Secure Outsourcing of Linear Programming in Cloud Computing Environment: A Review

Shephali Singh .et.al. Int. Journal of Engineering Research and Application www.ijera.com
ISSN : 2248-9622, Vol. 7, Issue 4, ( Part -6) April 2017, pp.64-68
www.ijera.com DOI: 10.9790/9622-0704066468 64 | P a g e
Secure Outsourcing of Linear Programming in Cloud Computing
Environment: A Review
Shephali Singh1
,Puneet Sharma2
,Dr. Deepak Arora3
Department of Computer Science & Engineering, Amity University, Lucknow
ABSTRACT
Cloud computing provides immense computing power with reduced cost. User can outsource their vast
computational work to the cloud and use massive computational power, storage, software, network etc. Despite
all these benefits there are still few obstacles in cloud computing regarding confidentiality and integrity of data.
Outsourcing and computation compromises the security of data being stored on cloud computing. Considering
cloud as insecure platform a system must be designed that protects data by encryption and as well as produces
correct result without any cheating resilience with the help of result verification. In this paper, we study the
secure outsourcing and computation of linear programming by capturing the effects of arguments which are of
first order and that provides practical efficiency. To achieve efficiency linear programming conditions are
implemented. The LP computation are done explicitly decomposing LP problem that are run on cloud. The
parameters of LPare owned by the customer. For validating the obtained output of computation, we use duality
theorem of linear programming that derives the required condition that the result must fulfil.
Keywords: Cloud Computing, Data Security, Duality theorem, Linear Programming and Outsourcing.
I. INTRODUCTION
On demand network access is provided by
cloud computing such as computing resources and
storage of data with more efficiency and less
management overhead. The cloud computing has
advantage of computational outsourcing where the
strength of user is not restrained to its resources or
devices. The outsourcing of workloads into cloud
provides customer huge computing resources
without huge investments in hardware or software
purchase. With all these advantages comes the
concern of security of cloud platform. The main
concern is with the security of data stored in cloud.
The outsourced data may contain crucial
information such as financial records, research
data, military information, personal records etc.
The leakage or modification of these data may lead
to inevitable changes or problems.
To protect the data outsourced on cloud,
encryption of sensitive data must be done. Before
outsourcing the data should be encrypted so as to
maintain confidentiality of data stored in cloud.
Other than encryption, the cloud itself is sometimes
not very faithful which may lead to incorrect
results. Though it is possible that software bugs,
hardware failure or even outsider attack may
decrease the result quality. From the viewpoint of
customer the cloud is insecure. It would be difficult
for customer to give their workin control of cloud
from the local machine without the assurance of
security of their data i.e. to save valuable I/P and
O/P information and verify the correctness of
result.Cryptographic and computer recent
researches have lead to advancement in “safe
outsourcing costly computations” (e.g. [1]-[5]).
The working of secure computation in cloud has
been found to be feasible in theory [6] by Yao’s
garbled circuits [7] and Gentry’s research work on
fully homomorphic encryption (FHE) algorithm [8]
that represents the computation on Boolean circuit
as the combination of encryption that can be
assessed with the help of inputs that are encrypted.
But using this method will be not so practical due
to high complexity and large Boolean circuits.
Other outsourcing computation method include
sequence comparison, matrix multiplication etc. It
is still hard to apply them practically in large
problems. In these heavy cloud side cryptography
computation [3], complexity related to
communication [8] are involved.
Here we look into effective methods of
outsourcing computations of linear programming
safely [9]. However ordinary encryption techniques
does not allow cloud to perform any operations of
the plaintext data, making it difficult to perform
computation over encrypted data. Linear
programming works on algorithm that finds the
first order effect of different parameters of system
that must give optimal solution to increase
efficiency. Its usage is in routing of packets, flow
control of network, data centres power
management etc. [10]. Since linear programming
problem requires lot computational resources and it
involves very sensitive data that is why it is
RESEARCH ARTICLE OPEN ACCESS

