保护LSB嵌入以抵抗结构隐写分析
Securing LSB embedding against structural steganalysis
摘要：
这项工作探讨了在何种程度上LSB嵌入可以通过修改信息嵌入前的封面图像统计信息来对抗结构隐写分析。自然图像具有通过连续像素的某些$k$元组集合的近似相等基数来表示的对称性。LSB嵌入扰乱了这种平衡，并且$k^{\rm th}$顺序的结构攻击推断出隐藏消息的存在，该隐藏消息的长度与$k$元组的集合之间的不平衡的大小成比例。为了防止$k^{\rm th}$顺序的结构攻击，覆盖修改涉及到重新分配的$k$元组之间的不同的集合，使覆盖图像的对称性被打破，然后通过LSB嵌入的行为进行修复，使隐藏图像承载的统计，原来的封面。为了防止直到某个阶$k$的所有阶，必须保留$n$ -元组的统计信息，其中$n$是所有阶$\leq k$的最小公倍数。我们发现，这是唯一可行的，以防止高达$3^{\rm rd}$阶攻击（样本对和三重分析），因为高阶保护的结果几乎为零嵌入容量。保护高达$3^{\rm rd}$ -order的安全需要重新分配六联体：我们没有执行这些$6^{\rm th}$ -order覆盖修改（这会导致嵌入容量很小），而是将问题简化为三联体的重新分配，同时保留对的统计信息。这是通过仅嵌入到每个六元组的某些像素中来完成的，将最大嵌入速率约束为每通道$\leq 2/3$位。各种图像格式的测试，我们报告的JPEG压缩图像的最佳性能，平均最大嵌入率不可检测的$2^{\rm nd}$ -和$3^{\rm rd}$ -每通道0.21位的顺序攻击。
英文摘要：
This work explores the extent to which LSB embedding can be made secure against structural steganalysis through a modification of cover image statistics prior to message embedding. Natural images possess symmetries that are expressed through approximately equal cardinalities of certain sets of $k$-tuples of consecutive pixels. LSB embedding disturbs this balance and a $k^{\rm th}$-order structural attack infers the presence of a hidden message with a length in proportion to the size of the imbalance amongst sets of $k$-tuples. To protect against $k^{\rm th}$-order structural attacks, cover modifications involve the redistribution of $k$-tuples among the different sets so that symmetries of the cover image are broken, then repaired through the act of LSB embedding so that the stego image bears the statistics of the original cover. To protect against all orders up to some order $k$, the statistics of $n$-tuples must be preserved where $n$ is the least common multiple of all orders $\leq k$. We find that this is only feasible for securing against up to $3^{\rm rd}$-order attacks (Sample Pairs and Triples analyses) since higher-order protections result in virtually zero embedding capacities. Securing up to $3^{\rm rd}$-order requires redistribution of sextuplets: rather than perform these $6^{\rm th}$-order cover modifications, which result in tiny embedding capacities, we reduce the problem to the redistribution of triplets in a manner that also preserves the statistics of pairs. This is done by embedding into only certain pixels of each sextuplet, constraining the maximum embedding rate to be $\leq 2/3$ bits per channel. Testing on a variety of image formats, we report best performance for JPEG-compressed images with a mean maximum embedding rate undetectable by $2^{\rm nd}$- and $3^{\rm rd}$-order attacks of 0.21 bits per channel.
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