addition, we propose some of the non-linear primitive designs with good cryptographic properties. The main results of this dissertation are as follows:(1). The security of filter generators is provided by the filter function. For the resistance to algebraic attacks, functions with maximum algebraic immunity should be selected for use in the design of filter functions. However, the algebraic immune functions found so far have a strong property of rotation symmetry. In this dissertation, we introduce an attack on the rotation-symmetric nature of the filter functions, and discuss the rotation-symmetric property of filter functions and its influence on the rotation-symmetric attack. After the survey of the vulnerability of algebraic immunity function to the rotation-symmetric attack, we point out that the choice of filter function should be far away from rotation-symmetric functions properly.(2). In 2002, the notation of T-functions was introduced by Klimov and Shamir. T-functions are widely used in cryptographic designs, however, the efficient construction of large variety of such T-functions possessing single cycle property is a bottleneck for their applications. In this dissertation, we focus on the construction of single cycle T-functions. Two classes of single cycle T-functions on single-word are presented, and they can be efficiently implemented in software environment and produce sequences with high linear complexity and being stable. Moreover, we study the relationship between parameters and single cycle T-functions and give a method to construct new single cycle T-functions from given single cycle T-functions and even parameters. In 2005, J. Hong presented a class of multi-word single cycle T-functions with parameters as critical components. In this dissertation, we discuss how to determine whether a given parameter is even or odd, and present a class of odd parameters for multi-word T-functions and their enumeration. Based on that, we propose a construction of pseudo-random sequence generator which is composed of a Linear Feedback Shift Register (LFSR) and a multi-word T-function. It is proved that the generator can generate sequences with very large period and possess good pseudo-random properties. (3). BOMM is a byte-oriented mixed type algorithm with memory which is used to disorder a given byte sequence. It has been used as a main component in a new stream cipher called Loiss for having many good cryptographic properties. In this dissertation, we build an algebraic equation system with degree 5 for BOMM, and based on this equation system, we discuss the complexity of algebraic attack on Loiss. In addition, we also find a statistic weakness of BOMM and give an analysis of the security of Loiss under a specific class of weak keys. (4). ZUC algorithm is a word-oriented stream cipher algorithm based on LFSR. We investigate the resistance of ZUC algorithm against algebraic attacks. We study an algebraic system of equations over GF(2) for ZUC and valuate the complexity of solving the algebraic system. As the LFSR of ZUC is defined over Z/(2^{31}-1), we also give an attempt at constructing a system of equations over Z/(2^{31}− 1) for ZUC algorithm. The bit-reorganization connects the linear feedback registers and the nonlinear function in ZUC, we analyze impact of the choice of taps for the bit-reorganization to some cryptographic properties of ZUC, and give a better choice of taps for the bit-reorganization. |
