Toward Practical Joint Decoding of Binary Tardos Fingerprinting Codes

Abstract

The class of joint decoder in fingerprinting codes is of utmost importance in theoretical papers to establish the concept of fingerprint capacity. However, no implementation supporting a large user base is known to date. This paper presents an iterative decoder which is the first attempt toward practical large-scale joint decoding. The discriminative feature of the scores benefits on one hand from the side-information of previously found users, and on the other hand, from recently introduced universal linear decoders for compound channels. Neither the code construction nor the decoder makes assumptions about the collusion size and strategy, provided it is a memoryless and fair attack. The extension to incorporate soft outputs from the watermarking layer is straightforward. An extensive experimental work benchmarks the very good performance and offers a clear comparison with previous state-of-the-art decoders.

Decoding fingerprints using the Markov Chain Monte Carlo method

“…The first topic uses theoretical arguments to fine-tune the code construction [2], [3]. Our paper has no contribution on this side: we use the classical code construction originally proposed by Tardos in [1] for benchmarking, WIFS'2012, December, [2][3][4][5]2012, Tenerife, Spain. 978-1-4673-2287-4/12/ $31.00 c 2012 IEEE.…”

“…Some decoders compute a score per user, which is provably good whatever the collusion strategy, whereas others algorithms first estimate the collusion attack and adapt their scoring function. This paper pertains to this 'Learn and Match' trend [5]. Last but not least, information theory tells us that a joint decoder considering groups of users is potentially more powerful than a single decoder computing a score per user.…”

“…If we consider groups of e people among n users, then we need to browse n e = O(n e ) such groups, which is not tractable for a large database of users. The approach first proposed in [6] for pair decoding and generalized for bigger subsets in [5] is an iterative decoder. The iteration t considers subsets of t users, which are taken from a small pool of most likely colluders of size n t .…”

“…Another point is that the scoring function used in [5] is not optimal for three reasons. The scoring is based on the likelihood that a group of users are all guilty, whereas it should be the likelihood that some of them are guilty.…”

Challenging Differential Privacy:The Case of Non-interactive Mechanisms

“…This score is computed by taking into account L symbols but the complexity of a joint decoder is proportional to |P| (i.e., O(N c )), which is computationally expensive. Yet, there exists at least three possible approaches that approximate joint decoding with a reasonable complexity: 1) Monte Carlo Markov Chain (MCMC) [19,20], 2) Belief Propagation Decoder [21] and 3) Joint Iterative Decoder [22].…”