This paper proposes a new compressive sensing based method for simultaneous data compression and convergent encryption for secure deduplication to efficiently use for the cloud storage. It performs signal acquisition, its compression and encryption at the same time. The measurement matrix is generated using a hash key and is exploited for encryption. It seems that it is very suitable for the cloud model considering both the data security and the storage efficiently.

1. Compressive Sensing Based Simultaneous Data
Compression and Convergent Encryption for
Secure Deduplication
M. Tanooj Kumar Dr. M. Babu Reddy
Research Scholar Assistant Professor
Department of Computer Science Department of Computer Science
Krishna University Krishna University
Machilipatnam, India Machilipatnam, India
Abstract -- This paper proposes a new compressive
sensing based method for simultaneous data
compression and convergent encryption for secure
deduplication to efficiently use for the cloud storage. It
performs signal acquisition, its compression and
encryption at the same time. The measurement matrix
is generated using a hash key and is exploited for
encryption. It seems that it is very suitable for the cloud
model considering both the data security and the
storage efficiently.
Keywords –Convergent Encryption, Compressive Sensing,
Sparsity, Measurement Matrix, Deduplication, Cloud
storage.
I.INTRODUCTION
Enterprises, Organizations and Individuals
outsource data storage to cloud storage because of its
less maintenance, accessibility, disaster recovery and
cost savings. A survey [1] publishes that nearly 75%
of our digital world is a copy - in other words, solely
25% is unique. Keeping it in view, most of the Cloud
Storage Providers (CSP’s) have taken up the data de-
duplication, a way that avoids the storage of single
data copy multiple times. Several data deduplication
schemes have been proposed by the researchers [2]
show how data deduplication minimizes redundant
data and maximize space savings.
To outsource data optimally and securely,
the data is compressed and encrypted. Conventional
cryptography is not suitable with data de-duplication.
In conventional cryptography, users will encrypt /
decrypt the data with their individual keys. If
conventional cryptography is used, identical data
copies {of totally different or of various} users can
create different cipher-texts, causes the data de-
duplication impossible. To resolve this problem, most
of the researchers use Convergent Encryption [3] to
produce identical cipher text from identical plaintext.
The major difficulty with the existing
compression and encryption methods is the
performance and the complexity of using two
different processes [4, 5, 6]. To resolve the problem,
a new compressive sensing based method is proposed
for simultaneous data compression and convergent
encryption for secure de-duplication, which is useful
for effective utilization of cloud storage. This method
International Journal of Computer Science and Information Security (IJCSIS),
Vol. 15, No. 9, September 2017
144 https://sites.google.com/site/ijcsis/
ISSN 1947-5500

2. performs both encryption and compression at the
same time and decreases the processing time.
The reminder of this paper is as following.
Section 2 provides background; Section 3 gives the
design and implementation of our deduplication
framework; Section 4 evaluates the implementation;
and, finally, we mention conclusion in Section 5.
II. BACKGROUND
A) Convergent Encryption
In convergent Encryption, any user derives
the convergent key from the data and encrypts the
data with the key derived. By applying this
technique, two users with same plain texts will obtain
the same cipher text because the encryption key is the
same; hence the CSP will be able to perform de-
duplication on such cipher texts. Furthermore, Users
need not interact with each other for establishing an
agreement on the key because the key is generated
deterministically and users have to retain and protect
the encryption keys. Therefore, convergent
encryption becomes a good and efficient technique
for the selection of encryption and deduplication in
the cloud storage [6].
B) Compressive sensing (CS)
In compressive sensing, the input signal (x)
with N samples is converted into some domain (DCT,
DFT etc.), in which the signal(x) has sparse
representation, produces K-sparse signal. Where K is
the largest coefficients, which contains the large
portion of information about the signal, obtained
using thresolding. Finally,to produce the compressed
and encrypted signal, M-length measurement matrix,
the K-sparse signal is multiplied with sensing matrix
(Φ).
On the other side, different optimization techniques
are used for rebuilding the original signal. First
multiply the signal with sensing matrix, which gives
N samples from M measurements. Then K-sparse
signal is recovered by using convex optimization
techniques. Once again apply inverse scarcity to get
the original signal.
C) Chaotic Measurement Matrix
Chaotic sequence is used to construct the
measurement matrix, which has been proved to as
Toeplitz-structured and sufficient to satisfy Restricted
Isometry Property (RIP) with high probability.The
definitionof logistic map is
Xn+1 = μ xn(1_xn); xn ε (0,1) (1)
It becomes chaotic when μ ε [3.57, 4].
III. PROPOSED SYSTEM
The main aim of designing this system is to
introduce a simple simultaneous compression and
convergent encryption technique for optimized cloud
storage based on compressive sensing. In this
algorithm sampling, compression and encryption can
be done at the same time.
Assume that User selects a file to store it in
the cloud storage. The content of the file (message) is
changed into digital signal (x) utilizing extended
ASCII code. This accomplishes a 1D digital signal. If
the message is too long, it is divided to smaller
blocks (segments) which are encrypted separately.
Compute the hash value of the message by using
SHA-512 algorithm. If the file is not sufficiently
sparse, user uses some suitable basis (Ψ) to “sparsify”
its representation. Use hash value as key to generates
pseudo-random Chaotic measurement matrix Φ
(Hash key serves as a seed for Chaotic pseudo-
International Journal of Computer Science and Information Security (IJCSIS),
Vol. 15, No. 9, September 2017
145 https://sites.google.com/site/ijcsis/
ISSN 1947-5500

