Subset selection circumvents the square root law

Scott Craver; Jun Yu

doi:10.1117/12.839168

27 January 2010 Subset selection circumvents the square root law

Scott Craver, Jun Yu

Proceedings Volume 7541, Media Forensics and Security II; 754103 (2010) https://doi.org/10.1117/12.839168
Event: IS&T/SPIE Electronic Imaging, 2010, San Jose, California, United States

Abstract

The square root law holds that acceptable embedding rate is sublinear in the cover size, specifically O(square root of n), in order to prevent detection as the warden's data and thus detector power increases. One way to transcend this law, at least in the i.i.d.case, is to restrict the cover to a chosen subset whose distribution is close to that of altered data. Embedding is then performed on this subset; this replaces the problem of finding a small enough subset to evade detection with the problem of finding a large enough subset that possesses a desired type distribution. We show that one can find such a subset of size asymptotically proportional to n rather than the square root of n. This works in the case of both replacement and tampering: Even if the distribution of tampered data depends on the distribution of cover data, one can find a fixed point in the probability simplex such that cover data of that distribution yields stego data of the same distribution. While the transmission of a subset is not allowed, this is no impediment: wet paper codes can be used, else in the worst case a maximal desirable subset can be computed from the cover by both sender and receiver without communication of side information.

Citation Download Citation

Scott Craver and Jun Yu "Subset selection circumvents the square root law", Proc. SPIE 7541, Media Forensics and Security II, 754103 (27 January 2010); https://doi.org/10.1117/12.839168

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