Trace Function Monomials Approximation Of Hyper Bent Functions And Decimation Attack

The cryptographic technology is the key to assuring information safety and cryptographic functions have been paid great attention recently.Further,the hyper bent function is defined by Boolean function with well performance of cryptographic.Based on the security analysis of the cryptographic functions.The main purpose of this study is to research the cryptographic properties of the hyper bent function and provide a sequence decimation attack of the feedforward function which through analyzing the hyper bent function.To do this,we determine the paper includes two parts:First,We initially discuss the YG-type hyper bent function which constructed by the Boolean functions,and proved that some of them can be showed by a trace function monomials approximation.Moreover,if the n-variables hyper bent sequence obtained by changing the trace generation sequence less than s-bits,then the equivalent probability of the hyper bent function to the trace function monomials is not less than1-s?2m+1?.In particular,ifs?2^m-2-K/2,the equivalent probability of the hyper bent function to the trace function monomials is exceed 0.75,where K is a constant determined by the hamming weight which generated by the trace function within one period.Thus,our results provide a lower bound of the total M of the YG-type n variables hyper bent function which be high probably approximated by the trace function monomials.Most of works focus on YG-type hyper bent function and the well property functions that can be used as cryptographic functions are less proposed.Moreover,there is a high probably between the sequence with the better run length characteristic of the hyper bent function and the d-sequence of the m-sequence,or even equal.At this time,the feedforward sequence cipher has a biggest hidden danger.To recover the initial state,we adopt the method of the decimation attack with the feedforward function of the hyper bent functions is presented.With the specific instance,we show that the theory and methods are viable.