基于2-adic有限状态自动机的序列密码研究

序列密码是密码学的重要领域。近十几年来，序列密码算法设计的发展趋势是采用非线性驱动方法替代传统的线性反馈移位寄存器（LFSR）生成源序列。进位反馈移位寄存器（FCSR）能够生成一类具有代数结构的非线性序列：l-序列，被认为是LFSR的一个很好的替代。2-adic有限状态自动机（2-adic FSA）是一类由FCSR推广而来的自动机，同样能够生成l-序列，可定制比FCSR更丰富更灵活的硬件结构。本项目将研究2-adic FSA应用于序列密码的结构设计理论，包括：（1）2-adic FSA电路实现方法的研究；（2）面向硬件序列密码算法设计的2-adic FSA的构造；（3）2-adic FSA前馈滤波序列的密码学性质研究。目标是通过以上研究，完善2-adic FSA的结构设计理论，并为基于2-adic FSA的序列密码算法设计制定一些安全高效的结构。

Stream cipher is a really important part of Cryptography. In recent ten years, the trend of stream cipher algorithm design is to adopt non-linear driver to replace the traditional Linear Feedback Shift Registers (LFSRs) for generating source sequences. Feedback with Carry Shift Registers (FCSRs) can generate l-sequences, a class of non-linear sequences with algebraic structure. They have been proposed as a good alternative to LFSRs. 2-adic Finite State Automata （2-adic FSA）are generalized from FCSRs. They can also generate l-sequences. Moreover, they have more flexibilities for hardware implementation than FCSRs. This project will study the theory of the structure design of 2-adic FSA for stream ciphers, including: (1) the research of the circuit implementation method of 2-adic FSA; (2) the construction of 2-adic FSA for hardware stream cipher design; (3) the study of some cryptographic properties of sequences generated from a filtered 2-adic FSA. Through these aspects research, our object is to improve the structural design theory of 2-adic FSA and produce some secure and efficient structures for 2-adic FSA based stream cipher design.