encoding constants in watermarking graph

7/27/2019 Encoding constants in Watermarking graph

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Encoding constants in Watermarking Structure

A Graph-based Software Watermarking Technique

Riya Rajan

Computer Science and Engineering DepartmentCollege of Engineering SNGIST

Ernakulam, Kerala

[email protected]

Jyothimon C

Computer Science and Engineering DepartmentCollege of Engineering SNGIST

Ernakulam, Kerala

[email protected]

AbstractSoftware watermarking technique embeds an

identification mark, i.e. a watermark value within software to

discourage software theft. There are several graph theoretic

watermarking techniques which encode the watermark values as

graph structures and this graph structure is embedded in

application programs. In this paper we propose an efficient

algorithm which encodes both constants in the program and

watermark value in a graph called Reducible Permutation

Graph. Since both watermark value and constants in theprogram are encoded in a single graph structure, any

modification on this graph will lead to execution failure. This

property causes the watermarking system resilient to attacks.

Moreover, our encoding and decoding algorithm have low time

complexity and can be easily implemented.

Keywords- Software watermarking, Watermark value,

encoding, Reducible Permutation Graph, Self Inverting

Permutation.

INTRODUCTION

Development in Internet Technology, wide spread

use of peer-to-peer resource sharing technology, software

products are spreading faster. A survey conducted by BusinessSoftware Alliance [1] shows that more than 41% of software

using worldwide are pirated.

To protect intellectual property rights of software

products become a serious challenge to the software industry.

Software Watermarking is a technique to prevent or

discourage software piracy and copyright infringement.

This paper is structured as follows. In section 2, we

describe the formal definition of graph based software

watermarking. Preliminary section will be discussed in section

3. Different models of attacks that can occur in graph based

watermarking algorithms are expressed in section 4.

We propose an algorithm which effectively

overcomes the previously mentioned attacks is discussed insection 5. In section 6, we conclude by discussing the main

advantages of our proposed algorithm.

SOFTWARE WATERMARKING

Software Watermarking

Software Watermarking can be described as the

problem of embedding a structure w into a program P such

that w can be reliably located and extracted from P even after

P has be subjected to code transformations. Precisely, given aprogram P, a watermark w, a key k, the software

watermarking problem can be described by the following two

functions:

embed( P, w, k) P and

extract( P, k ) w.

A. Classification of Watermarking algorithmsWatermarking algorithms can be generally divided

into static algorithms and dynamic algorithms [2,3,4]. A

watermark is stored inside a program code in a certain format,

and it does not change during the program execution is called

static software watermarking. A dynamic watermark isbuiltduring program execution, perhaps only after a particularsequence of input.

According to the representation of

watermark information there are two types of static

watermarks: data watermarks and code watermarks. Data

watermark stores watermark information as program data, and

can be stored anywhere inside a program, such as in comments

or in variables. A code watermark is represented by choosing

particular sequence of instructions has an equivalent effect.

There are three dynamic watermarking techniques [2]: Easter

Egg Watermarking, Execution Trace Watermarking and

Dynamic Data Structure Watermarking.

B. Characteristics of a good watermarking algorithmsDate rate, stealth, and resilience are the

characteristics of software watermarking [2]. The data rate

expresses the quantity of hidden data that can be embedded

within the cover message. The stealth expresses how

imperceptible the embedded data is to an observer, and the

resilience express the hidden messages degree of immunity to

attack by an adversary [10,11,12].

Identify applicable sponsor/s here. (sponsors)


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C.Attacks against WatermarksA successful attack against the watermarked program

Pw prevents the recognizer from extracting the watermark

while not seriously harming the performances or correctness

of the program Pw. Attacks against software watermarks can

be classified into subtractive attacks, distortive attacks and

additive attacks. A subtractive attack is one where the attacker,perhaps with some tool support, tries to locate and remove the

watermark. If the attacker cannot locate the watermark and is

willing accept some degradation in quality of watermarked

program, he can apply distortive transformations uniformly

over the watermarked program is known as distortive attacks.

