Maria Chroni

Encoding watermark integers as self-inverting permutations

In a software watermarking environment, several graph theoretic watermark methods use integers as watermark values, where some of these methods encode the watermark integers as reducible permutation graphs (RPG; these are reducible control-flow graphs with a maximum out-degree of two). Since there is a one-to-one correspondence between self-inverting permutations and isomorphic classes of RPGs, for encoding watermark integers most of the watermarking methods use only those permutations that are self-inverting. In this paper we present an efficient algorithm for encoding integers as self-inverting permutations. More precisely, our algorithm takes as input an integer w, computes its binary representation b1b2...bn, and then produces a self-inverting permutation π* in O(n) time. Moreover, we also present an algorithm for decoding a self-inverting permutation; our algorithm takes as input a self-inverting permutation π* produced by the encoding algorithm and returns its corresponding integer w in O(n) time, where n is the length of the input permutation.

An Efficient Graph Codec System for Software Watermarking

In this paper we propose an efficient and easily implemented codec system for encoding watermark numbers as reducible permutation flow-graphs. More precisely, in light of our recent encoding algorithms which encode a watermark value w as a self-inverting permutation π*, we present an efficient algorithm which encodes a self-inverting permutation π* as a reducible permutation flow-graph F[π*] by exploiting domination relations on the elements of π* and using an efficient DAG representation of π*. The whole encoding process takes O(n) time and space, where n is the binary size of the number w or, equivalently, the number of elements of the permutation π*. We also propose efficient decoding algorithms which extract the permutation π* from the reducible permutation flow-graph F[π*] within the same time and space complexity. The two main components of our proposed codec system, i.e., the self-inverting permutation π* and the reducible permutation graph F[π*], incorporate important structural properties which make our codec system resilient to attacks.

Encoding watermark numbers as cographs using self-inverting permutations

In a software watermarking environment, several graph theoretic watermark methods encode the watermark values as graph structures and embed them in application programs. In this paper we extended the class of graphs which can be efficiently used in a software watermarking system by proposing an efficient codec system, i.e., encoding and decoding algorithms that embed/extract watermark values into/from cographs through the use of self-inverting permutations. More precisely, we present a codec system which takes as input an integer ω as watermark value, converts it into a self-inverting permutation π*, and then encodes the permutation π* as a cograph. The main property of our codec system is its ability to encode the same integer ω, using a self-inverting permutation π*, into more than one cograph. This property causes our system to be resilient to attacks since it can embed multiple copies of the same watermark number ω into an application program. Moreover, the proposed codec system has low time complexity and can be easily implemented.

An Embedding Graph-based Model for Software Watermarking

In a software watermarking environment, several graph theoretic watermark methods encode the watermark values as graph structures and embed them in application programs. In this paper we first present an efficient codec system for encoding a watermark number w as a reducible permutation graph F[π*] through the use of the self-inverting permutation π* which encodes the number w and, then, we propose a method for embedding the watermark graph F[π*] into a program P. The main idea behind the proposed embedding method is a systematic use of appropriate calls of specific functions of the program P. That is, our method embeds the graph F[π*] into P using only real functions and thus the size of the watermarked program P* remains very small. Moreover, the proposed codec system has low time complexity, can be easily implemented, and incorporates such properties which cause it resilient to attacks.

Multiple encoding of a watermark number into reducible permutation graphs using cotrees

Software watermarking involves embedding a unique identifier, i.e., a watermark value, within a software to discourage software theft; to this end, several graph theoretic watermark methods encode the watermark values as graph structures and embed them in application programs using a wide range of algorithmic techniques. In this paper we propose an efficient method for encoding the same watermark value into several different graphs, we call it multiple encoding, answering thus the question we have recently left open. In particular, we propose an efficient algorithm which embed a cograph G[π*] into a reducible permutation graph F[π*] by first computing the cotree of G[π*] then computing a rooted binary tree having specific node-value and child-parent properties, and finally, based on these properties, producing a reducible permutation graph F[π*]. In light of our recent encoding algorithms which encode a watermark value w as a self-inverting permutation π* and the permutation π* into several cographs G1[π*], G2[π*],...,Gn[π*], we conclude that we can efficiently encode the same watermark value w into several reducible permutation graphs F1[π*], F2[π*],..., Fn[π*], n ≥ 2. This property causes a codec watermarking system resilient to attacks since we can embed multiple copies of the same watermark value w into an application program. We also propose decoding algorithms which efficiently extract the watermark value w from the reducible permutation graph F[π*].

