Protection of data using linear programming and fhe technique in cloud computing

International Journal of Information Technology & Management Information System (IJITMIS), ISSN
0976 – 6405(Print), ISSN 0976 – 6413(Online) Volume 4, Issue 1, January – April (2013), © IAEME
24
PROTECTION OF DATA USING LINEAR PROGRAMMING AND FHE
TECHNIQUE IN CLOUD COMPUTING
G.Ashok kumar1,
P.Srinivasulu2
1
Pursuing M. Tech (CSE), 2
Professor&HOD (CSE)
1
QIS college of Engineering and technology, Vengamukkalapalem, ongole, Andhra Pradesh,
India.
2
QIS college of Engineering and technology, Vengamukkalapalem, ongole, Andhra Pradesh,
India.
ABSTRACT
Cloud computing has good services like virtualization. Virtualization provides the
unlimited computational resources. Cloud computing provides robust design with low cost.
Different security constraints are satisfied in outsourcing with the implementation of new
encryption standards. These above services give the reliable solution in secure transmission.
Previous systems cloud environment enables the computational resources are limited
whenever access the resources in outsourcing. These resources utilization are pay per use
manner here. Previous servers have processing storage, memory levels are less. There is no
possibility for encryption complete content. Some content available as a plain text, remaining
content available as a cipher text. This two type’s format content starts the transmission.
Attackers are entering automatically leakage of data problems generate here. That’s why this
type of network comes under insecure. It can deliver the incorrect data in destination. Users
are not satisfies with the help of these services. Security is the primary obstacle that prevents
the wide adoption of this promising computing model, especially for customers when their
confidential data are consumed and produced during the computation.
The above limitations are overcome using the linear programming in cloud
computing. These types of techniques are providing good secure network and optimization
solution. User is ready for transfer the large file to another user. Here large file assume as a
large problem. Using linear programming large files divide into sub parts using
decomposition. Transformation techniques start the allocation of decomposed parts in
different servers. Different servers provide the perfect infrastructure for encryption with
sufficient computational resources. Before starts the outsourcing total content is encrypted in
client side. After deliver the content verifies the proof. Proof it is matched with server proof
then performs the decryption. It’s delivers as a correct data.
INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY &
MANAGEMENT INFORMATION SYSTEM (IJITMIS)
ISSN 0976 – 6405(Print)
ISSN 0976 – 6413(Online)
Volume 4, Issue 1, January – April (2013), pp. 24-30
© IAEME: www.iaeme.com/ijitmis.html
Journal Impact Factor (2013): 5.2372 (Calculated by GISI)
www.jifactor.com
IJITMIS
© I A E M E

25
Keywords: linear programming, cloud computing, encryption techniques, outsourcing
techniques
I. INTRODUCTION
Cloud computing is a comprehensive Internet-based computing solution. The
flexibility of cloud computing is a function of the allocation of resources on demand. While a
traditional computer setup requires you to be in the same location as your data storage device,
the cloud takes away that step .It makes possible for us to access our information from
anywhere at any time. The main concerns voiced by those moving to the cloud are security
and privacy. The companies supplying cloud computing services know this and understand
that without reliable security, their businesses will collapse. So security and privacy are high
priorities for all cloud computing entities. The main focus of this paper is not only to protect
confidential data from various malicious modifications but also to give a proof that the
computed result is correct as per request. For this, linear programming computations are
decomposed into public LP solvers. Here the original LP problem is converted into an
arbitrary problem which helps to protect confidential information’s stored in the cloud and
also facilitates the users with an efficient result verification mechanism. One fundamental
advantage of the cloud paradigm is computation outsourcing; On the one hand, the
outsourced computation workloads often contain sensitive information, such as the business
financial records, proprietary research data, or personally identifiable health information etc.
However, ordinary data encryption techniques in essence prevent cloud from performing any
meaningful operation of the underlying plaintext data, making the computation over
encrypted data a very hard problem. On the other hand, the operational details inside the
cloud are not transparent enough to customers. As a result, there do exist various motivations
for cloud server to behave unfaithfully and to return incorrect results. To protect the sensitive
input and output information of the workloads and to validate the integrity of the computation
result. Based on Yao’s garbled circuits and Gentry’s breakthrough work on fully
homomorphism encryption (FHE) scheme, a general result of secure computation
outsourcing has been shown viable in theory, where the computation is represented by an
encrypted combinational Boolean circuit that allows to be evaluated with encrypted private
inputs. due to the extremely high complexity of FHE operation as well as the pessimistic
circuit sizes that cannot be handled in practice when constructing original and encrypted
circuits. Linear programming is an algorithmic and computational tool which captures the
first order effects of various system parameters that should be optimized, and is essential to
engineering optimization. As LP computations need enough computational power & involve
confidential data, in this paper a mechanism is introduced to decompose the LP computation
outsourcing into public LP solvers running on the cloud and private LP parameters which is
owned by the customer. The first step in this LP problem solving mechanism is to formulate
the private data of the customer into some set of vectors and matrices. This representation
helps us to deploy some set of privacy preserving problem transformation techniques.
In order to validate the computational result, the fact that the result is from cloud
server solving the transferred LP problem can be utilized and along with that the duality
theorem, together with the piece wise construction of auxiliary LP problem is used for
devising some necessary conditions that the correct result should satisfy.

