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收稿：2023-04-07，
修回：2023-09-20，
纸质出版：2024-07-16
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目的
2
密文评估方法在衡量和增强混沌图像加密系统的安全性方面发挥着至关重要的作用。现有以密钥空间、密文密钥敏感性、像素个数变化率和统一平均变化强度等为代表的评估方法虽无法保证通过测试的加密系统一定具有非常高的安全性。而以选择明文攻击为代表的分析方法，与前者相比缺乏通用性和一致性，需要针对不同的加密系统设计不同的攻击方案。针对上述问题，本文基于深度学习模型面向混沌图像加密系统提出了一种兼具通用性和有效性的密文评估方法。
方法
2
该方法的核心思路是以降噪自编码器为基础模型，使用编码器分别对图像加密方法中的扩散密文、置乱密文和完整加密密文进行深度表示，然后使用解码器以上述深度表示为输入生成相应的不同明文，最后统计该明文与真实明文间的结构相似度作为度量加密方法抵抗密码学常用攻击手段能力的量化指标。对于一个加密方法来说，不仅其完整加密密文必须完全不可破译，而且其置乱阶段和扩散阶段的密文中也必须有一项是完全不可破译的，否则表明加密方法存在严重的安全缺陷。另外，密文数据集是影响上述方法有效性的关键因素。针对该问题，本文提出了一种相关性密文生成方法，该方法充分利用了明文敏感性密钥的特性，确保了生成的密文和本文评估方法的真实性和有效性。
结果
2
本文以Arnold置乱、2D-SCL（2D chaotic map based on the sine map， the chebyshev map and a linear function）加密和基于二维交叉混沌映射的量子加密为例对提出的密文评估方法进行了实验验证，实验中用到的数据集分别是MNIST（modified national institute of standards and technology database）和Fashion-MNIST。实验结果显示，本文提出的密文分析模型对上述加密方法及其各个阶段生成的密文图像表现出不同的密文分析能力：对Arnold置乱、2D-SCL扩散和量子bite置乱的密文来说，破译图像与真实图像间结构相似性指数（structural similarity，SSIM）的值均大于0.6；虽然在其他阶段的密文分析方面的效果较低，但也能破译出部分关键明文信息，呈现出较高的结构相似度。
结论
2
本文提出的密文图像分析方法通过客观的评价指标数据，能够有效地评估加密方法的安全性，为提升混沌图像加密方法的安全性提供了直观有效的量化依据，具有较高的指导意义。
Objective
2
Cryptography security analysis methods play a vital role in measuring and enhancing the security of chaotic image encryption systems. The existing ciphertext analysis methods for chaotic image encryption are generally divided into two categories. Although the evaluation methods based on numerical statistics， which are represented by key space analysis， sensitivity analysis of ciphertext to secret key， numbers of pixels change rate， and unified average changing intensity， have excellent versatility and consistency， the security of the test-passed encryption scheme cannot be ensured. While common attack methods in cryptography， which are represented by selective plaintext attack， can intuitively and effectively assess the security of chaotic encryption schemes， they lack versatility and consistency compared with security analysis methods， and different attack schemes need to be designed for different encryption schemes. To address the problem， this paper proposes a cryptanalysis method of chaotic image encryption system that is both versatile and effective based on denoising autoencoder.
