A New Characterization of Almost Bent Functions [chapter]

Anne Canteaut, Pascale Charpin, Hans Dobbertin
1999 Lecture Notes in Computer Science  
We study the functions from F m 2 into F m 2 for odd m which oppose an optimal resistance to linear cryptanalysis. These functions are called almost bent. It is known that almost bent functions are also almost perfect nonlinear, i.e. they also ensure an optimal resistance to differential cryptanalysis but the converse is not true. We here give a necessary and sufficient condition for an almost perfect nonlinear function to be almost bent. This notably enables us to exhibit some infinite
more » ... of power functions which are not almost bent. L. Knudsen (Ed.): FSE'99
doi:10.1007/3-540-48519-8_14 fatcat:7bj4pa3gcnbixpb3ykrjccwuda