与3类向量值密码函数仿射等价的函数数量研究

摘要

Qu-Tan-Tan-Li函数、Zha-Hu-Sun函数和Tang-Carlet-Tang函数是近些年提出的差分均匀度为4、各项安全性指标均优良的向量值密码函数.研究与这3种密码函数仿射等价函数的计数问题.利用有限域的一些性质,分别计算出与Zha-Hu-Sun函数仿射等价函数数量的上下界,与Qu-Tan-Tan-Li函数和Tang-Carlet-Tang函数仿射等价函数数量的上界.此外,对于Zha-Hu-Sun函数仿射等价函数数量的精确值提出了猜测.研究结果表明,有限域GF(28)上至少有253[8Πi=1(2i-1]2个与Zha-Hu-Sun函数仿射等价的密码函数可直接用于分组密码的S盒.%In recent years, Qu-Tan-Tan-Li function, Zha-Hu-Sun function and Tang-Carlet-Tang function have been pro-posed with differential uniformity 4 and many good cryptographic properties. the counting problem of affine equivalent to the three families cryptographic functions was investigated. By using some properties of finite fields, the upper and lower bound of the number of affine equivalent to the Zha-Hu-Sun function, and the upper bound of the number of affine equivalent to the Qu-Tan-Tan-Li function and Tang-Carlet-Tang function were computed, respectively. Moreover, a conjecture was given about the exact number of affine equivalent to the Zha-Hu-Sun function. Results show that there are at least 253[8Πi=1(2i-1]2cryptographic functions of affine equivalent to the Zha-Hu-Sun function over finite field GF(28), which can be chosen as S-boxes of block ciphers.