On semi-bent functions with Niho exponents  

作　　者：HE YeFeng MA WenPing KANG Parminder 

机构地区：[1]State Key Laboratory 2School of Telecommunications of Integrated Service Networks,Xidian University Xi'an 710071,China [2]Information Engineering,Xi'an Institute of Posts and Telecommunications,Xi'an 710121,China [3]Lean Engineering Research Group Faculty of Technology,The Gateway,De Monfort University Leicester LE19BH,UK

出　　处：《Science China(Information Sciences)》2012年第7期1624-1630,共7页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 61072140);111 Project (Grant No. B08038)

摘　　要：Semi-bent functions are a kind of Boolean functions with high nonlinearity. They have important applications in cryptography and communications. In this paper, two classes of semi-bent functions with Niho exponents are proposed. It is shown that all semi-bent functions of the first class attain the maximum algebraic degree, and there exists one subclass of semi-bent functions with maximum algebraic degree in the second class. Furthermore, two examples of semi-bent functions in a small field are given by using the zeros of some Kloosterman sums. Based on the result given by Kim et al., two examples of infinite families of semi-bent functions are also obtained. These results provide more available Boolean functions with high nonlinearity and high algebraic degrees for designing the filter generators of stream ciphers.Semi-bent functions are a kind of Boolean functions with high nonlinearity. They have important applications in cryptography and communications. In this paper, two classes of semi-bent functions with Niho exponents are proposed. It is shown that all semi-bent functions of the first class attain the maximum algebraic degree, and there exists one subclass of semi-bent functions with maximum algebraic degree in the second class. Furthermore, two examples of semi-bent functions in a small field are given by using the zeros of some Kloosterman sums. Based on the result given by Kim et al., two examples of infinite families of semi-bent functions are also obtained. These results provide more available Boolean functions with high nonlinearity and high algebraic degrees for designing the filter generators of stream ciphers.

关 键 词：CRYPTOGRAPHY Boolean function Hadamard transform semi-bent function Kloosterman sum 

分 类 号：TN918.1[电子电信—通信与信息系统] O156.4[电子电信—信息与通信工程]