基于LWE的密文域可逆信息隐藏

该文提出了一种基于LWE(Learning With Errors)算法的密文域可逆隐写方案，利用LWE公钥密码算法对数据加密，用户在密文中嵌入隐藏信息，对于嵌入信息后的密文，用户使用隐写密钥可以有效提取隐藏信息，使用解密密钥可以无差错恢复出加密前数据实现了提取过程与解密过程的可分离。通过推导方案在解密与提取信息过程中出错的概率，得到直接影响方案正确性的参数为所选噪声的标准差，实验获得并验证了标准差的合理取值区间；通过推导嵌入后密文的分布函数，分析密文统计特征的变化情况，论证了嵌入密文的隐藏信息的不可感知性。该方案是在密文域进行的可逆隐写，与原始载体无关，适用于文本、图片、音频等各类载体。实验仿真结果表明该方案不仅能够保证可逆隐写的可靠性与安全性，而且1 bit明文在密文域最大可负载1 bit隐藏信息。

Reversible Steganography in Encrypted Domain Based on LWE

This paper proposes a novel scheme of reversible steganography in encrypted domain based on Learning With Errors (LWE). The original data is encrypted by the cryptographic algorithms with LWE. Then additional data could be embedded into the cipher text. With embedded cipher text, the additional data can be extracted by using data-hiding key, and the original data can be recovered by using encryption key, and the processes of extraction and decryption are separable. By deducing the error probability of the scheme, the standard deviation of noise sequence which directly related to the schemes correctness is mainly discussed, and reasonable range of the standard deviation is obtained by experiments. The probability distribution function of the embedded cipher text is deduced, that proves the embedded cipher text is not detective. The proposed scheme based on encrypted domain can apply to different kinds of media vehicle such as text, image or audio. Experimental results demonstrate that the proposed scheme can not only achieve statistical security without degrading the quality of encryption or data embedding, but realize that 1 bit original data can maximally load 1 bit additional data in encrypted domain.