Olawale Simon O. A.et.al. Int. Journal of Engineering Research and Application www.ijera.com
decomposed and outsourced into LP problem
solvers that are public and executing on cloud and
LP parameters that are of customers and are
private. Vectors and matrices are used to transform
LP problems of customer. This transformations
makes privacy preserving techniques such as
matrix multiplication and affine mapping easily
applicable. This allows insecure input and output
data to be safe and secure. Other than this, the
duality theorem along with bit by bit formation of
LP problem derives basic conditions that are
required to be correct to satisfy the result. This
method to validate the result is very effective and
has very less appended overhead on the customer
cloud as well as server cloud.
Figure. 1: Pictorial representation of secure
outsourcing and computation of LP problem in
Cloud.
II. L
ITERATURE SURVEY
Researcher Gennaro et al. [5] has shown
literary working of secure computation
outsourcing. He has shown feasibility of input and
output privacy maintenance as well as correctness
and soundness of the result. However, it is not
practically sound method due to high computing
complexity. Later Atallah et al. did a list of works
[1] [3] [4] [8] for secure outsourcing computation.
The set of techniques used were string matching,
linear algebra, sorting etc. However, these
mechanism were not very efficient in securing
input and output information and did not confirmed
correctness of result, which is the main concern in
secure computation on cloud. Atallah et al. [3] [4]
gave two protocols later that were used for secure
sequence outsourcing and algebraic computation
outsourcing. Since these two protocols used
burdened cryptography algorithm like
homomorphic encryption [11]. Thus were not very
successful for large problem set due to huge
complexity. Based on above concept, Hohenberger
[2] defined secure outsourcing protocol of modular
exponentiation, which was taken to be a public key
cryptography method that was very expensive.
Latest, Atallah [8] et al. presented a safe
protocol based on secret key concept for secure
outsourcing that used matrix multiplication [12].
This mechanism performed very well due to
assumption of only one server and computation
effectiveness. The only lacking point is lot of
overhead because of message passing. Concluding,
these methods are still not efficient enough for
secure LP outsourcing computation.
Safe multiparty working was given by
Yao [6]. Two or more parties are allowed to
execute functions for obtaining result along with
preserving their input from each other. Result is
computed along with hiding the input from both the
parties individually. Basic SMC is efficient, Du and
Atallah et al. gave customized solution under SMC
context for problem such as scientific computation,
sequence comparison, statistical analysis etc. [13].
Though applying these concepts directly to the
cloud is problematic. The computational power of
customer and cloud was not similar which could
not be handled effectively, which is avoided in the
given design by shifting all computational load to
cloud only. The other problem is security
asymmetry because no party alone knows all
problem input, leading to difficulty in result
validation.
In SMC, Li and Atallah [14] gave a
solution to the participating parties to applyadditive
split of constraint matrix along with few
cryptographic techniquesthat are executed in each
step of simplex algorithm. The above method does
show practical performance for big size problem
and does not guarantee optimal solution. With the
same method, Toft [15] gave a secret key sharing
secure simplex algorithm that had less complexity
than other protocols. In [16], Vaidya formulated a
new improved simplex algorithm that worked on
safe scalar product and protocol comparisons.
Lately, Catrina et al. [17] gave a safe multiparty LP
using fixed point arithmetic. Some other works are
of Du [18] and Vaidya [19] who studies
distinguished approaches of matrix based
transformation to look inti privacy preserving
linear programming. Later, Bednarz et al. [20]
proved Du’s and Vaidya’s approach infeasible and
proposed to use permutation matrices. Recently,
Mangasarian gave two privacy protecting methods
of linear programming on vertical [21] and
horizontal divided [22] constraints
matrix.Although, many techniques were proposed
but all had computation asymmetry issues.
Cloud computing is not a very trustworthy
platform. It may behave unfaithfully during
computation which may lead to incorrect

