This article proposes an algorithm which allows Alice to simulate the game played between her and Eve. Under the condition that the set of detectors that Alice assumes Eve to have is sufficiently rich (e.g. CNNs), and that she has an algorithm enabling to avoid detection by a single classifier (e.g adversarial embedding, gibbs sampler, dynamic STCs), the proposed algorithm converges to an efficient steganographic algorithm. This is possible by using a min max strategy which consists at each iteration in selecting the least detectable stego image for the best classifier among the set of Eve’s learned classifiers. The algorithm is extensively evaluated and compared to prior arts and results show the potential to increase the practical security of classical steganographic methods. For example the error probability $P_{err}$ of XU-Net on detecting stego images with payload of 0.4 bpnzAC embedded by J-Uniward and QF 75 starts at 7.1% and is increased by +13.6% to reach 20.7% after eight iterations. For the same embedding rate and for QF 95, undetectability by XU-Net with J-Uniward embedding is 23.4%, and it jumps by +25.8% to reach 49.2% at iteration 3.

中文翻译：

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最小最大隐写游戏的显式优化

本文提出了一种算法，该算法允许Alice模拟她和Eve之间玩的游戏。在爱丽丝假设夏娃拥有的一组检测器足够丰富的条件下（例如CNN），并且她有一种算法可以避免单个分类器的检测（例如对抗嵌入，吉布斯采样器，动态STC），该算法收敛为高效的隐写算法。这可以通过使用最小最大策略来实现，该策略在每次迭代中都包括在Eve学习的分类器中为最佳分类器选择最少可检测到的隐身图像。该算法得到了广泛的评估，并与现有技术进行了比较，结果表明，有可能提高经典隐写方法的实用安全性。例如错误概率 $ P_ {err} $ XU-Net对J-Uniward和QF 75嵌入的有效载荷为0.4 bpnzAC的隐身图像的检测始于7.1％，经过八次迭代后增加了13.6％，达到20.7％。对于相同的嵌入率和QF 95，具有J-Uniward嵌入的XU-Net的不可检测性为23.4％，并且在迭代3时跃升了25.8％，达到49.2％。