基于正形置换的密码函数的构造

平衡性，非线性度，代数次数，扩散特性和线性结构是衡量密码安全布尔函数的重要指标，这种密码函数的个数对于密码体制的设计也是应当考虑的。正形置换的对分效应具有一定的密码学意义。该文基于正形置换构造了一类密码性能良好的布尔函数，并给出了这种函数的计数下界。这些结果为正形置换的密码学应用了开辟了一个方向。

Construction of cryptographic functions based on orthomorphic permutation

Some important indicators for evaluating the security of cryptographic Boolean functions consist of balancedness, nonlinearity, algebraic degree, propagation characteristics and linear structure. Also, the number of these functions should be taken into consideration in designing a cryptosystem based on some Boolean functions. Orthomorphic permutation has the property of certain halving effect which may be useful in cryptography. On the basis of such permutation, we construct a family of Boolean functions with perfect cryptographic characteristics, and present the lower bound on the enumeration of such functions. The results obtained may show a direction for the application of orthomorphic permutation to cryptography.