Research On Heuristic Algorithm Of Boolean Functions With Excellent Cryptographic Properties

The symmetric cryptographic algorithms provide a strong theoretical foundation and technical support for ensuring the security of data storage and the security of information transmission in communication networks.Boolean functions are the core components in symmetric cryptosystems,and their cryptographic criteria directly determine the security of the symmetric cryptosystems.Boolean functions in symmetric cryptographic algorithms must satisfy excellent cryptographic criteria to ensure the security of the algorithms.This paper mainly focuses on how to design Boolean functions with excellent cryptographic properties.The main work is as follows:(1)By combining the advantages of tabu search algorithm and hill climbing algorithm,a new heuristic generation algorithm—hybrid tabu search(HTS)algorithm for excellent Boolean functions is proposed.A large number of Boolean functions with high nonlinearity,low autocorrelation,1-resilient,optimal algebraic degree,optimal algebraic immunity,optimal(suboptimal)fast algebraic immunity can be obtained quickly by applying this algorithm.Simulation results demonstrate that the cryptographic properties of the Boolean functions obtained by the proposed algorithm with strong search ability and fast running speed are better than the results of known optimization algorithms.The 8-variable 1-resilient Boolean functions obtained by HTS algorithm have currently the best nonlinearity.(2)The rotation symmetric and dihedral symmetric Boolean functions are studied and the improved hybrid tabu search(IHTS)algorithm is designed.Through IHTS algorithm,many rotation symmetric and dihedral symmetric Boolean functions with 1-resilience and propagation criterion of order 1 have been found.In addition to obtaining many 1-resilient functions with optimal algebraic degree,maximum algebraic immunity,suboptimal fast algebraic immunity,high nonlinearity and low absolute indicator,an open problem posed by Sun et al.in 2022 is resolved.In particular,several 9-variable 1-resilient functions with nonlinearity 240,propagation criterion of order 2,optimal algebraic immunity and suboptimal fast algebraic immunity,and 9-variable 2-resilient functions with nonlinearity 240,algebraic degree 6 and propagation criterion of order 1 are discovered.When 8 ≤n ≤11,the 1-resilient Boolean functions obtained by IHTS algorithm satisfy currently the best nonlinearity.(3)Some subclasses of rotation symmetric and dihedral symmetric Boolean functions on12-14 variables are constructed.These subclasses are not only small in cardinality,but also rich in Boolean functions with excellent cryptographic properties.Using IHTS algorithm to search for these subclasses,many rotation symmetric Boolean functions satisfying both 1-resilient and propagation criterion of order 1 have been found.In particular,seveal 13-variable rotation symmetric Boolean functions with nonlinearity 4032,2-resilience,and propagation criterion of order 2,and 13-variable 3-resilient functions with optimal algebraic degree are obtained.Moreover,the nonlinearities of these 12 and 13-variable 1-resilient Boolean functions obtained are currently the best.