26
II. THE PROPOSED SYSTEM ARCHITECTURE
Fully homomorphic encryption (FHE) scheme, a general result of secure computation
outsourcing has been shown viable in theory, where the computation is represented by an
encrypted combinational Boolean circuit that allows to be evaluated with encryption of their
input to produce an encryption of their output. We also investigate duality theorem and derive
a set of necessary and sufficient condition for result verification. Such a cheating resilience
design can be bundled in the overall mechanism with close-to-zero additional overhead. Both
security analysis and experiment results demonstrate the immediate practicality of the
proposed mechanism.
Duality in linear programming is essentially a unifying theory that develops the
relationships between given linear program and another related linear program stated in terms
of variables with this shadow-price interpretation. The importance of duality is twofold. First,
fully understanding the shadow-price interpretation of the optimal simplex multipliers can
prove very useful in understanding the implications of a particular linear-programming
model. Second, it is often possible to solve the related linear program with the shadow prices
as the variables in place of, or in conjunction with, the original linear program, thereby taking
advantage of some computational efficiency. The importance of duality for computational
procedures will become more apparent in later chapters on network-flow problems and large-
scale systems.
III. AIM OF THE SYSTEM
To enable secure and practical outsourcing of LP under the aforementioned model,
our mechanism design should achieve the following security and performance guarantees.
• Correctness: Any cloud server that faithfully follows the mechanism must produce
an output that can be decrypted and verified successfully by the customer.
• Soundness: No cloud server can generate an incorrect output that can be decrypted
and verified successfully by the customer with non-negligible probability.
• Input/output privacy: No sensitive information from the customer’s private data can
be derived by the cloud server during performing the LP computation.
• Efficiency: The local computations done by customer should be substantially less
than solving the original LP on his own. The computation burden on the cloud server
should be within the comparable time complexity of existing practical algorithms solving
LP problems.

27
IV. ALGORITHM USED
The general working procedure is adopted from a generic approach proposed by R.
Gennaro, C. Gentry,and B. Parno while the instantiation in this paper is completely different.
According to this approach, the process on cloud server can be represented by algorithm
ProofGen and the process on customer can be organized into three algorithms (KeyGen,
ProbEnc, ResultDec).
• KeyGen (1k) → {K}. This is a randomized key generation algorithm which takes a system
security parameter k, and returns a secret key K that is used later by customer to encrypt the
target LP problem.
• ProbEnc (K, _) → {_K}. This algorithm encrypts the input tuple _ into _K with the secret
key K. According to problem transformation, the encrypted input _K has the same form as _,
and thus defines the problem to be solved in the cloud.
• ProofGen (_K) → {(y, )}. This algorithm augments a generic solver that solves the
problem _K to produce both the output y and a proof . The output y later Decrypts to x,
and is used later by the customer to verify the correctness of y or x.
• ResultDec (K, _, y, ) → {x, }. This algorithm may choose to verify either y or x via the
proof . In any case, a correct output x is produced by decrypting y using the secret K. The
algorithm outputs when the validation fails, indicating the cloud server was not
performing the computation faithfully.
The proposed algorithm provides one-time-pad types of flexibility where we should
never use the same secret key K to two different problems. Overall, the basic techniques
would choose a secret key K = (Q, λ, θ) and encrypt the input tuple γ into γk = (A′ ,B′ , b′ ,
θc), which gives reasonable strength of problem input hiding. Also, these techniques are
clearly correct in the sense that solving γk would give the same optimal solution as solving γ.
However, it also implies that although input privacy is achieved, there is no output privacy.
Essentially, it shows that although one can change the constraints to a completely different
form, it is not necessary the feasible region defined by the constraints will change. Therefore,
any secure linear programming mechanism must be able to not only encrypt the constraints
but also to encrypt the feasible region defined by the constraints.
V. RESULT OF FULLY HOMOMORPHISM ENCRYPTION: SECURITY
Homomorphism encryption schemes that are not semantically secured, like basic
RSA, may also have stronger attacks on their one-wayness. A homomorphic encryption (HE)
scheme encrypts data in such a way that computations can be performed on the encrypted
data without knowing the secret key. fully homomorphic encryption schemes is based on
creating a function to perform two atomic operations which will allow the user to build any
kind of circuit. Effectively, any circuit can be built with two atomic functions, namely
addition + and multiplication *. Therefore, to evaluate any circuit, we are only required to be
able to add and multiply over F2 two encrypted bits. Gentry used a simple model. Gentry
defined the two functions f+ and f* which are equivalent to decrypting both encrypted bits,
adding or multiplying such decrypted bits and then encrypting the resulting bits. Hence, it can
remove the first encryption securely to perform the addition or the multiplication. Using such
a technique, Gentry simplified the quest of constructing a fully homomorphic encryption that