Method
2
The ciphertext analysis method is improved based on the denoising autoencoder. It uses a cryptographic system with a known specific encryption steps to encrypt the plaintext image dataset and constructs the ciphertext analysis model， which takes the ciphertext image dataset as input and the original image dataset as the target data. The cryptanalysis model uses the encoder to obtain the depth representation of the diffusion ciphertext， scrambling the ciphertext and fully encrypted cipher image generated by the image encryption scheme， which is the structural features of images extracted from ciphertext images， and then uses the decoder to generate the different deciphered plaintext with the above depth representation as input. In this way， a deciphering model for a certain known encryption scheme can be trained， thereby achieving the purpose of ciphertext analysis. The effect of cryptanalysis is measured objectively and comprehensively by proposing three types of evaluation indicators suitable for ciphertext analysis based on peak signal to noise ratio（PSNR） and structural simitarity（SSIM）： max PSNR（MPSNR）， max SSIM（SSIM）， average of PSNR（APSNR）， avarage of SSIM（ASSIM）， cumulative distribution of PSNR（CDPSNR）， and cumulative distribution of SSIM（CDSSIM）， which measure the ability of an encryption scheme to resist popular attacks in cryptography by counting the structural similarity between the generated deciphered plaintext and real plaintext. This evaluation indicator， in addition to the subjective perception of human eyes， can visually display the differences between plaintext images and deciphered images by real data and complete the evaluation of the security of encryption schemes. For the one encryption scheme， not only the fully encrypted ciphertext but also one of the ciphertexts in the scrambling stage and the diffusion stage must be completely undecipherable； otherwise， the encryption scheme has serious security flaws. In addition， the ciphertext dataset is a key factor that affects the effectiveness of the above method. A correlation ciphertext generation method that generates three kinds of ciphertext sets——scrambled ciphertext， diffused ciphertext， and encrypted ciphertext—is proposed to address this issue. This generation method makes full use of the characteristics of chaotic image encryption systems and plaintext sensitive keys to ensure the authenticity and effectiveness of the generated ciphertext and the proposed evaluation method. When cryptanalyzing different chaotic image encryption schemes， changing only the generation scheme of ciphertext in each encryption stage based on the encryption algorithm is necessary. Without changing the training stage， testing stage， and model， the cryptanalysis and security evaluation of different chaotic encryption schemes can be completed.
Result
2
This paper takes Arnold scrambling， 2D-SCL image encryption scheme， and quantum image encryption scheme based on 2D Sine2-Logistic chaotic map as examples to verify the proposed ciphertext evaluation method. The datasets used in the experiment are MNIST and Fashion-MNIST. Experimental results show that the proposed cryptanalysis model has a different analysis ability for the ciphertexts generated by the above encryption scheme and their various stages. For the ciphertexts of Arnold scrambling， 2D-SCL’s diffusion， and bite scrambling in quantum encryption， the SSIM values between the decrypted images and the real plain-images are all greater than 0.6. The cryptanalysis model can learn low-dimensional structural features， same as the equivalent keys， to restore the ciphertext image. Although the effect of cryptanalysis in other stages is lower， it can also decipher some key plaintext information， showing a high degree of structural similarity. This finding also indicates that， for an encryption scheme， a high plaintext sensitivity of the secret key corresponds to a high security of the chaotic sequence， and a strong plaintext sensitivity of its equivalent key corresponds to a reduced likelihood that it can be cracked.
Conclusion
2
The proposed ciphertext image analysis method can evaluate the security of encryption schemes comprehensively and effectively by using objective data as the evaluation index， which provides an intuitive and effective quantitative basis for improving the security of chaotic image encryption methods， and has high guiding significance.
