By Nicholas J Hopper
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Extra info for Provably Secure Steganography
In a ﬁngerprinting scheme, each watermarked copy is slightly diﬀerent, hence, malicious users will collect t copies D1 , . . , Dt with respective watermark X 1 , . . , X t in order to remove/alter the watermark. A simple, yet eﬀective way is to average them because when t copies are averaged, D∗ = (D1 + . . + Dt )/t, the similarity value calculated by Eq. (1) results in shrinking by a factor of t, √ which will be roughly n/t . Even in this case, we can detect the embedded watermark and identify the colluders by using an appropriately designed threshold.
4) approximate to that of non-watermarked components, which is an ideal estimation. In 2 , which accuracy will be a basic scheme, all components are used to calculate σm degraded by the watermarked components. In order to exclude such components eﬃciently, Eq. (4) is applied in our optimized scheme. The results are shown in Table 2. It is certiﬁed that the optimized scheme can obtain proper variances, hence thresholds can be designed based on the statistical property. 2 0 -40 -20 0 0 20 40 60 80 100 120 the size DCT coefficient (a) Detection sequence dˆ0.
Fig. 26 dB. (a) Original image (b) Watermarked image α0 = α1 = 500 Fig. 5. 2 Evaluation of Statistical Property In our scheme, we set a threshold based on the statistical property of the distribution of each detection sequence. In order to examine the property, we ﬁrst show the histogram of detection sequence dˆ0 and dˆ1 in Fig. 6 (a) and (b), respectively. In the simulation, watermarked images are averaged by 10 colluders with random groups and performed JPEG compression with quality 35 %. We set the watermark strength α0 = α1 = 500, and evaluate the performance using randomly selected 103 patterns of user ID.
Provably Secure Steganography by Nicholas J Hopper