利用素数和自然数的数据隐藏技术
Data Hiding Techniques Using Prime and Natural Numbers
摘要：
本文提出了几种新的数据隐藏技术。这些技术是对经典LSB数据隐藏技术和Battisti等人提出的Fibonacci LSB数据隐藏技术的改进。\cite{r1}。经典的LSB技术是最简单的，但是使用该技术，可以仅嵌入在前几个位平面中，因为当嵌入在更高的位平面中时，图像质量会急剧失真。Battisti等人的\cite{r1}通过使用Fibonacci分解技术并一起生成不同的虚拟位平面集合，从而增加位平面的数量，提出了对此的改进。在本文中，首先，我们数学模型和推广这种特殊的虚拟位平面生成方法。然后，我们提出了两个新的嵌入技术，这两个都是我们的广义模型的特殊情况。第一种嵌入方案基于素数和中的数字（像素值）的分解，而第二种嵌入方案基于自然数和中的分解。这些特定表示中的每一个都生成一组不同的（虚拟）位平面，适合于嵌入目的。它们不仅允许在更高的位平面上嵌入秘密信息，而且在没有太大失真的情况下，以可靠和安全的方式，以更好的隐写图像质量，保证有效地检索秘密信息。对经典的最低有效位（LSB）方法、基于Fibonacci-p序列分解的数据隐藏技术和我们提出的方案进行了性能比较研究。理论分析表明，Fibonacci分解隐写图像的质量比单纯的LSB替换隐写图像的质量有明显提高，而素数分解隐写图像的质量比Fibonacci分解隐写图像的质量有明显提高，自然数分解隐写图像的质量比素数分解隐写图像的质量有进一步的提高。此外，最后的技术的最优性被证明。实验结果表明，对于我们的两种数据隐藏技术，隐写图像与原始封面图像在视觉上是不可区分的。
英文摘要：
In this paper, a few novel data hiding techniques are proposed. These techniques are improvements over the classical LSB data hiding technique and the Fibonacci LSB data-hiding technique proposed by Battisti et al. \cite{r1}. The classical LSB technique is the simplest, but using this technique it is possible to embed only in first few bit-planes, since image quality becomes drastically distorted when embedding in higher bit-planes. Battisti et al. \cite{r1} proposed an improvement over this by using Fibonacci decomposition technique and generating a different set of virtual bit-planes all together, thereby increasing the number of bit-planes. In this paper, first we mathematically model and generalize this particular approach of virtual bit-plane generation. Then we propose two novel embedding techniques, both of which are special-cases of our generalized model. The first embedding scheme is based on decomposition of a number (pixel-value) in sum of prime numbers, while the second one is based on decomposition in sum of natural numbers. Each of these particular representations generates a different set of (virtual) bit-planes altogether, suitable for embedding purposes. They not only allow one to embed secret message in higher bit-planes but also do it without much distortion, with a much better stego-image quality, in a reliable and secured manner, guaranteeing efficient retrieval of secret message. A comparative performance study between the classical Least Significant Bit (LSB) method, the data hiding technique using Fibonacci -p-Sequence decomposition and our proposed schemes has been done. Theoretical analysis indicates that image quality of the stego-image hidden by the technique using Fibonacci decomposition improves against simple LSB substitution method, while the same using the prime decomposition method improves drastically against that using Fibonacci decomposition technique, and finally the natural number decomposition method is a further improvement against that using prime decomposition technique. Also, optimality for the last technique is proved. For both of our data-hiding techniques, the experimental results show that, the stego-image is visually indistinguishable from the original cover image.
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