This paper studies the use of Set Shaping Theory (SST) as a reversible payload-shaping layer for least significant bit (LSB) image steganography. The proposal is not intended to replace existing steganographic methods or to compete with them as a new embedding scheme. Instead, SST is positioned as a complementary preprocessing stage that makes an existing embedding method easier to apply with lower statistical disturbance. The SST transformation increases the message length by K symbols and is implemented with the approximate and fast transformation algorithm developed by Glen Tankersley. Although the embedded payload is lengthened from N to N+K bits, the selected representation can reduce D_KL(P||Q) and therefore make the subsequent steganographic insertion less detectable under histogram-based criteria. Across 1,800 controlled simulations on four synthetic cover-image models, SST reduced D_KL(P||Q) by an average of 25.16 percent relative to a fair N+K LSB baseline, with a 95 percent confidence interval of +/- 1.22 percent. For K=8, the average reduction reached 42.81 percent. Additional robustness simulations with keyed random embedding paths confirmed the effect across several distances: at K=8, SST reduced KL divergence by 42.44 percent, Jensen-Shannon divergence by 29.62 percent, total variation by 12.41 percent, and symmetric chi-square distance by 28.30 percent. An additional image-based matrix-embedding/STC-like simulation showed that SST also reduces the minimum weighted insertion cost: relative to the unshaped K=0 reference, K=8 reduced the cost by 6.93 percent.

翻译：本文研究使用集合塑形理论（Set Shaping Theory, SST）作为最低有效位（LSB）图像隐写的可逆有效载荷塑形层。该方案并非旨在替代现有隐写方法，或作为新的嵌入方案与之竞争。相反，SST被定位为互补的预处理阶段，使现有嵌入方法更易于应用，且统计扰动更低。SST变换使消息长度增加K个符号，并通过Glen Tankersley开发的近似快速变换算法实现。尽管嵌入的有效载荷从N比特延长至N+K比特，但所选表示可降低D_KL(P||Q)，从而在基于直方图的检测标准下使后续隐写插入更不易被察觉。在四种合成封面图像模型的1800次受控仿真中，相对于公平的N+K LSB基线，SST使D_KL(P||Q)平均降低25.16%，95%置信区间为±1.22%。当K=8时，平均降低幅度达到42.81%。采用密钥化随机嵌入路径的额外鲁棒性仿真验证了该效果在多个距离度量上的表现：当K=8时，SST使KL散度降低42.44%，Jensen-Shannon散度降低29.62%，总变差降低12.41%，对称卡方距离降低28.30%。基于图像的矩阵嵌入/STC类额外仿真显示，SST还降低了最小加权插入成本：相对于未塑形的K=0参考，K=8使成本降低6.93%。