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.
翻译:这项工作探索了LSB嵌入安全到结构分析的程度上, 通过在信息嵌入之前修改封面图像统计, 能够让 LSB 嵌入安全到结构分析 。 自然图像具有最大程度的对称性, 表现方式大致相同, 某些组合的美元- 连续像素。 LSB 嵌入会扰乱这个平衡, 美元- 美元- 顺序结构攻击会显示隐藏的信息, 其长度相当于 美元- tuple 之间的比例。 要保护 美元- 美元- tuple 结构攻击 之前的不平衡。 要保护美元- 美元- 美元- 美元- 系统结构攻击, 包括在不同组合之间重新分配 美元- 美元- tupreal 美元- 结构攻击 的对美元- 数字的对美元- 美元- 数字- 数字- 数字- 数字- 货币- 数字- 数字- 数字- 数字- 数字- 数字- 数字- 数据- 数字- 速度- 数据- 速度- 速度- 速度- 数据- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 只能- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度- 速度-