The Study Of Rotation Symmetric Boolean Functions With Good Cryptographic Properties

Cryptographic functions play an important role in the design of keystream generators for stream ciphers and S-boxes for block ciphers.In order to resist known attacks,cryptographic functions used in the cryptosystems need to satisfy certain cryptographic properties.However,there exist constraints between these properties of cryptographic functions.It is difficult to design a function that achieves optimal performance in all aspects.Therefore,constructing cryptographic functions with multiple desirable properties has been a longstanding research challenge in the field of cryptography.The constructions of two types of cryptographic functions are proposed and their cryptographic properties are studied in this paper.The main results are as follows:1.Based on the theory of integer partitions,rotation symmetric Boolean functions（RSBFs）with optimal algebraic immunity are constructed by modifying the truth tables of the majority functions.The nonlinearity,algebraic degree,and fast algebraic immunity of the constructed RSBFs are analyzed.Compared with known theoretically constructed RSBFs with optimal algebraic immunity,the constructed functions not only have the highest nonlinearity,but also achieve the optimal algebraic degree for certain variables.The constructed functions are further verified to be optimal with fast algebraic immunity by using the Simon Fischer algorithm.2.Based on the action of cyclic group on the_n-dimensional vector space over binary field,sufficient conditions for the existence of balanced or 1-resilient multi-output_k-rotational symmetric Boolean functions are proposed by the methods of orbital partition and constructing orthogonal tables when_nk₌pr（p is prime,r⁺）.Several methods of constructing rotational symmetric Boolean functions with these good cryptographic properties are also provided.