Abstract: The block cipher algorithm with trapdoor is a kind of cipher algorithm that can meet the special needs in specific scenarios.The trapdoor function is widely used in asymmetric encryption algorithms.The idea of trapdoor function in asymmetric encryption is considered to be introduced into block cipher.the S-box isthe core of block cipher,which is the only non-linear component in mostly block cipher algorithm.It plays a role of confusion in the encryption process.Therefore,when constructing the trapdoor of the block cipher,the main research is to implant trapdoor into S-box.Aiming at this problem,this paper first studies the method of constructing trapdoor S-box based on the algebraic properties of linear partition of finite fields based on cosets.The trapdoor information is the linear partition method.This article first introduces the principle of trapdoor algorithm and trapdoor S-box based on linear partition.The 8×8 trapdoor S-box mapped on the linear partition is constructed,and the specific construction method is given.The linear and differential properties of this type of S-box are analyzed.In order to illustrate the safety and practicability of this type of S-box,the trapdoor block cipher proposed by Bannier et al is used as a model to briefly verify andana-lyze the effectiveness of the trapdoor,and prove the safety of trapdoor S-box and trapdoor algorithm to linear analysis and differential analysis.

Key words: Coset partition, Differential analysis, Linear analysis, Trapdoor function, Trapdoor S-box