关键词: 对称密码算法, 密码S盒, 图形处理器, 并行计算, 差分均匀度, 非线性度, 透明阶

Abstract:

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.

Key words: symmetric encryption algorithm, cryptographic S-box, Graphics Processing Unit (GPU), parallel computing, differential uniformity, nonlinearity, revised transparency order