Research On The Anti-differential Power Attack Indicator Of Cryptographic Function

Cryptographic function（Includes Boolean functions and S boxes）is an important part of a variety of cryptographic systems.To some extent,the quality of its cryptographic properties reflects the ability of the cryptographic system to resist all kinds of existing attacks.Therefore,how to design and analyze cryptographic functions satisfying various cryptographic properties is an important problem in cryptographic system research.With the further research on the side channel analysis of cryptographic algorithms,some indicators such as transparency order（TO）,signalto-noise ratio（SNR）and confusion coefficient（CC）have emerged in the resistance of cryptographic function to differential power attack,and these indicators also began to become an important reference standard to measure its safety.In this paper,the transparency order,signal-to-noise ratio and confusion coefficient of cryptographic function are studied,and the following results are obtained:First,the bounds of transparency order of cryptographic functions and the relationship between transparency order and other cryptographic indicators are studied.Firstly,the upper and lower bounds of the transparency order of Boolean function are analyzed by using the absolute indicator of Boolean function,and more upper and lower bounds of cryptographic function are derived.In addition,the general upper and lower bounds on the transparency order of S-boxes are proved,and the relationship between the transparency order and the signal-to-noise ratio of the Boolean functions is given,and the upper bound of transparency order of the balanced Boolean functions is described.Finally,based on the correlation,a concatenation Boolean function with good transparency order is constructed.Second,based on the relationship between SNR of（n,m）function and sum of squares,a lower bound of SNR of n element Boolean function on k-dimensional linear space is given.According to the relationship between the sum of squares of two Boolean functions and their respective sum of squares,as well as the relationship between the Signal-to-noise ratio and the sum of squares,the relationship between the signal-to-noise ratio of sum functions and their cross-correlation sum of squares is further deduced,so as to analyze the effect of the cryptographic function against DPA attack at this time.Finally,the upper and lower bounds of signal-to-noise ratio of various types of Boolean functions are summarizes.Third,according to the relationship between the nonlinearity of Boolean function and the confusion coefficient and the transparency order,the upper bounds on the transparency order of Boolean function is given by using the confusion coefficient.Then,through the definition of transparency order and the relationship between the sum of squares of confusion coefficient and signal-to-noise ratio,the relationship among the sum of squares of confusion coefficient,transparency order and signal-tonoise ratio of Boolean function is obtained.Then,the bounds on the balanced splateaued function are obtained by using the relationship between the sum of squares of the confusion coefficient of the balanced Boolean function and the transparency order,and the relationship between the signal-to-ratio and the nonlinearity.Finally,the lower bound of the sum of squares of the confusion coefficient of the Hamming weight k Boolean function is obtained.