Chen C ， Sun K H and He S B . 2020 . An improved image encryption algorithm with finite computing precision . Signal Processing ， 168 ： # 107340 ［ DOI： 10.1016/j.sigpro.2019.107340 http://dx.doi.org/10.1016/j.sigpro.2019.107340 ］
Dou Y Q and Li M . 2020 . Cryptanalysis of a new color image encryption using combination of the 1D chaotic map . Applied Sciences ， 10 （ 6 ）： # 2187 ［ DOI： 10.3390/app10062187 http://dx.doi.org/10.3390/app10062187 ］
Farwa S ， Muhammad N ， Shah T and Ahmad S . 2017 . A novel image encryption based on algebraic S-box and Arnold transform . 3D Research ， 8 （ 3 ）： # 26 ［ DOI： 10.1007/s13319-017-0135-x http://dx.doi.org/10.1007/s13319-017-0135-x ］
Fridrich J . 1998 . Symmetric ciphers based on two-dimensional chaotic maps . International Journal of Bifurcation and Chaos ， 8 （ 6 ）： 1259 - 1284 ［ DOI： 10.1142/S021812749800098X http://dx.doi.org/10.1142/S021812749800098X ］
Hou B T ， Li Y Q ， Zhao H Y and Wu B . 2020 . Linear attack on round-reduced DES using deep learning // Proceedings of the 25th European Symposium on Research in Computer Security . Guildford， UK ： Springer： 131 - 145 ［ DOI： 10.1007/978-3-030-59013-0_7 http://dx.doi.org/10.1007/978-3-030-59013-0_7 ］
Hu M T ， Li J Q and Di X Q . 2023 . Quantum image encryption scheme based on 2D Sine 2 -Logistic chaotic map . Nonlinear Dynamics ， 111 （ 3 ）： 2815 - 2839 ［ DOI： 10.1007/s11071-022-07942-1 http://dx.doi.org/10.1007/s11071-022-07942-1 ］
Joshi A B ， Kumar D ， Mishra D C and Guleria V . 2020 . Colour-image encryption based on 2D discrete wavelet transform and 3D logistic chaotic map . Journal of Modern Optics ， 67 （ 10 ）： 933 - 949 ［ DOI： 10.1080/09500340.2020.1789233 http://dx.doi.org/10.1080/09500340.2020.1789233 ］
Kingma D P and Ba J . 2015 . Adam： a method for stochastic optimization // Proceedings of the 3rd International Conference on Learning Representations . San Diego， USA ： ［s.n.］
Lecun Y ， Bottou L ， Bengio Y and Haffner P . 1998 . Gradient-based learning applied to document recognition . Proceedings of the IEEE ， 86 （ 11 ）： 2278 - 2324 ［ DOI： 10.1109/5.726791 http://dx.doi.org/10.1109/5.726791 ］
Li M ， Guo Y Z ， Huang J and Li Y . 2018 . Cryptanalysis of a chaotic image encryption scheme based on permutation-diffusion structure . Signal Processing： Image Communication ， 62 ： 164 - 172 ［ DOI： 10.1016/j.image.2018.01.002 http://dx.doi.org/10.1016/j.image.2018.01.002 ］
Li M ， Wang P C ， LIU Y F and Fan H J . 2019 . Cryptanalysis of a novel bit-level color image encryption using improved 1D chaotic map . IEEE Access ， 7 ： 145798 - 145806 ［ DOI： 10.1109/ACCESS.2019.2945578 http://dx.doi.org/10.1109/ACCESS.2019.2945578 ］
Li Y Z ， Jin X ， Zhao G ， Li X D ， Tian Y L and Wang Z Y . 2016 . Color image encryption scheme based on Zigzag transformation and chaotic map . Computer Engineering and Design ， 37 （ 8 ）： 2002 - 2006
李玉珍 ， 金鑫 ， 赵耿 ， 李晓东 ， 田玉露 ， 王子亦 . 2016 . 基于Zigzag变换与混沌的彩色图像加密方案 . 计算机工程与设计 ， 37 （ 8 ）： 2022 - 2006 ［ DOI： 10.16208/j.issn1000-7024.2016.08.005 http://dx.doi.org/10.16208/j.issn1000-7024.2016.08.005 ］
Liang Y and Zhang S W . 2018 . Image encryption algorithm based on bit-level synchronous permutation diffusion and pixel-level annular diffusion . Journal of Image and Graphics ， 23 （ 6 ）： 814 - 826
梁颖 ， 张绍武 . 2018 . 位级同步置乱扩散和像素级环形扩散图像加密算法 . 中国图象图形学报 ， 23 （ 6 ）： 814 - 826 ［ DOI： 10.11834/jig.170433 http://dx.doi.org/10.11834/jig.170433 ］
