Estimating Steganographic Fisher Information in Real Images

Proceedings of the 11th ACM Workshop on Multimedia and Security

2009

Self Cite

We extend the square root law of steganographic capacity, for the simplest case of iid covers, in two ways. First, we show that the law still holds under a more realistic embedding assumption, where the payload is of fixed length (instead of, in the classic result, independent embedding at each location). Second, we consider the case of nonuniform embedding paths, which is forced when the stegosystem's secret key is of limited size: we show that the secret key must be of length at least linear in the payload size, if a square root law is to hold. The latter is parallel to Shannon's perfect cryptography bound.

Section: Classic Resultsmentioning

confidence: 99%

The square root law requires a linear key

Proceedings of the 11th ACM Workshop on Multimedia and Security

2009

Self Cite

“…This question is related to Steganographic Fisher Information (SFI), which is studied in [13] and [4]. Those papers refer to embedding in particular cover models, but the general concept applies more widely.…”

Section: Steganographic Fisher Informationmentioning

confidence: 99%

“…3. The rate of convergence to perfect security is related to Steganographic Fisher Information [13,4], and we examine this in Sect. 4: we are able to prove that the keyless embedding is equally secure as uniform embedding requiring unfeasibly large keys, so that no security is lost.…”

Section: Introductionmentioning

confidence: 99%

The square root law does not require a linear key

Proceedings of the 12th ACM Workshop on Multimedia and Security

2010

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Square root laws are theorems about imperfect steganography, embedding which fails to preserve all statistical properties of covers. They show that, in various situations, capacity of covers grows only with the square root of the available cover size. In a paper given at this conference last year [14], we showed an important caveat: when the sender's and recipient's shared embedding key determines the embedding path, its length must be at least linear in the size of the hidden payload to avoid their enemy exhausting over all possible sets of locations. It was left open to show that a linear key is sufficient.There is no necessity, however, for the recipient to know exactly which locations were changed during the embedding process. In this paper we remove that condition, allowing the embedder to combine more than one cover location to convey one bit of payload. As long as the embedder lives beneath the classic square root law bound, we can do more than prove the sufficiency of a linear key: we can even show that asymptotically perfect steganographic security is possible with no key at all. Furthermore, by computing Steganographic Fisher Information, we can show that the keyless embedding tends to perfect security at least as fast as the "ideal" embedding, which requires an unfeasibly large key to spread payload uniformly at random over the cover. Finally, we show asymptotic perfect security of a simple matrix embedding, which allows payload capacity of order √ n log n to be achieved.

“…In fact, of course, all that is required is for γ to be sufficiently small to ensure that the risk of detection is sufficiently low. Quantifying this, over and above the asymptotic relationship, is a problem related to Steganographic Fisher Information (SFI) [10,11], and a direction for future research. It should not be infeasible to estimate the SFI and hence find a concrete capacity bound, in terms of m n and p, given a KL divergence limit on the risk of detection.…”

Section: Discussionmentioning

confidence: 99%

“…Finally, the theorem does not address the critical case when γ = c/ √ n, in which case the value of c determines a maximum possible detection accuracy. This is arguably the most important situation because it gives the embedder a genuine "secure" capacity for their embedding; this is related to Steganographic Fisher Information which has recently been examined in [10,11]. One other minor limitation is that formalising the embedding as affecting each symbol independently with probability γ is not quite right for embedding a fixed-length message; this is addressed in [5].…”

Section: The Square Root Law For Imperfect Detectorsmentioning

confidence: 99%

The Square Root Law in Stegosystems with Imperfect Information

2010

Information Hiding

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Abstract. Theoretical results about the capacity of stegosystems typically assume that one or both of the adversaries has perfect knowledge of the cover source. So-called perfect steganography is possible if the embedder has this perfect knowledge, and the Square Root Law of capacity applies when the embedder has imperfect knowledge but the detector has perfect knowledge. The epistemology of stegosystems is underdeveloped and these assumptions are sometimes unstated. In this work we consider stegosystems where the detector has imperfect information about the cover source: once the problem is suitably formalized, we show a parallel to the Square Root Law. This answers a question raised by Böhme.