基于循环移位和异或运算的对合线性变换研究

在对称密码算法的设计中,为达到良好的扩散作用,设计者一般均选择分支数较大的线性变换.基于循环移位和异或运算的线性变换由于其实现效率较高,已经在很多密码算法中被采用,比如分组密码SMS4、HIGHT,Hash函数SHA -2、MD6等.此外,如果线性变换是对合的,还为解密带来了方便.研究了基于循环移位和异或运算设计的对合线性变换,给出了这类线性变换的计数公式,指出它们的分支数上界为4,并讨论了循环移位的参数与分支数之间的关系,从而为基于这类运算设计的线性变换提供了理论依据.

Research on involutional linear transformations based on rotation and XOR

Linear transformation with good branch number plays a significant role in designing components of symmetric key primitives.Linear transformation based on XOR of several rotations can be efficiently implemented,and has been widely used in the block ciphers such as SMS4,HIGHT and the hash functions SHA-2,MD6.Besides,if the linear transformation is involutional,it will facilitate the decryption process.In view of this,a kind of involutional linear transformation based on the XOR of several rotations was studied,the numeration of this kind of linear transformation was given and the branch number was shown to be upper bounded by 4.Meanwhile,the relationship between the parameters of the rotations and the branch number was discussed,which provides a theoretical basis for the design.