Abstract
We introduce the concept of reliability in watermarking as the ability of assessing that a probability of false alarm is very low and below a given significance level. We propose an iterative and self-adapting algorithm which estimates very low probabilities of error. It performs much quicker and more accurately than a classical Monte Carlo estimator. The article finishes with applications to zero-bit watermarking (probability of false alarm, error exponent), and to probabilistic fingerprinting codes (probability of wrongly accusing a given user, code length estimation).
Highlights
Watermark decoders are in essence stochastic processes
The number of trials n1 is several times bigger than p1−1, while being far less than pf−a1, the order of magnitude of the number of trials needed for a direct Monte Carlo (MC) estimator of the probability of false alarm
This part first applies the method to a well-known watermarking detector for which there exist bounds and a numerical method to derive the probability of false alarm
Summary
Watermark decoders are in essence stochastic processes. There are at least three sources of randomness: the unknown original content (for blind decoders), the unknown hidden message, and the unknown attack the watermarked content has undergone. The output of the decoder is a random variable and this leads to a very disturbing fact: there will be errors in some decoded messages. This holds for watermark detectors which have to take the decision whether the content under scrutiny has been watermarked or not
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