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

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