基于GPU的密码S盒代数性质评估方法

密码S盒即黑盒，作为对称密码算法中的非线性部件，其代数性质往往决定着密码算法的安全性能。差分均匀度、非线性度及透明阶作为衡量密码S盒安全性质的三个基本指标，分别刻画了S盒抵御差分密码分析、线性密码分析及差分功耗攻击的能力。当密码S盒输入尺寸较大（如S盒输入长度大于15比特）时在中央处理器（CPU）中的求解所需时间仍过长，甚至求解不可行。如何针对大尺寸输入密码S盒的代数性质进行快速评估是目前业界的研究热点。基于图形处理器（GPU）提出一种快速评估密码S盒代数性质的方法。该方法利用切片技术将内核函数拆分至多线程，并结合求解差分均匀度、非线性度及透明阶的特征提出优化方案，从而实现并行计算。测试结果表明，与基于CPU的实现环境相比，基于单块GPU的环境下的实现效率得到了显著的提升。具体来说，计算差分均匀度、非线性度及透明阶所花时间分别节省了90.28%、78.57%、60%，验证了该方法的有效性。

GPU-based method for evaluating algebraic properties of cryptographic S-boxes

Cryptographic S-boxes （or black boxes） are nonlinear components in symmetric encryption algorithms， and their algebraic properties usually determine the security performance of these encryption algorithms. Differential uniformity， nonlinearity and revised transparency order are three basic indicators to evaluate the security properties of cryptographic S-boxes. They describe the S-box’s ability against differential cryptanalysis， linear cryptanalysis and differential power attack respectively. When the input size of the cryptographic S-box is large （for example， the input length of the S-box is larger than 15 bits）， the needed solving time in Central Processing Unit （CPU） is still too long， or even the solution is impracticable. How to evaluate the algebraic properties of the large-size S-box quickly is currently a research hot point in the field. Therefore， a method to evaluate the algebraic properties of cryptographic S-boxes quickly was proposed on the basis of Graphics Processing Unit （GPU）. In this method， the kernel functions were split into multiple threads by slicing technique， and an optimization scheme was proposed by combining the characteristics of solving differential uniformity， nonlinearity and revised transparency order to realize parallel computing. Experimental results show that compared with CPU-based implementation environment， single GPU based environment has the implementation efficiency significantly improved. Specifically， the time spent on calculating differential uniformity， nonlinearity， and revised transparency order is saved by 90.28%， 80%， and 66.67% respectively， which verifies the effectiveness of this method.