CAJ | 학술논문

旋转对称布尔函数是一类重要的密码学函数，研究其重量和非线性度等密码学性质具有很好的理论价值。区别于已有的计算方法，该文利用特定的正规基把这些布尔函数的问题转化为有限域上的指数和问题，得到了4?n和n?2s时一些二次旋转对称布尔函数的重量和非线性度的新结果。使用所提的方法，可以计算几乎全部的二次旋转对称布尔函数的重量和非线性度。所提的新方法对于研究一般的旋转对称布尔函数具有一定的参考意义。
선전대칭포이함수시일류중요적밀마학함수，연구기중량화비선성도등밀마학성질구유흔호적이론개치。구별우이유적계산방법，해문이용특정적정규기파저사포이함수적문제전화위유한역상적지수화문제，득도료4?n화n?2s시일사이차선전대칭포이함수적중량화비선성도적신결과。사용소제적방법，가이계산궤호전부적이차선전대칭포이함수적중량화비선성도。소제적신방법대우연구일반적선전대칭포이함수구유일정적삼고의의。
Rotation-symmetric Boolean function is a class of Boolean functions with good cryptographic properties, and researches on its weight and nonlinearity cryptographic properties have good theoretical value. Different from the conventional calculation method, in this paper, these problems are converted to the evaluation of exponential sum on finite fields with a specific normal basis. Some new results about the weight and nonlinearity of some rotation-symmetric Boolean functions of degree 2 with 4?nandn?2sare obtained. Using the proposed method, the weight and nonlinearity of almost all Rotation-symmetric Boolean functions of degree 2 can be evaluated. This new method is also interesting for studies on the other Boolean functions.