CAJ | 학술논문

Bent函数一直是密码学研究中的重要课题,如何判断给出的布尔函数是否为bent函数是必须要解决的问题.通过对Gold型函数中指数的分析,得到了Gold型函数成为bent函数的充要条件,此充要条件是Leander文献中定理的部分推广,用该结论判断bent函数更加简便.同时还讨论了多个迹函数之和成为bent函数的一个充要条件.
Bent함수일직시밀마학연구중적중요과제,여하판단급출적포이함수시부위bent함수시필수요해결적문제.통과대Gold형함수중지수적분석,득도료Gold형함수성위bent함수적충요조건,차충요조건시Leander문헌중정리적부분추엄,용해결론판단bent함수경가간편.동시환토론료다개적함수지화성위bent함수적일개충요조건.
Bent functions are important in cryptography,and one must know how to judge whether a Boolean function is bent.We obtain a sufficient and necessary condition by analyzing the power in functions of Gold case.This sufficient and necessary condition is a partial generalization of the theorem in Leandefs reference.Our result makes the judgement of bentness of Gold case much easier.We also discuss a sufficient and necessary condition for that the sum of a few trace functions is bent.