computation of result without the knowledge of the
customer. Detecting this is not an easy task that
when the data is being modified in cloud which
results in incorrect computation outsourcing.
Verifiable computation delegation has found huge
interest in theoretical computer science
communities where weak customers can find out
the correctness of computational result with the
help of powerful but not trusted servers with the
use of very less resources.Some of latest results and
outcome is specified by Glodwasser et al. [23].
Golle et al. [24], to defeat the untrusted servers
presented the idea to append pre-calculated results
along with the computation. In [25], Szada et al.
further worked on ringer scheme to defeat servers
that cannot be trusted.In [26] Du. Et al. gave a
mechanism for grid computing to find the cheating
done in outsourcing computation. Based on Merkle
tree the servers gives a commitment on the result
computed by it. This commitment is then used by
the customer followed by a sampling technique to
do result verification.
The above schemes looks into data and the
computed result by it that is prohibited in cloud
computing for security and safety of data. Thus it
becomes tough task to provide result verification as
well as input/output privacy. The introduction of
concept of duality of LP problem efficiently
performs the result validation, appending some
overhead on customer server as well as cloud
server.
Cong Wang [9], recently, gave an efficient
and feasible method for securely outsourcing linear
programming that will protect input/output and also
find cheating servers. The data that are outsourced
contains very insecure information such as medical
history, financial details, research related works
etc. To protect these important data and ensure its
confidentiality it is encrypted before being
outsourced to the cloud for computation. On the
other hand, the details of computation is not
transparent to user so there exists chances of cloud
to behave unfaithfully and produce wrong output.
Fully homomorphism encryption(FHE) scheme,
has been shown feasible in theory for secure
computation outsourcing
Computation outsourcing involves two
different parts, cloud customer and cloud server.
Cloud customer outsources LP problems to cloud
server for computation. The cloud server has huge
computing resources such as memory, storage and
processing power. The customer sends its LP
problem to CS after encrypting it with a secret key.
The CS then computes the solution with the help of
public LP solver running on the cloud and also
produces a correctness proof. The customer on
receiving the result verifies the result with the
appended proof and then decrypt the result. The
algorithm [27] is as follows:
 KeyGen( ) {K}. It generates secret key K
as an output on taking input the parameter k.
This key K is used by the customer to perform
encryption.
 ProbEnc(K,ɸ) { }. This step functions to
encrypt the input, tuple ɸ into , using the
secret key K.
 ProofGen( ) {y,Γ}. This algorithm
provides solution of the LP problem to give
the output or result y and proof Γ.
 ResultDec(K,ɸ,y,Γ) {x, }. Later the
algorithm checks either x or y with the given
proof Γ. The x is obtained by decrypting the
output y with the help of secret key K. The
output is returned if correctness of output is
not proved, that means the cloud has been
compromised.
Table 1: Comparison between different
mechanisms of secure outsourcing in cloud
computing.

