Graph-structured Watermarking using Bitonic Sequences of Self-inverting Permutations

Mpanti, Anna; Nikolopoulos, Stavros D.

doi:10.1145/3003733.3003741

Cited by 5 publications

(3 citation statements)

References 13 publications

(37 reference statements)

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“…Recently, Mpanti and Nikololopoulos proposed two different reducible permutation flow-graphs, namely, F s [π * ] and F t [π * ], incorporating important structural properties which are derived from the bitonic subsequences forming the self-inverting permutation π * [19].…”

Section: Graph-based Software Watermarkingmentioning

confidence: 99%

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Characterizing Watermark Numbers encoded as Reducible Permutation Graphs against Malicious Attacks

Mpanti,

Nikolopoulos,

Palios

2018

Preprint

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In the domain of software watermarking, we have proposed several graph theoretic watermarking codec systems for encoding watermark numbers w as reducible permutation flowgraphs F [π * ] through the use of self-inverting permutations π * . Following up on our proposed methods, we theoretically study the oldest one, which we call W-RPG, in order to investigate and prove its resilience to edge-modification attacks on the flow-graphs F [π * ]. In particular, we characterize the integer w ≡ π * as strong or weak watermark through the structure of self-inverting permutations π * which encodes it. To this end, for any integer watermarkwhere n is the length of the binary representation b(w) of w, we compute the minimum number of 01-modifications needed to be applied on b(w) so that the resulting b(w ′ ) represents the valid watermark number w ′ ; note that a number w ′ is called valid (or, true-incorrect watermark number) if w ′ can be produced by the W-RPG codec system and, thus, it incorporates all the structural properties of π * ≡ w.

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Section: Graph-based Software Watermarkingmentioning

confidence: 99%

“…while the last two algorithms incorporate important properties which are derived from the bitonic subsequences composing the self-inverting permutation π * [19]. We have also presented efficient decoding algorithms which efficiently extract the number w from the four reducible permutation graphs F [π * ].…”

Section: Introductionmentioning

confidence: 99%

Characterizing Watermark Numbers encoded as Reducible Permutation Graphs against Malicious Attacks

Mpanti,

Nikolopoulos,

Palios

2018

Preprint

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“…The first dynamic watermarking algorithm (CT) was proposed by Collberg and Thomborson [10]; it embeds the watermark through a graph structure which is built on a heap at runtime. Recently, authors of this paper have contributed in this area by proposing several codec and embex systems [3][4][5]23].…”

Section: Introductionmentioning

confidence: 99%

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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Software Watermarking: Progress and Challenges

2018

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Graph-structured Watermarking using Bitonic Sequences of Self-inverting Permutations

Cited by 5 publications

References 13 publications

Characterizing Watermark Numbers encoded as Reducible Permutation Graphs against Malicious Attacks

Characterizing Watermark Numbers encoded as Reducible Permutation Graphs against Malicious Attacks

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

Software Watermarking: Progress and Challenges

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