Research on affine equivalence enumeration of the three families vectorial function

Abstract

In recent years,Qu-Tan-Tan-Li function,Zha-Hu-Sun function and Tang-Carlet-Tang function have been proposed 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 2 53 [ ∏ i=1 8 ( 2 i −1) ] 2 cryptographic 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.

Keywords

• cryptography
• cryptographic functions
• S-box
• affine equivalence
• enumeration