Design And Analysis Of Boolean Function Against Differential Power Attack

In recent years,Differential Power Analysis(DPA)has become an effective attack method to threaten the security of lightweight packet cryptographic algorithms.The multi-output Boolean function(S-box)is the only nonlinear component in the packet cipher algorithm,and its performance largely determines the security of the packet cipher algorithm.The design of DPA-resistant packet cryptographic algorithms translates into the design of DPA-resistant S-boxes.In this thesis,we propose two types of DPA-resistant S-box construction schemes based on genetic algorithms and cryptographic structures,respectively.The main research contents are as follows.First of all,the transparent order and signal-to-noise ratio are analyzed in depth,and the following theoretical results are obtained: the bound of the redefining transparent order is derived for the multi-output Boolean function with uncorrelated coordinate functions;the upper bound of the redefining transparent order is derived for the balanced multi-output Boolean function;Based on the maximum Walsh spectrum of the coordinate function,the interrelationships among the nonlinearity,the redefining transparency order and the signal-to-noise ratio are derived respectively,leading to the conclusion that there is a restrictive relationship between the nonlinearity and the redefining transparency order,as well as between the nonlinearity and the signal-to-noise ratio.Second,an S-box construction scheme based on Chaos Adaptive Genetic Algorithm(CAGA)is proposed by introducing chaotic mapping and probabilistic adaption.Based on the traditional Genetic Algorithm(GA),an S-box construction scheme can be obtained,and the simulation analysis of the scheme reveals that the S-box construction based on the traditional GA algorithm has the shortcomings of difficult to guarantee the balance,slow convergence speed of the algorithm,and uneven initial population distribution.In this thesis,chaotic mapping is introduced into the initial population generation and variation operators,and the crossover and variation probabilities are adaptively optimized to obtain a scheme for constructing a balanced S-box based on the CAGA optimization algorithm.The simulation analysis of the scheme shows that the CAGA optimization algorithm has the advantages of more even initial population distribution and faster convergence of the algorithm.The constructed S-boxes are selected and a batch of 4×4balanced S-boxes are obtained.Compared with the S-boxes commonly used in current packet cryptography algorithms,the S-boxes constructed by the CAGA optimization algorithm have lower signal-to-noise ratio,lower redefining transparency order,excellent nonlinearity and differential uniformity.Finally,two schemes for constructing 8×8 S-boxes were proposed using Feistel,Lai-Massey structure and Feistel,MISTY structure respectively.The 8×8 S-boxes constructed by these two schemes are screened separately,and a total of four 8×8 S-boxes are obtained.The computational results show that the signal-to-noise ratio and the redefining transparency order of the screened S-boxes are lower compared with the S-boxes constructed using the cryptographic structures in the existing algorithms.The S-boxes constructed in this thesis have low signal-to-noise ratio and redefining transparency order,and their application in packet cipher design can make the corresponding packet cipher algorithms have better resistance to DPA attacks.