用集合构造理论提升隐写嵌入效率,降低被检测概率。
Set Shaping Theory as a Complementary Payload-Shaping Layer for Steganography
- 将集合构造理论作为预处理层,优化最低位图隐写
- 使信息容量增加8比特时,检测距离下降42.81%
- 适合需要隐蔽性更强的图像隐写应用
本文研究将集合构造理论(SST)作为最小有效位(LSB)图像隐写中的可逆载荷整形层。该方法并非取代现有隐写方案,而是作为补充预处理阶段,使已有嵌入方法更易实施且统计扰动更低。SST变换将消息长度增加K位,采用Glen Tankersley提出的近似快速算法实现。尽管嵌入载荷从N增至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更难被发现。在四种合成载体图像模型上进行的1,800次受控模拟显示,相比公平的N+K LSB基线,SST平均降低D_KL(P||Q) 25.16%(95%置信区间±1.22%)。当K=8时,平均降幅达42.81%。带密钥随机嵌入路径的鲁棒性模拟进一步验证:在K=8时,SST使KL散度减少42.44%,Jensen-Shannon散度减少29.62%,总变差减少12.41%,对称卡方距离减少28.30%。另一组基于图像矩阵嵌入/STC类模拟表明,SST也降低了最小加权插入成本:相较于未整形的K=0参考,K=8时成本降低6.93%。
原文摘要 · Abstract (English)
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.
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