28
can evaluate any circuit on encrypted data by finding an encryption system that can evaluate
only some short circuits, namely f+ and f*. that RSA supports multiplications over encrypted
data, i.e., given the encryptions of two messages anyone can compute the encryption of their
product . It turns out that many public-key encryption schemes are homomorphic including
multiplicatively homomorphic to do addition, multiplications and XOR over encrypted data
for a long time and even being able to perform these simple operations has been
tremendously useful
Fig 2. Fully homomorphic encryption model
Protecting FHE with Verifiable Computation cloud will not be able to modify the
computation circuit without be detected. As a result, our attack will be unsuccessful.
However, we argue that in order to use FHE in those models, one must use verifiable
computation all the time. Although the cost of verification is low, to generate the minimum
circuit and to homomorphically modify it is costly. Thus, whether this technique can be used
in practice is doubtful.
VI. ESTIMATING PERFORMANCE
Customer side computation overhead consists of key generation, problem encryption
operation, and result verification, which corresponds to the three algorithms KeyGen,
ProbEnc, and ResultDec, respectively. Because KeyGen and Result-Dec only require a set of
random matrix generation as well as vector-vector and matrix-vector multiplication, the
computation complexity of these two algorithms are upper bounded via O(n2). Thus, it is
straight-forward that the most time consuming operations are the matrix-matrix
multiplications in problem encryption algorithm ProbEnc. Since m ≤ n, the time complexity
for the customer local computation is thus asymptotically the same as matrix-matrix
multiplication.
For cloud server, its only computation overhead is to solve the encrypted LP problem
γk as well as generating the result proof ∂, both of which correspond to the algorithm
ProofGen. If the encrypted LP problem γk belongs to normal case, cloud server just solves it
with the dual optimal solution as the result proof ∂, which is usually readily available in the
current LP solving algorithms and incurs no additional cost for cloud. If the encrypted
problem γk does not have an optimal solution, additional auxiliary LP problems can be solved
to provide a proof. Thus, in all the cases, the computation complexity of the cloud server is
asymptotically the same as to solve a normal LP problem, which usually requires more than
O (n3) time.

29
VII. CONCLUSION & FUTURE GOAL
In this paper, Customers to secretly transform the original LP into some arbitrary one
while protecting sensitive input/output information. Fully homomorphic encryption (FHE)
scheme, a general result of secure computation outsourcing has been shown viable in theory,
where the computation is represented by an encrypted combinational Boolean circuit that allows
to be evaluated with encrypted private inputs we also investigate duality theorem and derive a set
of necessary and sufficient condition for result verification. we show that for any problem γ and
its encrypted version γk, solution µ computed by honest cloud server will always be verified
successfully. This follows directly from the duality theorem of linear programming. Therefore all
conditions derived from duality theorem and auxiliary LP problem construction for result
verification is necessary and sufficient. Similar to correctness argument, the soundness of the
proposed mechanism follows from the facts that the LP problem γ and γk are equivalent to each
other through affine mapping, and all the conditions thereafter for result verification are
necessary and sufficient. In near future a goal is set to work around some interesting concepts
such as to devise robust algorithms to achieve numerical stability; to explore the sparsity structure
of problem for further efficiency improvement; to establish formal security framework; and also
to extend our result to non-linear programming computation outsourcing in cloud.
REFERENCES
[1] M. J. Atallah, K. N. Pantazopoulos, J. R. Rice, and E. H. Spafford,“Secure outsourcing of
scientiﬁc computations,” Advances in Computers,vol. 54, pp. 216–272, 2001.
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review and open problems,” in Proc. of New Security Paradigms Workshop (NSPW), 2001,
pp. 13–22.
[3] S. Goldwasser, Y. T. Kalai, and G. N. Rothblum, “Delegating computation: interactive proofs
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AUTHOR’S PROFILE
G. ASHOK KUMAR Pursuing M.Tech (CSE), QIS College of
Engineering and Technology Vengamukkalapalem, Ongole, Prakasham
Dist, Andhra Pradesh, India. His researches interests include cloud
computing and linear Programming.
P. SRINIVASULU received his B. Tech from Acharya Nagarjuna
University, Guntur, Andhra Pradesh in 1994 and completed post graduation
from Jawaharlal Nehru Technological University, Hyderabad in 1998. He
is received Ph.D from Acharya Nagarjuna University, Guntur and working
as Professor in QIS College of Engineering and Technology, in the
Department of Computer Science and Engineering, Vengamukkalapalem,
Ongole, Prakasham Dist, Andhra Pradesh. His research interests include Data Mining and
Data Warehousing, Computer Networks, Network security and Parallel Computing. He has
more than 16 years of experience in teaching in many subjects, industry and in research. He
is the member of Indian Society of Technical Education (ISTE) and also member of
Computer Society of India (CSI). He has many publications in National and International
conferences.

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