Perfectly Secure Steganography: Capacity, Error Exponents, and Code Constructions

An analysis of steganographic systems subject to the following perfect undetectability condition is presented in this paper. Following embedding of the message into the covertext, the resulting stegotext is required to have exactly the same probability distribution as the covertext. Then no statistical test can reliably detect the presence of the hidden message. We refer to such steganographic schemes as perfectly secure. A few such schemes have been proposed in recent literature, but they have vanishing rate. We prove that communication performance can potentially be vastly improved; specifically, our basic setup assumes independently and identically distributed (i.i.d.) covertext, and we construct perfectly secure steganographic codes from public watermarking codes using binning methods and randomized permutations of the code. The permutation is a secret key shared between encoder and decoder. We derive (positive) capacity and random-coding exponents for perfectly-secure steganographic systems. The error exponents provide estimates of the code length required to achieve a target low error probability. We address the potential loss in communication performance due to the perfect-security requirement. This loss is the same as the loss obtained under a weaker order-1 steganographic requirement that would just require matching of first-order marginals of the covertext and stegotext distributions. Furthermore, no loss occurs if the covertext distribution is uniform and the distortion metric is cyclically symmetric; steganographic capacity is then achieved by randomized linear codes. Our framework may also be useful for developing computationally secure steganographic systems that have near-optimal communication performance.Comment: To appear in IEEE Trans. on Information Theory, June 2008; ignore Version 2 as the file was corrupte

Determinants for stability of the chloroplast <i>psbD</i> RNA are located within its short leader region in <i>Chlamydomonas reinhardtii</i>

Stability of the chloroplast psbD mRNA encoding the D2 protein of the photosystem II reaction center is drastically decreased in the nuclear photosynthetic mutant nac2‐26 of Chlamydomonas reinhardtii. Using biolistic transformation and genetic crosses we have introduced chimeric genes consisting of the psbD leader fused to a reporter gene into the chloroplast in both wild‐type and mutant nuclear backgrounds. The chimeric message is destabilized in the latter, but not in the former case, indicating that the 74 nt psbD leader includes one of the target sites for psbD RNA degradation in the absence of wild‐type NAC2 function. Increased instability of the psbD leader in mutant versus wild‐type chloroplast lysates is also demonstrated in vitro and the primary cleavage sites have been mapped. The instability of the psbD RNA in the mutant correlates with the loss of binding of a 47 kDa protein to the psbD leader RNA, suggesting that this factor acts as message stabilizer in wild‐type