Towards a Provably Resilient Scheme for Graph-Based Watermarking

Bento, Lucila M. S.; Boccardo, Davidson R.; Machado, Raphael C. S.; Sá, Vinícius Gusmão Pereira de; Szwarcfiter, Jayme Luiz

doi:10.1007/978-3-642-45043-3_6

Cited by 9 publications

(23 citation statements)

References 12 publications

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“…, S i−1 }. For example, the increasing subsequences of the permutation π = (5,6,2,8,1,9,7,4,3) are S 1 = (5,6,8,9), S 2 = (2, 7) since π ′ = π\S 1 = (2, 1, 7, 4, 3), S 3 = (1, 4), and S 4 = (3), while its decreasing subsequences are S 1 = (5, 2, 1), S 2 = (6, 4, 3), S 3 = (8, 7), and S 4 = (9).…”

Section: Preliminariesmentioning

confidence: 99%

“…if the element i d-dominates the element j in π * ; (iii) we create two dummy vertices s = v n * +1 and t = v 0 and we add them both in V (D[π * ]); then, we add in E(D[π * ]) the directed edge (s, v i ) for every v i with indegree equal to 0, and the edge (v j , t) for every v j with outdegree equal to 0. Figure 3 depicts the graph D[π * ] of the permutation π * = (5,6,9,8,1,2,7,4,3). Note that, by construction, i > j for every directed edge (v i , v j ) of D[π * ] since the element i d-dominates the element j in π * .…”

Section: Codec Algorithms For Phase Sip-rpgmentioning

confidence: 99%

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Encoding watermark numbers as reducible permutation graphs using self-inverting permutations

Chroni

Nikolopoulos

Palios

2018

Discrete Applied Mathematics

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Several graph theoretic watermark methods have been proposed to encode numbers as graph structures in software watermarking environments. In this paper we propose an efficient and easily implementable codec system for encoding watermark numbers as reducible permutation flow-graphs and, thus, we extend the class of graphs used in such a watermarking environment. More precisely, we present an algorithm for encoding a watermark number w as a self-inverting permutation π * , an algorithm for encoding the self-inverting permutation π * into a reducible permutation graph F [π * ] whose structure resembles the structure of real program graphs, as well as decoding algorithms which extract the permutation π * from the reducible permutation graph F [π * ] and the number w from π * . Both the encoding and the decoding process takes time and space linear in the length of the binary representation of w. The two main components of our proposed codec system, i.e., the self-inverting permutation π * and the reducible permutation graph F [π * ], incorporate the binary representation of the watermark w in their structure and possess important structural properties, which make our system resilient to attacks; to this end, we experimentally evaluated our system under edge modification attacks on the graph F [π * ] and the results show that we can detect such attacks with high probability.

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Section: Preliminariesmentioning

confidence: 99%

Section: Codec Algorithms For Phase Sip-rpgmentioning

confidence: 99%

Encoding watermark numbers as reducible permutation graphs using self-inverting permutations

Chroni

Nikolopoulos

Palios

2018

Discrete Applied Mathematics

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“…We start with this basic version to better understand each proposed modification, and we evolve to the final protocol step by step after considering several possible attack models. Concretely, Alice, a software developer, generates a large number of equivalent versions of the same softwarewhich can be achieved via the use of software diversity tools-and each version is distinctly watermaked by Alice-using an watermarking scheme at choice, such as the ones in [36] and references thereby. …”

Section: Initial Fingerprinting Protocol Based On Oblivious Transfermentioning

confidence: 99%

“…To avoid this attack, the arbitrator must verify that Alice, in fact, generated α artifacts with distinct fingerprints. A recent work about the generation and verification of distinct fingerprints based on a randomized graph-based scheme can be found in [36].…”

Section: Fingerprinting Protocol With Guarantee Of Distinct Fingerprintsmentioning

confidence: 99%

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Software control and intellectual property protection in cyber-physical systems

Machado

Boccardo

Sá

et al. 2016

EURASIP J. on Info. Security

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Software control is a critical issue in cyber-physical systems (CPS); if the expected behavior of the software embedded in a single device of a CPS cannot be enforced then the behavior of the whole CPS may be in jeopardy. Thus, CPS stakeholders like having some level of control over the embedded software. Third-party demands to control the software, however, conflict with the intellectual property protection demanded by software developers, since some level of detail about the software at hand would have to be disclosed. In the present paper, we discuss the issue of controlling the software embedded in CPS devices and address the problem of how to achieve an increased level of software control without compromising the protection of intellectual property. We propose a two-party fingerprinting scheme that allows for attribution of responsibility in the case of intellectual property leaks. Our fingerprinting scheme is such that neither party may obtain an advantage over the other by misbehaving, misrepresenting or by prematurely aborting the protocol, therefore providing a fair means to resolve disputes.

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Models and Algorithms for Graph Watermarking

Eppstein

Goodrich

Lam

et al. 2016

Lecture Notes in Computer Science

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We introduce models and algorithmic foundations for graph watermarking. Our frameworks include security definitions and proofs, as well as characterizations when graph watermarking is algorithmically feasible, in spite of the fact that the general problem is NP-complete by simple reductions from the subgraph isomorphism or graph edit distance problems. In the digital watermarking of many types of files, an implicit step in the recovery of a watermark is the mapping of individual pieces of data, such as image pixels or movie frames, from one object to another. In graphs, this step corresponds to approximately matching vertices of one graph to another based on graph invariants such as vertex degree. Our approach is based on characterizing the feasibility of graph watermarking in terms of keygen, marking, and identification functions defined over graph families with known distributions. We demonstrate the strength of this approach with exemplary watermarking schemes for two random graph models, the classic Erdős-Rényi model and a random power-law graph model, both of which are used to model real-world networks.

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Towards a Provably Resilient Scheme for Graph-Based Watermarking

Cited by 9 publications

References 12 publications

Encoding watermark numbers as reducible permutation graphs using self-inverting permutations

Encoding watermark numbers as reducible permutation graphs using self-inverting permutations

Software control and intellectual property protection in cyber-physical systems

Models and Algorithms for Graph Watermarking

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