3. random number generator; using this generator, a
sequence of pseudo-random numbers is generated
and this sequence forms the columns of the
measurement matrix).
The Simultaneous Compression-Convergent
Encrypted signal is produced by multiplying the
sparse signal (x) with a random chaotic measurement
matrix (Φ). The resultant signal has a lower
dimension than initial sparse signal. Mathematically,
the compressed-encrypted signal (y) is given by y=Φ
x. The signal thus obtained is not sparse. The
resultant signal (y) is sent to the server. It is
important to note that the random matrix (Φ), which
acts as secret key,is not sent along with the cipher
text. The proposed method is shown in Algorithm1.
Algorithm 1: CS based Convergent
Encryption
Input: File Selected
Output: File Uploaded to Cloud
Procedure: CS based Convergent Encryption
begin CS-Based-Convergent-Encryption
/* select file to upload */
Sparse representation of the file (content) of
order N x1
Generate Hash value of the file (content)
Generate µ of chaotic based on Hash Value
Generate Chaotic Measurement Matrix of order
M x N
Multiply chaotic measurement matrix with
sparse representation of file (content)
Develop an M-dimensional measurement vector
end
Whenever user requests the same fie, user has to
perform decompress-decrypt the message.
Decryption of the message is done by using a greedy
algorithm (either orthogonal matching pursuit
(OMP), or matching pursuit (MP), or greedy LS etc.)
or convex relaxation algorithm (basis pursuit (BP))
with the following: random matrix encryption (Φ),
the encrypted message (the cipher text) Y, and the
base for sparsity Ψ. Any extremely small decryption
error can be corrected by rounding the decrypted
values to the nearest integer values because extended
ASCII code is built from integers.
IV. EXPERIMENTAL RESULTS
This part shows simple examples of simultaneous
compression–convergent encryption based on
compressed sensing. Let assume that the message of
the text file is
TOTO JE TAJNY VZKAZ PRO BOBA
(The message is in Czech with the meaning “This is a
secret message for Bob”). After assigning the
Extended ASCII code to each character in the
message, The binary code forms a vector of length
216; 81 vector elements are non-zero so this vector
has relative sparsity 0.375. It was checked
experimentally that measurement matrix (generated
with secret key) must have at least compression ratio
0:8 (i. e. matrix size 173 x 216) for successful
reconstruction of message.
V. CONCLUSIONS
This paper presents a possibility of using
compressed sensing for simultaneous compression
International Journal of Computer Science and Information Security (IJCSIS),
Vol. 15, No. 9, September 2017
146 https://sites.google.com/site/ijcsis/
ISSN 1947-5500

4. and convergent encryption. Chaotic Measurement
matrix (in CS) is generated according to the hash key
and it is used also for convergent encryption. Results
show that this algorithm can provide good security
and compression performance.
REFERENCES
[1] I.D. Corporation, The digital universe – are you
ready? Online 2010.
[2] Wen Xia., Hong jiang, Dan Feng et al., A
comprehensive study of the past, present, and future
of data deduplication, Proceedings of IEEE, Vol. No
104(9), (2016).
[3] Madhuri Kavade, A.C. Lomte, Secure De-
dulication using convergent keys (convergent
cryptography) for cloud storage., International
Journal of computer Applications, Vol. 126(10),
(2015).
[4] Adrain, Monica Fira, Marius Daniel, Compressed
sensing based Encryption approach for tax forms
data, International Journal of Advanced Research in
Artificial Intelligence, Vol. 4(11), (2015).
[5] Nanrun Zhou, Aidi Zhang, Fen Zheng, Lihua
Gong, Novel image compression-encryption hybrid
algorithm based on Key-controlled measurement
matrix in compressive sensing, Optics & Laser
Technology, Vol. 62, (2014).
[6] Wang et al., Simultaneous encryption and
compression of medical images based on optimized
tensor compressed sensing, Bio Med Engg. online
(2016).
AUTHOR PROFILES
M. Tanooj Kumar is presently
pursuing Ph.D from Krishna
University, working as Assistant
professor in Department of CSE, K. L.
University, Vaddeswaram. His Research interest
includes Internet of Things, Information security and
privacy. He is a member of IETE.
Dr. M. Babu Reddy, Assistant
Professor and Head of the Department
(I/C), Department of Computer
Science, Krishna University,
Macilipatnam. Completed his Ph.D in CSE from
Acharya Nagarjuna University. His Research Interest
includes Software Engineering, Data Mining, Neural
Networks and Machine Learning. He is a member of
IEEE, CSI, ISTE and African Computational Society.
International Journal of Computer Science and Information Security (IJCSIS),
Vol. 15, No. 9, September 2017
147 https://sites.google.com/site/ijcsis/
ISSN 1947-5500