SM4密码算法S盒的量子电路实现

Quantum Circuit Implementation of S-box for SM4 Cryptographic Algorithm

SM4密码算法是我国国家密码管理局2006年公开发布的用于WAPI的分组密码算法,2021年6月成为国际标准。S盒作为唯一的非线性组件,其安全性直接影响到SM4算法的安全性。该文首次给出SM4密码算法S盒的量子电路实现。根据S盒的代数表达式,首先利用高斯消元法给出表达式中仿射变换的量子电路,然后把求逆元运算转换为求该元素的254次方,再分别给出对应的平方计算和乘法计算的量子电路,最后通过改进的Itoh-Tsujii算法给出S盒的量子电路。量子电路的复杂度分析表明:所给出的S盒的量子电路共用48个量子比特,592个量子门,电路深度为289,具有较高的效率。该研究将会对量子环境下SM4密码算法的安全性分析奠定基础。

SM4 cryptographic algorithm is a block cipher algorithm for WAPI published by China's state cryptography administration in 2006.It was published as an international standard in June 2021.As the only nonlinear component,the security of S-box directly affects the security of SM4 algorithm.In this paper,the quantum circuit implementation of S-box for SM4 cryptographic algorithm is given for the first time.According to the algebraic expression of S-box,firstly,the affine transformation quantum circuit is given by Gaussian elimination method,then the inverse element operation is converted to the 254 power of the corresponding element,and then the corresponding quantum circuits for square calculation and multiplication calculation are given respectively.Finally,the quantum circuit of S-box is given by using improved Itoh-Tsujii algorithm.The complexity analysis shows that the given S-box quantum circuit uses 48 qubits,592 quantum gates and the circuit depth is 289,which has high efficiency.The research of this paper will lay a foundation for the security analysis of SM4 cryptographic algorithm in quantum environment.