Melicher W ， Ur B ， Segreti S M ， Komanduri S ， Bauer L ， Christin N and Cranor L F . 2016 . Fast， lean， and accurate： modeling password guessability using neural networks // The 25th USENIX Conference on Security Symposium . Austin， USA ： USENIX Association： 175 - 191
Pak C ， An K ， Jang P ， Kim J and Kim S . 2019 . A novel bit-level color image encryption using improved 1D chaotic map . Multimedia Tools and Applications ， 78 （ 9 ）： 12027 - 12042 ［ DOI： 10.1007/s11042-018-6739-1 http://dx.doi.org/10.1007/s11042-018-6739-1 ］
Pak C and Huang L L . 2017 . A new color image encryption using combination of the 1D chaotic map . Signal Processing ， 138 ： 129 - 137 ［ DOI： 10.1016/j.sigpro.2017.03.011 http://dx.doi.org/10.1016/j.sigpro.2017.03.011 ］
Rehman A U ， Liao X F ， Ashraf R ， Ullah S and Wang H W . 2018 . A color image encryption technique using exclusive-OR with DNA complementary rules based on chaos theory and SHA-2 . Optik ， 159 ： 348 - 367 ［ DOI： 10.1016/j.ijleo.2018.01.064 http://dx.doi.org/10.1016/j.ijleo.2018.01.064 ］
Solak E ， Cokal C ， Yildiz O T and Biyikoğlu T . 2010 . Cryptanalysis of Fridrich’s chaotic image encryption . International Journal of Bifurcation and Chaos ， 20 （ 5 ）： 1405 - 1413 ［ DOI： 10.1142/S0218127410026563 http://dx.doi.org/10.1142/S0218127410026563 ］
Sun X Y and Chen Z . 2021 . A new image encryption strategy based on Arnold transformation and logistic map //Liu Q， Liu X D， Chen B， Zhang Y M and Peng J S， eds. Proceedings of the 11th International Conference on Computer Engineering and Networks . Singapore， Singapore ： Springer： 721 - 729 ［ DOI： 10.1007/978-981-16-6554-7_77 http://dx.doi.org/10.1007/978-981-16-6554-7_77 ］
Vincent P ， Larochelle H ， Bengio Y and Manzagol P A . 2008 . Extracting and composing robust features with denoising autoencoders // Proceedings of the 25th International Conference on Machine Learning . Helsinki， Finland ： Association for Computing Machinery： 1096 - 1103 ［ DOI： 10.1145/1390156.1390294 http://dx.doi.org/10.1145/1390156.1390294 ］
Wen H P . 2019 . Cryptanalysis of Some Chaotic Ciphers . Guangzhou ： Guangdong University of Technology
温贺平 . 2019 . 若干混沌加密算法的密码分析 . 广州 ： 广东工业大学
Wu J H ， Xia W X ， Zhu G L ， Liu H ， Ma L J and Xiong J P . 2021 . Image encryption based on adversarial neural cryptography and SHA controlled chaos . Journal of Modern Optics ， 68 （ 8 ）： 409 - 418 ［ DOI： 10.1080/09500340.2021.1900440 http://dx.doi.org/10.1080/09500340.2021.1900440 ］
Xiao H ， Rasul K and Vollgraf R . 2017 . Fashion-MNIST： a novel image dataset for benchmarking machine learning algorithms ［EB/OL］. ［ 2023-04-07 ］. https://arxiv.org/pdf/1708.07747.pdf https://arxiv.org/pdf/1708.07747.pdf
Zhang W ， Yu H ， Zhao Y L and Zhu Z L . 2016 . Image encryption based on three-dimensional bit matrix permutation . Signal Processing ， 118 ： 36 - 50 ［ DOI： 10.1016/j.sigpro.2015.06.008 http://dx.doi.org/10.1016/j.sigpro.2015.06.008 ］
Zhou H ， Xie H W ， Zhang H and Zhang H T . 2021 . Parallel remote sensing image encryption algorithm based on chaotic map and DNA encoding . Journal of Image and Graphics ， 26 （ 5 ）： 1081 - 1094
周辉 ， 谢红薇 ， 张昊 ， 张慧婷 . 2021 . 混沌系统和DNA编码的并行遥感图像加密算法 . 中国图象图形学报 ， 26 （ 5 ）： 1081 - 1094 ［ DOI： 10.11834/jig.200344 http://dx.doi.org/10.11834/jig.200344 ］
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