Encoding numbers into reducible permutation graphs using heap-ordered trees

Information hiding is widely used in almost all intelligence and security software systems as a standard technology to prevent piracy and copyright infringement. This technology mainly involves the idea of digital watermarking where a unique identifier (or, watermark number) is embedded into software, image, audio, or video data through the introduction of errors not detectable by human perception. In software watermarking, the proposed graph theoretic methods usually encode watermark numbers as graphs whose structure resembles that of real program graphs. In this paper, in light of our recently published algorithms which encode a watermark number w as a self-inverting permutation, we present an efficient encoding method, along with its corresponding decoding one, which embeds a self-inverting permutation π* into reducible permutation graphs F[π*]. More precisely, we present an encoding algorithm which embeds the permutation π* into F[π*] by first computing the heap-ordered tree of π* (i.e., a rooted binary tree having specific node-value and child-parent properties) using the lattice representation of π* and then, based on the heap node-value properties, producing a reducible permutation graph F[π*]. Moreover, we exploit the max-heap and min-heap representation tree of permutation π* and show that we can efficiently encode the same watermark w into two different reducible permutation graphs F1[π*] and F2[π*]. In general, such a property increases the safety performance of a watermarking system against attacks since it can embed multiple copies of the same watermark value w into a digital object.

Evaluating the WaterRpg software watermarking model on Java application programs

Recently, we have presented a dynamic watermarking model, which we named WaterRpg, for embedding a reducible permutation graph <i>F</i>[<i>π</i>*] into an application program <i>P</i>. The main idea behind the proposed watermarking model is to modify the dynamic call-graph <i>G</i>(<i>P</i>, <i>I</i>_<i>key</i>) of the program <i>P</i>, taken by the specific input <i>I</i>_<i>key</i>, so that the dynamic call-graph <i>G</i>(<i>P</i>*, <i>I</i>_<i>key</i>) of the resulting watermarked program <i>P</i>* and the the reducible permutation graph <i>F</i>[<i>π</i>*] are isomorphic; within this idea the program <i>P</i>* is produced by only altering appropriate calls of specific functions of the input application program <i>P</i>. Our model belongs to execution trace watermarks category. In this paper, we implement our WaterRpg watermarking model on several Java application programs and evaluate it under various criteria in order to gain information about its practical behavior. More precisely, we selected a number of Java application programs and watermark them using two main watermarking approaches supported by our WaterRpg model, namely naive and stealthy approachs. The experimental results show the stable functionality of all the Java programs <i>P</i>* watermarked under both the naive and stealthy cases. The experiments also show that the watermarking approaches supported by our model can help develop efficient watermarked Java programs with respect to resilience, size, time, space, and other watermarking metrics.

An experimental study of stability in heterogeneous networks

A distinguishing feature of todays large-scale communication networks, such as the Internet, is their heterogeneity, predominantly manifested by the fact that a wide variety of communication protocols are simultaneously running over different network hosts. A fundamental question that naturally poses itself for such common settings of heterogeneous networks concerns their ability to preserve the number of packets in the system upper bounded at all times. This property is well-known as stability. We focus on the Adversarial Queueing Theory framework, where an adversary controls the rates of packet injections and determines packet paths. In this work, we present specific network constructions with different protocol compositions and we show experimentally their stability behavior under an adversarilly strategy. In particular, we study compositions of universally stable protocols with unstable protocols like FIFO. Interestingly, some of our results indicate that such a composition leads to a worst stability behavior than having a single unstable protocol for contention-resolution. This suggests that the potential for instability incurred by the composition of one universally stable protocol with one unstable protocol may be worse than that of some single protocol.

Watermarking PDF Documents using Various Representations of Self-inverting Permutations

This work provides to web users copyright protection of their Portable Document Format (PDF) documents by proposing efficient and easily implementable techniques for PDF watermarking; our techniques are based on the ideas of our recently proposed watermarking techniques for software, image, and audio, expanding thus the digital objects that can be efficiently watermarked through the use of self-inverting permutations. In particular, we present various representations of a self-inverting permutation

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

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