Randomness Efficient Steganography (original) (raw)

Information-Theoretic Approach to Steganographic Systems

2007 IEEE International Symposium on Information Theory, 2007

We propose a simple universal (that is, distributionfree) steganographic system in which covertexts with and without hidden texts are statistically indistinguishable. The stegosystem can be applied to any source generating i.i.d. covertexts with unknown distribution, and the hidden text is transmitted exactly, with zero probability of error. Sequences of covertexts with and without hidden information obey the same distribution (the stegosystem is perfectly secure). The proposed steganographic system has two important properties. First, the rate of transmission of hidden information approaches the Shannon entropy of the covertext source as the size of blocks used for hidden text encoding tends to infinity. Second, if the size of the alphabet of the covertext source and its minentropy tend to infinity then the number of bits of hidden text per letter of covertext tends to log(n!)/n where n is the (fixed) size of blocks used for hidden text encoding. Besides, the resource complexity of the proposed algorithms grows only polynomially.

Provably Secure Universal Steganographic Systems

IACR Cryptology ePrint Archive, 2006

We propose a simple universal (that is, distribution-free) steganographic system in which covertexts with and without hidden texts are statistically indistinguishable. Moreover, the proposed steganographic system has two important properties. First, the rate of transmission of hidden information approaches the Shannon entropy of the covertext source as the size of blocks used for hidden text encoding tends to infinity. Second, if the size of the alphabet of the covertext source and its minentropy tend to infinity then the the number of bits of hidden text per letter of covertext tends to log(n!)/n where n is the (fixed) size of blocks used for hidden text encoding. The proposed stegosystem uses randomization.

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

IEEE Transactions on Information Theory, 2000

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.

Constructing perfect steganographic systems

Information and Computation, 2011

We propose steganographic systems for the case when covertexts (containers) are generated by an i.i.d. or a finite-memory distribution, with known or unknown statistics. The probability distributions of covertexts with and without hidden information are the same; this means that the proposed stegosystems are perfectly secure, i.e. an observer cannot determine whether hidden information is being transmitted. In contrast, existing results only include methods for which the distributions of covertexts with and without hidden text are close but not equal.

On The Limits Of Perfect Security For Steganographic System

Until now the discussion on perfect security for steganographic systems has remained confined within the realm of mathematicians and information theory experts whose concise and symbolic representation of their philosophies, postulates, and inference thereafter has made it hard for the na\"ive academics to have an insight of the concepts. This paper is an endeavor not only to appraise on the limitations of one of such pioneer comprehensions but also to illustrate a pitfall in another scheme that asserts on having perfect security without the use of public or secret key. Goals set are accomplished through contrasting test results of a steganographic scheme that exploits English words with corresponding acronyms for hiding bits of secret information in chat - a preferred way to exchange messages these days. The misapprehension about perfect security and reign in characteristic of stego key in bit embedding process are unfolded respectively by launching elementary chosen-message a...

Provably Secure Steganography: Achieving Zero K-L Divergence using Statistical Restoration

2006

In this paper, we present a framework for the design of steganographic schemes that can provide provable security by achieving zero Kullback-Leibler divergence between the cover and the stego signal distributions, while hiding at high rates. The approach is to reserve a number of host symbols for statistical restoration: host statistics perturbed by data embedding are restored by suitably modifying the symbols from the reserved set. A dynamic embedding approach is proposed, which avoids hiding in low probability regions of the host distribution. The framework is applied to design practical schemes for image steganography, which are evaluated using supervised learning on a set of about 1000 natural images. For the presented JPEG steganography scheme, it is seen that the detector is indeed reduced to random guessing.

Asymptotically optimal perfect steganographic systems

Problems of Information Transmission, 2009

In 1998 C. Cachin proposed an information-theoretic approach to steganography. In particular, in the framework of this approach, so-called perfectly secure stegosystems were defined, where messages that carry and do not carry hidden information are statistically indistinguishable. There was also described a universal steganographic system, for which this property holds only asymptotically, as the message length grows, while encoding and decoding complexity increases exponentially. (By definition, a system is universal if it is also applicable in the case where probabilistic characteristics of messages used to transmit hidden information are not known completely.) In the present paper we propose a universal steganographic system where messages that carry and do not carry hidden information are statistically indistinguishable, while transmission rate of "hidden" information approaches the limit, the Shannon entropy of the source used to "embed" the hidden information.

Using Kolmogorov complexity for understanding some limitations on steganography

2009 IEEE International Symposium on Information Theory, 2009

Perfectly secure steganographic systems have been recently described for a wide class of sources of covertexts. The speed of transmission of secret information for these stegosystems is proportional to the length of the covertext. In this work we show that there are sources of covertexts for which such stegosystems do not exist. The key observation is that if the set of possible covertexts has a maximal Kolmogorov complexity, then a high-speed perfect stegosystem has to have complexity of the same order.

An Information-Theoretic Model for Steganography * Christian Cachin

An information-theoretic model for steganography with a passive adversary is proposed. The adversary's task of distinguishing between an innocent cover message C and a modified message S containing hidden information is interpreted as a hypothesis testing problem. The security of a steganographic system is quantified in terms of the relative entropy (or discrimination) between the distributions of C and S, which yields bounds on the detection capability of any adversary. It is shown that secure steganographic schemes exist in this model provided the covertext distribution satisfies certain conditions. A universal stegosystem is presented in this model that needs no knowledge of the covertext distribution, except that it is generated from independently repeated experiments. * To appear in Information and Computation. A preliminary version of this work was presented at the 2nd