A Novel S-Box GenerationMethodology Based on the Optimized GANModel

S-boxes can be the core component of block ciphers,and how to efficiently generate S-boxes with strong cryptographic properties appears to be an important task in the design of block ciphers.In this work,an optimized model based on the generative adversarial network(GAN)is proposed to generate 8-bit S-boxes.The central idea of this optimized model is to use loss function constraints for GAN.More specially,the Advanced Encryption Standard(AES)S-box is used to construct the sample dataset via the affine equivalence property.Then,three models are respectively built and cross-trained to generate 8-bit S-boxes based on three extended frameworks of GAN,i.e.,Deep Convolution Generative Adversarial Networks(DCGAN),Wasserstein Generative Adversarial Networks(WGAN),and WassersteinGenerativeAdversarial NetworkwithGradient Penalty(WGANGP).Besides,an optimized model based onWGAN-GP referred to asWGPIM is also proposed,which adds the loss function constraints to the generator network of the WGAN-GP model,including bijection loss,differential uniformity loss,and nonlinearity loss.In this case,8-bit S-boxes can be generated with cross-training.Experimental results illustrate that the WGP-IM model can generate S-boxes with excellent cryptographic properties.In particular,the optimal differential uniformity of the generated S-boxes can be reduced to 8,and the nonlinearity can be up to 104.Compared with previous S-box generation methods,this new method is simpler and it can generate S-boxes with excellent cryptographic properties.