具有最优代数免疫度的偶数元旋转对称布尔函数的构造

Construction of Even-variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity

代数免疫度是布尔函数的一个具有重要意义的密码学指标,具有高代数免疫度的布尔函数能够更有效地抵抗代数攻击,旋转对称布尔函数因其良好的密码学性质而成为密码学函数的优良选择,这类布尔函数已被广泛应用在不同的密码系统本文在对代数免疫度最优的旋转对称布尔函数构造研究的基础上,给出了一种偶数元旋转对称布尔函数的构造.而且,证明了新构造的九元旋转对称布尔函数不但代数兔疫最优,而且比已知同类研究构造出的函数具有更高的非线性度,达到2^(n-1)—(n-1/n/2)+2~k-2k,其中n=2k.同时,本文也详细讨论研究了所构造的函数的代数次数。

Algebraic immunity is considered as a very significant cryptographic property for Boolean functions.Boolean functions with high algebraic immunity can resist algebraic attacks more effectively.Rotation symmetric Boolean functions are good choices of cryptographic functions because of their good cryptographic properties.Hence,these Boolean functions have been used in different cryptosy stems.In this paper,based on the study of the constructions of rotation symmetric Boolean functions with optimal algebraic immunity,a new construction of even-variable rotation symmetric Boolean functions is proposed.Moreover,it is proved that,the constructed n-variable rotation symmetric Boolean functions have a nonlinearity of 2^(n-1)(n-1/n/2)+2~k-2k(n=2k),which is much higher than the previously known nonlinearity of rotation symmetric Boolean functions with optimal algebraic immunity.The algebraic degrees of the constructed functions are also discussed.