An additive attack is one where the attacker inserts his own

watermark in an attempt to override owners watermark, or at

least make it plausible that the owners watermark was not

inserted before the attackers [5,6,7].

We can classify the most relevant existing software

watermarking techniques as Graph-based software

watermarking, register based software watermarking, thread

based software watermarking, obfuscation based softwarewatermarking, branch based software watermarking, program

slicing based software watermarking and abstract

interpretation based software watermarking[6,7,12,13]. In this

paper we propose a graph based software watermarking

algorithm in which constants used in the programs and

watermark information are encoded into a graph called

Reducible Permutation Graph. This graph is embedded into

the graph. Hence any modification in the graph will destroy

the proper execution of the program.

GRAPH BASED SOFTWARE WATERMARKING

There are several software watermarking algorithms have been

proposed that encode watermarks as graph structures [9, 10,

11]. In general, such encoding make use of an encoding

function encode which converts a watermarking number w

into a graph G, Encode(w)G and also a decoding function

decode that convert the graph G into the number w,

decode(G)w.

We usually call the pair (encode, decode) as graph

codec. From a graph theoretic point of view we are looking for

a class of graph G and corresponding codec.

(encode, decode)G.Collberg and Thomborson[2,4] proposed the first dynamic

graph watermarking scheme CT to overcome problems with

static watermarking schemes. Static watermarks are highly

fragile and therefore susceptible to semantics preservingtransformation attacks. Dynamic graph watermarking schemes

are similar to static graph watermarking except the graph is

built at run-time.

Preliminaries

This section describes an efficient and easily implemented

algorithm for encoding numbers as reducible permutation

graphs through the use of self-inverting permutations. This

section also gives some basic definitions required for

understanding how to produce a self inverting permutation

from a watermark value. An algorithm for converting

watermark value W to Self inverting permutation and the

reverse process proposed by Maria Chroni and Nikolopolos

[14,15] is described. They also presented an algorithms for

embedding the reducible permutation graphs into the program

code and explains how we can extracts the reducible

permutation graphs from the program code.

We consider finite graphs with no multiple edges. Fora graph G, we denote V (G) and E (G) the vertex set and edge

set of G, respectively. Next they introduce some definitions

that are key-objects in our algorithms for encoding numbers as

graphs. Let be a permutation over the set N n=1, 2, 3,,n.

We think of permutation as a sequence (1, 2, 3, n).

Definition 1:

The inverse of a permutation (1, 2, 3, n) is the

permutation (q1,q2,,qn) with qi=qi. A self inverting

permutation is a permutation that is its own inverse: i = i. By

definition, every permutation has a unique inverse, and the

inverse of the inverse is the original permutation. Clearly, a

permutation is a self-inverting permutation if and only if all its

cycles are of length 1 or 2; hereafter, we shall denote a 2-cycleas c = (x, y) and an 1-cycle as c(x), or, equivalently, c = (x, x).

Definition 2:

Let C1,2={c1=(x1, y1), c2=(x2 ,y2),, ck=(xk ,yk)} be the

set of all the cycles of a self-inverting permutation such that

xi < yi (1


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ENCODING CONSTANTS IN WATERMARKING STRUCTURE

A program consists of n number of functions or

objects. These functions or objects are the real block of

programs having some unique properties with respect to the

program requirements. Constants are usual in most of the

program code which actually decide the proper execution in

most of the time. We use this property of constants in our new

Watermarking technique.

Suppose P is the program consists of n number offunctions or objects and C1,C2,...,Cn are the constants

collected. We select one constant from a function. If there is

more than one constant, select one. If there is no constants add

any constant. W is the value of the watermark to be encoded

and B is the binary representation of W. Suppose p is the

number of bits needed to represent W in binary. The or SIP

have 2p+1 bits. Select 2p+1 constant from Program P.

