Secure distributed deduplication systems

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1
Secure Distributed Deduplication Systems with
Improved Reliability
Jin Li, Xiaofeng Chen, Xinyi Huang, Shaohua Tang and Yang Xiang Senior Member, IEEE and
Mohammad Mehedi Hassan Member, IEEE and Abdulhameed Alelaiwi Member, IEEE
Abstract—Data deduplication is a technique for eliminating duplicate copies of data, and has been widely used in cloud storage to
reduce storage space and upload bandwidth. However, there is only one copy for each file stored in cloud even if such a file is owned
by a huge number of users. As a result, deduplication system improves storage utilization while reducing reliability. Furthermore,
the challenge of privacy for sensitive data also arises when they are outsourced by users to cloud. Aiming to address the above
security challenges, this paper makes the first attempt to formalize the notion of distributed reliable deduplication system. We propose
new distributed deduplication systems with higher reliability in which the data chunks are distributed across multiple cloud servers.
The security requirements of data confidentiality and tag consistency are also achieved by introducing a deterministic secret sharing
scheme in distributed storage systems, instead of using convergent encryption as in previous deduplication systems. Security analysis
demonstrates that our deduplication systems are secure in terms of the definitions specified in the proposed security model. As a proof
of concept, we implement the proposed systems and demonstrate that the incurred overhead is very limited in realistic environments.
Keywords—Deduplication, distributed storage system, reliability, secret sharing
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1 INTRODUCTION
With the explosive growth of digital data, deduplication
techniques are widely employed to backup data and
minimize network and storage overhead by detecting
and eliminating redundancy among data. Instead of
keeping multiple data copies with the same content,
deduplication eliminates redundant data by keeping
only one physical copy and referring other redundant
data to that copy. Deduplication has received much
attention from both academia and industry because it
can greatly improves storage utilization and save storage
space, especially for the applications with high dedupli-
cation ratio such as archival storage systems.
A number of deduplication systems have been pro-
posed based on various deduplication strategies such
as client-side or server-side deduplications, file-level or
block-level deduplications. A brief review is given in
Section 6. Especially, with the advent of cloud storage,
data deduplication techniques become more attractive
and critical for the management of ever-increasing vol-
umes of data in cloud storage services which motivates
enterprises and organizations to outsource data storage
• Jin Li is with the School of Computer Science, Guangzhou University,
China, e-mail: lijin@gzhu.edu.cn.
• Xiaofeng Chen is with the State Key Laboratory of Integrated
Service Networks (ISN), Xidian University, Xi’an, China, e-mail:
xfchen@xidian.edu.cn.
• Xinyi Huang is with the School of Mathematics and Computer Science,
Fujian Normal University, China, e-mail: xyhuang81@gmail.com.
• Shaohua Tang is with the Department of Computer Science, South China
University of Technology, China, e-mail: shtang@ieee.org.
• Yang Xiang is with the School of Information Technology, Deakin Univer-
sity, Australia, e-mail: yang@deakin.edu.au.
• M. M. Hassan, A. Alelaiwi are with College of Computer and Information
Sciences, King Saud University, Riyadh, Saudi Arabia.
to third-party cloud providers, as evidenced by many
real-life case studies [1]. According to the analysis report
of IDC, the volume of data in the world is expected
to reach 40 trillion gigabytes in 2020 [2]. Today’s com-
mercial cloud storage services, such as Dropbox, Google
Drive and Mozy, have been applying deduplication to
save the network bandwidth and the storage cost with
client-side deduplication.
There are two types of deduplication in terms of
the size: (i) file-level deduplication, which discovers re-
dundancies between different files and removes these
redundancies to reduce capacity demands, and (ii) block-
level deduplication, which discovers and removes redun-
dancies between data blocks. The file can be divided into
smaller fixed-size or variable-size blocks. Using fixed-
size blocks simplifies the computations of block bound-
aries, while using variable-size blocks (e.g., based on
Rabin fingerprinting [3]) provides better deduplication
efficiency.
Though deduplication technique can save the storage
space for the cloud storage service providers, it reduces
the reliability of the system. Data reliability is actually
a very critical issue in a deduplication storage system
because there is only one copy for each file stored in
the server shared by all the owners. If such a shared
file/chunk was lost, a disproportionately large amount
of data becomes inaccessible because of the unavailabil-
ity of all the files that share this file/chunk. If the value
of a chunk were measured in terms of the amount of file
data that would be lost in case of losing a single chunk,
then the amount of user data lost when a chunk in the
storage system is corrupted grows with the number of
the commonality of the chunk. Thus, how to guarantee
high data reliability in deduplication system is a critical
For More Details Contact G.Venkat Rao
PVR TECHNOLOGIES 8143271457

