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 ...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.展开更多
基金supported in part by the National Natural Science Foundation of China(62062026,62272451)the Innovation Research Team Project of Guangxi in China(2019GXNSFGA245004)+1 种基金the Key Research and Development Program of Guangxi in China(2022AB05044)the Scientific Research Project of Young Innovative Talents of Guangxi(guike AD20238082).
文摘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.
基金the financial supports from the National Natural Science Foundation of China (No. 52101183)China Postdoctoral Science Foundation (Nos. 2017M623054, 2018T110993)