Suppose C = C1,C2,...Cm are the constants collected

from the program P and W is the watermark value and k is the

key used to extract the Watermark value. We also use the

algorithm Encode W to SIP and Encode RP G from SIP

proposed by Maria Chroni et al. for encoding the watermark

value W to Self Inverting Permutation and ReduciblePermutation Graph from Self Inverting Permutation. RP G 0 is

the new form after encoding the constants into RP G. We

embed the new graph RP G 0 into the program. The algorithm

for encoding both constants C and Watermark W is explained

in this section.

Algorithm computing Constants from Program

Suppose C consists of series or sequence of constants C1, C2,

, Cm collected from the program P having n functions or

objects (where m


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the value of the constant corresponding to RPG. A memory

location which holds the starting location of the reducible

permutation graph is represented by 'start'. k is the sequence

from which the decoding start.

This algorithm uses property of graph traversal

algorithm hence if there are n number of nodes in the graph

the maximum time taken to execute the algorithm is O(n). The

algorithm does not take any extra space other than to store the

graph of n nodes. So the space complexity is also O(n).

Algorithm to Extract W from RPG

We know that RPG is encoded graph of constants C,

hence to produce the RP G is the primary objective to extract

the watermark. We use the key value k to extract the

watermark which is inserted by the owner to prove ownership

mark. The inputs of the algorithm are RPGand W. Both RPG

and RPGdo not have any structural difference other than the

node values.

If n is the number of nodes in the reducible

permutation graph RPG'. Then O(n) is the time complexity to

replace n node values. Both the algorithm decode SIP from

RPG and Decode W from SIP takes O(n) time and space

respectively. Hence O(n) is the time complexity of above

algorithm.

IMPLEMENTATION AND RESULTS

All software watermarking algorithms need an

embedder to embed the watermark code in to the program

structure and a recognizer to recognize the watermark that we

encoded either in the program code or in a separate section

other than the program code which helps the user to locate the

watermark. We can find out or compute the number of

constants in the program either by manual cross check or with

a separate program for locating the constants.

The Reducible Permutation Graph have error

correcting properties which means that small modification onthe graph does not affect the graph from executing the

watermark value. Hence their algorithm is more efficient when

it compares with other graph based algorithms. Removal of a

node or some edges would seriously affect extraction of

watermark difficult. In the newly proposed algorithm we

proposed a technique to encode both watermark value and

constants in the program into graph called reducible

permutation graph. Even though we encode constants and

watermark value into a single graph, the property of the

reducible graph does not change. Because we do not make any

modification on the graph structure but only the node values

changed.

Next we would like check the correctness of the

algorithm. We have seen that the simply collects the constants

from the program. Then Reducible Permutation graph is

generated with a watermark value the correctness of the

algorithm is already proven. We compute the factors of the

least common multiples of the constant sequence which is a

simple arithmetic computation done to compute the algorithm.

There are algorithms which helps us to find the least common

factors of constants which is a simple computation. These

factors are supplied to the Reducible permutation graph. A

simple replacement procedure is carried out here to replace the

node values. Which is also a graph traversal algorithm. Hence

the algorithm always produce a RPG' which is an encoded

form of constants and watermark value.

CONCLUSION

We succeeded in developing the method of encoding a

sequence of numbers in an encoded watermarking graph. We

achieved double encoding of numbers. This is an entirely new

concept in software watermarking. Our algorithm's e

efficiency depends on the graph we select to encode multiple

sequences of values. The algorithm extract the constants

without harming the graph structure which is very simple


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compared to other methods. But we can use the similar

technique used in the extraction of watermark value in

extracting the constant. Then the algorithm produces more

stealth we leave it as a problem to investigate in future, we

also leave as problem that to and a graph where we can do

double encoding of sequence of values in the graph structure.

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encoding constants in watermarking graph

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