Analysis Of BENT Function And Its Application On S-box Design

Substitution boxes(S-boxes)are a nonlinear component of many symmetric ciphers and the property of S-boxes have a strong impact on the security of the corresponding cryptographic algorithms.S-boxes have Boolean structure,so constructing Boolean functions that are suitable for cryptographic applications is the basis of S-box design.BENT functions are Boolean functions that reach the upper bound of nonlinearity,satisfy the highest degree of the propagation criterion and the Strict Avalanche Criterion(SAC).In addition,Vectorial BENT functions have a uniform difference distribution table.Because of these good properties,BENT functions are widely used in designing S-boxes.BENT functions are not balanced.However,balance is an important cryptographic property of S-boxes.So balance modification of BENT functions is important in constructing S-boxes by BENT functions.In this dissertation,the relationship between BENT functions and balanced S-boxes is studied and balance modification methods of BENT functions are concluded by analyzing the properties and construction features of BENT functions.Based on these balance modification methods,the construction of Sboxes by BENT functions is studied.Finally,a S-boxes generation software which implements the S-boxes construction methods studied in this dissertation is developed.This study provides theoretical methods and an implementation tool for designing reliable S-boxes.This dissertation has conducted researches and obtained some results in the following three aspects.(1)Balance modification methods of BENT functionsBy analyzing the properties and construction features of BENT functions,three balance modification methods of BENT functions are concluded: applying balance modification function;extracting some outputs;expanding support.(2)Constructing S-boxes by BENT functionsBased on these balance modification methods,the construction of S-boxes by Maiorana McFarland BENT functions and Partial Spread BENT functions is studied and the nonlinearity,algebraic degree,avalanche property of these constructed S-boxes are analyzed.This study shows that changing the construction method of BENT functions,choosing different balance modification function or different outputs extracting pattern can generate different S-boxes and the cryptographic properties of these S-boxes can also be different.This result provides theoretical methods for designing reliable S-boxes.(3)Design and implementation of the S-boxes generation softwareA S-boxes generation software which implements the S-boxes construction methods studied in this dissertation is developed.This dissertion introduces the requirement analysis,function design,modular structure of this software.The examples of the generated S-boxes and the test results of their cryptographic properties show that this software provides an implementation tool for designing reliable S-boxes.