III. PERFORMANCE OVERVIEW
With respect to the mechanism of LP,
computation on side of customer consist of three
algorithm such as KeyGen, ProbEnc and
ResultDec. The complexity or overhead of
computation is of generation of key, encryption
operation and verification of result. The KeyGen
and ResultDec algorithm consist of generation of
random matrix along with multiplication of vector-
vector and matrix vector. O( ) is the complexity
of these two methods. The maximum time is
consumed by matrix-matrix multiplication in
ProbEnc algorithm. In cubic time method is used
for matrix multiplication with the complexity of
O( ). Other efficient methods are Strassen’s
algorithm [28] and Coppersmith Winograd
algorithm [29] having complexity of O( ) and
O( ) respectively.
The cloud server has to compute ProofGen
algorithm that consist of solving LP problem_K
that has been encrypted by the customer and
computing the proof of result. If the problem_K is
of normal case then the encrypted LP problem_K is
solved with duality theorem to find optimal
solution as the proof of result. The result proof is
given in LP solving problem, thus no extra
computation is required. In other case, an extra
auxiliary LP problem_K does not has optimal
solution. The LP is always computed at starting to
find out the practical solution, thus it incurs an
extra overhead.
Therefore in most of the cases, the
complexity of computation is similar i.e. O( )
[30], same as in case of normal LP problem.
Therefore, the more computation is performed on
cloud which provides customer huge computation
savings.
IV. ADVANTAGES AND
DISADVANTAGES
One of the most important advantage is
computational resources, the customer enjoys
resources of cloud server by outsourcing the
problem for computation. This saves capital
investment of customer in hardware and software.
It provides feature of correctness and soundness as
the mechanism decrypts the output and verifies the
result. Checks that if cloud has performed
unfaithfully. Computing original LP by itself is
more than the computation performed by customer.
The computation overhead on CS is in the
comparable time complexity of other practical
algorithm of LP problems.
The / [27], cloud efficiency,
representing total overhead of the computation
provides more than 30x savings.
Two different entities are involved in computation
outsourcing architecture, one is customer cloud and
the other is cloud server (CS) [9] [27]. The cloud
customer has a very huge amount of sensitive and
costly LP problems for being computed and
outsourced and the cloud server has enough
computing resources that provide computing
services like public LP solvers.
V. CONCLUSION
Cloud computing has been proved to
provide a lot of computation resources at less
expenses. It provides user with limited resources to
outsource their work or problem on cloud for
computation which has ample amount of resources
such as processing power, storage, bandwidth etc.
Although, cloud provides too many benefits but
security is a primary concern. The customer should
be able to trust the cloud for their sensitive and
confidential data being computed. Considering
cloud as not a secure platform, a mechanism must
be designed that not only protects user data but also
ensures that result being computed is correct and
verified.
This paper investigates about secure
outsourcing and computation of LP problem. To
attain efficiency LP problem is decomposed into
public LP solvers. These solvers run on cloud. The
resulting flexibility provides to find significant
security and efficiency trade off with help of higher
level abstraction of LP computation than the
general circuit level. The transformation of LP
problem in set of matrices and vector provides to
apply privacy preserving technique that helps to
change initial LP problem to an auxiliary one along
with preserving insecure input/output operation.
For verifying the computed output, fundamental
duality theorem of linear programming is explored
and necessary condition ae derived that should
satisfy the results correctness. Tending-to-zero
overhead is done by the mechanism on whole. The
main function of this mechanism is that, along with
security of data it also gives means to validate the
data and the result.
REFERENCES
[1]. M. J. Atallah, K.N. Pantazopoulos, J.R.
Rice, and E.H. Spafford, “Secure
Outsourcing of scientific computations”,
Adv. Comput., vol.54,pp. 216-272, 2001.
[2]. S. Hohenberger and A. Lysyanskaya,
“How to securely outsource cryptographic
computation”, in Proc. 2nd
Int. Conf.
Theory Cryptography, 2005, pp. 264-282.
[3]. M.J. Atallah and J. Li., “Secure
outsourcing of sequence comparisons,” in
Int. I. Inf. Sec., vol. 4, no. 4, pp. 277-287,
2005.

