Ensuring ciphertext indistinguishability is fundamental to cryptographic security, but empirically validating this property in real implementations and hybrid settings presents practical challenges. The transition to post-quantum cryptography (PQC), with its hybrid constructions combining classical and quantum-resistant primitives, makes empirical validation approaches increasingly valuable. By modeling IND-CPA games as binary classification tasks and training on labeled ciphertext data with BCE loss, we study deep neural network (DNN) distinguishers for ciphertext indistinguishability. We apply this methodology to PQC KEMs. We specifically test the public-key encryption (PKE) schemes used to construct examples such as ML-KEM, BIKE, and HQC. Moreover, a novel extension of this DNN modeling for empirical distinguishability testing of hybrid KEMs is presented. We implement and test this on combinations of PQC KEMs with plain RSA, RSA-OAEP, and plaintext. Finally, methodological generality is illustrated by applying the DNN IND-CPA classification framework to cascade symmetric encryption, where we test combinations of AES-CTR, AES-CBC, AES-ECB, ChaCha20, and DES-ECB. In our experiments on PQC algorithms, KEM combiners, and cascade encryption, no algorithm or combination of algorithms demonstrates a significant advantage (two-sided binomial test, significance level $α= 0.01$), consistent with theoretical guarantees that hybrids including at least one IND-CPA-secure component preserve indistinguishability, and with the absence of exploitable patterns under the considered DNN adversary model. These illustrate the potential of using deep learning as an adaptive, practical, and versatile empirical estimator for indistinguishability in more general IND-CPA settings, allowing data-driven validation of implementations and compositions and complementing the analytical security analysis.

翻译：确保密文不可区分性是密码安全的基础，但在实际实现和混合环境中实证验证该特性面临实践挑战。随着后量子密码向结合经典与抗量子原语的混合架构过渡，实证验证方法的价值日益凸显。通过将IND-CPA博弈建模为二分类任务，并利用带标签的密文数据与二元交叉熵损失进行训练，我们研究了用于密文不可区分性检测的深度神经网络区分器。将该方法应用于后量子密码密钥封装机制，重点测试了构建ML-KEM、BIKE和HQC等实例所用的公钥加密方案。进一步提出将深度神经网络建模扩展至混合密钥封装机制实证不可区分性检测的创新方法，并在后量子密码密钥封装机制与纯RSA、RSA-OAEP及明文的组合中进行了实现与测试。最后，通过将深度神经网络IND-CPA分类框架应用于级联对称加密（测试了AES-CTR、AES-CBC、AES-ECB、ChaCha20与DES-ECB的组合）展示了方法论的通用性。针对后量子密码算法、密钥封装机制组合器及级联加密的实验表明：所有算法及算法组合均未展现出显著优势（双尾二项检验，显著性水平$\alpha=0.01$），这与"至少包含一个IND-CPA安全组件的混合结构可保持不可区分性"的理论保证相符，亦验证了在特定深度神经网络敌手模型下不存在可资利用的模式特征。这揭示了深度学习作为自适应、实用且通用的不可区分性实证估计器在更广泛IND-CPA场景中的应用潜力，能够为实现方案与组合设计提供数据驱动的验证支持，补充分析性安全论证。