[4]. D. Benjamin and M.J. Atallah, “Private
and cheating-free outsourcing of algebraic
computation,” in Proc. Int. Conf. Privacy,
Secur., Trust, 2008, pp. 240-245.
[5]. R. Gennaro, C. Gentry, and B. Parno,
“Non-interactive verifiable computing:
Outsourcing computation to untrusted
workers,” in Proc. 30th
Annu. Conf. Adv.
Cryptol., Aug. 2010, pp. 465-482.
[6]. A. C.-C. Yao, “Protocols for secure
computations (extended abstract),” in
Proc. of FOCS, 1982, pp. 160–164.
[7]. C. Gentry, “Fully homomorphic
encryption using ideal lattices,” in Proc of
STOC, 2009, pp. 169–178.
[8]. M. Atallah and K. Frikken, “Securely
outsourcing linear algebra computations,”
in Proc. of ASIACCS, 2010, pp. 48–59.
[9]. Cong Wang, Kui Ren, and Jia Wang,
“Secure and Practical Outsourcing of
Linear Programming in Cloud
Computing”, IEEE, 2011, pp. 820-821.
[10]. D. Luenberger and Y. Ye, Linear and
Nonlinear Programming, 3rd ed. Springer,
2008.
[11]. P. Paillier, “Public-key cryptosystems
based on composite degree residuosity
classes,” in Proc. 17th Int. Conf. Theory
Appl. Cryptographic Tech., 1999, pp.
223–238.
[12]. A. Shamir, “How to share a secret,”
Commun. ACM, vol. 22, no. 11, pp. 612–
613, 1979.
[13]. W.Du and M. J. Atallah, “Secure multi-
party computation problems and their
applications: A review and open
problems,” in Proc. New Secur. Paradigms
Workshop, 2001, pp. 13–22.
[14]. J. Li and M. J. Atallah, “Secure and
private collaborative linear programming,”
in Proc. Int. Conf. Collaborative Comput.,
2006, pp. 1–8.
[15]. T. Toft, “Solving linear programs using
multiparty computation,” in Proc. 13th Int.
Conf. Financial Cryptography Data
Security, 2009, pp. 90–107.
[16]. J. Vaidya, “A secure revised simplex
algorithm for privacy-preserving linear
programming,” in Proc. IEEE Int. Conf.
Adv. Inf. Netw. Appl., 2009, pp. 347–354.
[17]. O. Catrina and S. De Hoogh, “Secure
multiparty linear programming using
ﬁxed-point arithmetic,” in Proc. 15th Eur.
Conf. Res. Comput. Security, 2010, pp.
134–150.
[18]. W. Du, “A study of several speciﬁc secure
two-party computation problems,” Ph.D.
dissertation, Comput. Sci. Dept., Purdue
Univ., West Lafayette, IN, USA, 2001.
[19]. J. Vaidya, “Privacy-preserving linear
programming,” in Proc. 24th ACM Symp.
Appl. Comput., 2009, pp. 2002–2007.
[20]. A. Bednarz, N. Bean, and M. Roughan,
“Hiccups on the road to privacy-
preserving linear programming,” in Proc.
ACM Workshop Privacy Electron. Soc.,
2009, pp. 117–120.
[21]. O. L. Mangasarian, “Privacy-preserving
linear programming,” Optim. Lett., vol. 5,
pp. 165–172, 2011.
[22]. O. L. Mangasarian, “Privacy-preserving
horizontally partitioned linear programs,”
Optim. Lett., vol. 6, no. 3, pp. 431–436,
2012.
[23]. S. Goldwasser, Y. Kalai, and G.
Rothblum, “Delegating computation:
interactive proofs for muggles,” in Proc.
40th Annu. ACM Symp. Theory Comput.,
2008, pp. 113–122.
[24]. P. Golle and I. Mironov, “Uncheatable
distributed computations,” in Proc. Conf.
Topics Cryptol.: The Cryptographer’s
Track RSA, 2001, pp. 425–440.
[25]. D. Szajda, B. G. Lawson, and J. Owen,
“Hardening functions for large scale
distributed computations,” in Proc. IEEE
Symp. Secur. Privacy, 2003, pp. 216–224.
[26]. D. Szajda, B. G. Lawson, and J. Owen,
“Hardening functions for large scale
distributed computations,” in Proc. IEEE
Symp. Secur. Privacy, 2003, pp. 216–224.
[27]. Cong Wang, Kui Ren, and Jia Wang,
“Secure Optimization Computation
Outsourcing in Cloud Computing: A Case
Study of Linear Programming”, in IEEE
transactions on computers, vol. 65, No. 1,
January 2016, pp. 219.
[28]. V. Strassen, “Gaussian elimination is not
optimal,” Numer. Math., vol. 13, pp. 354–
356, 1969.
[29]. D. Coppersmith and S. Winograd, “Matrix
multiplication via arithmetic
progressions,” in Proc. 19th Annu. ACM
Symp. Theory Comput., 1987, pp. 1–6.
[30]. D. Luenberger and Y. Ye, Linear and
Nonlinear Programming, 3rd ed. New
York, NY, USA: Springer, 2008.

Secure Outsourcing of Linear Programming in Cloud Computing Environment: A Review

More Related Content

What's hot (14)

Similar to Secure Outsourcing of Linear Programming in Cloud Computing Environment: A Review (20)

Recently uploaded (20)

Secure Outsourcing of Linear Programming in Cloud Computing Environment: A Review