2
problem. Most of the previous deduplication systems
have only been considered in a single-server setting.
However, as lots of deduplication systems and cloud
storage systems are intended by users and applications
for higher reliability, especially in archival storage sys-
tems where data are critical and should be preserved
over long time periods. This requires that the dedupli-
cation storage systems provide reliability comparable to
other high-available systems.
Furthermore, the challenge for data privacy also arises
as more and more sensitive data are being outsourced
by users to cloud. Encryption mechanisms have usu-
ally been utilized to protect the confidentiality before
outsourcing data into cloud. Most commercial storage
service provider are reluctant to apply encryption over
the data because it makes deduplication impossible. The
reason is that the traditional encryption mechanisms,
including public key encryption and symmetric key
encryption, require different users to encrypt their data
with their own keys. As a result, identical data copies
of different users will lead to different ciphertexts. To
solve the problems of confidentiality and deduplication,
the notion of convergent encryption [4] has been pro-
posed and widely adopted to enforce data confidentiality
while realizing deduplication. However, these systems
achieved confidentiality of outsourced data at the cost
of decreased error resilience. Therefore, how to protect
both confidentiality and reliability while achieving dedu-
plication in a cloud storage system is still a challenge.
1.1 Our Contributions
In this paper, we show how to design secure deduplica-
tion systems with higher reliability in cloud computing.
We introduce the distributed cloud storage servers into
deduplication systems to provide better fault tolerance.
To further protect data confidentiality, the secret sharing
technique is utilized, which is also compatible with the
distributed storage systems. In more details, a file is
first split and encoded into fragments by using the
technique of secret sharing, instead of encryption mech-
anisms. These shares will be distributed across multiple
independent storage servers. Furthermore, to support
deduplication, a short cryptographic hash value of the
content will also be computed and sent to each storage
server as the fingerprint of the fragment stored at each
server. Only the data owner who first uploads the data
is required to compute and distribute such secret shares,
while all following users who own the same data copy
do not need to compute and store these shares any more.
To recover data copies, users must access a minimum
number of storage servers through authentication and
obtain the secret shares to reconstruct the data. In other
words, the secret shares of data will only be accessible by
the authorized users who own the corresponding data
copy.
Another distinguishing feature of our proposal is that
data integrity, including tag consistency, can be achieved.
The traditional deduplication methods cannot be directly
extended and applied in distributed and multi-server
systems. To explain further, if the same short value is
stored at a different cloud storage server to support
a duplicate check by using a traditional deduplication
method, it cannot resist the collusion attack launched
by multiple servers. In other words, any of the servers
can obtain shares of the data stored at the other servers
with the same short value as proof of ownership. Fur-
thermore, the tag consistency, which was first formalized
by [5] to prevent the duplicate/ciphertext replacement
attack, is considered in our protocol. In more details, it
prevents a user from uploading a maliciously-generated
ciphertext such that its tag is the same with another
honestly-generated ciphertext. To achieve this, a deter-
ministic secret sharing method has been formalized and
utilized. To our knowledge, no existing work on secure
deduplication can properly address the reliability and
tag consistency problem in distributed storage systems.
This paper makes the following contributions.
• Four new secure deduplication systems are pro-
posed to provide efficient deduplication with high
reliability for file-level and block-level deduplica-
tion, respectively. The secret splitting technique, in-
stead of traditional encryption methods, is utilized
to protect data confidentiality. Specifically, data are
split into fragments by using secure secret shar-
ing schemes and stored at different servers. Our
proposed constructions support both file-level and
block-level deduplications.
• Security analysis demonstrates that the proposed
deduplication systems are secure in terms of the def-
initions specified in the proposed security model. In
more details, confidentiality, reliability and integrity
can be achieved in our proposed system. Two kinds
of collusion attacks are considered in our solutions.
These are the collusion attack on the data and the
collusion attack against servers. In particular, the
data remains secure even if the adversary controls
a limited number of storage servers.
• We implement our deduplication systems using the
Ramp secret sharing scheme that enables high re-
liability and confidentiality levels. Our evaluation
results demonstrate that the new proposed con-
structions are efficient and the redundancies are
optimized and comparable with the other storage
system supporting the same level of reliability.
1.2 Organization
This paper is organized as follows. In Section 2, we
present the system model and security requirements
of deduplication. Our constructions are presented in
Section 3 and Section 4. The security analysis is given in
Section 5. The implementation and evaluation are shown
in Sections 6, and related work is described in Section 7.
Finally, we draw our conclusions in Section 8.

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2 PROBLEM FORMULATION
2.1 System Model
This section is devoted to the definitions of the system
model and security threats. Two kinds entities will be
involved in this deduplication system, including the user
and the storage cloud service provider (S-CSP). Both
client-side deduplication and server-side deduplication
are supported in our system to save the bandwidth for
data uploading and storage space for data storing.
• User. The user is an entity that wants to outsource
data storage to the S-CSP and access the data later.
In a storage system supporting deduplication, the
user only uploads unique data but does not upload
any duplicate data to save the upload bandwidth.
Furthermore, the fault tolerance is required by users
in the system to provide higher reliability.
• S-CSP. The S-CSP is an entity that provides the
outsourcing data storage service for the users. In
the deduplication system, when users own and store
the same content, the S-CSP will only store a single
copy of these files and retain only unique data.
A deduplication technique, on the other hand, can
reduce the storage cost at the server side and save
the upload bandwidth at the user side. For fault
tolerance and confidentiality of data storage, we
consider a quorum of S-CSPs, each being an inde-
pendent entity. The user data is distributed across
multiple S-CSPs.
We deploy our deduplication mechanism in both file
and block levels. Specifically, to upload a file, a user
first performs the file-level duplicate check. If the file
is a duplicate, then all its blocks must be duplicates
as well, otherwise, the user further performs the block-
level duplicate check and identifies the unique blocks to
be uploaded. Each data copy (i.e., a file or a block) is
associated with a tag for the duplicate check. All data
copies and tags will be stored in the S-CSP.
2.2 Threat Model and Security Goals
Two types of attackers are considered in our threat
model: (i) An outside attacker, who may obtain some
knowledge of the data copy of interest via public chan-
nels. An outside attacker plays the role of a user that
interacts with the S-CSP; (ii) An inside attacker, who may
have some knowledge of partial data information such
as the ciphertext. An insider attacker is assumed to be
honest-but-curious and will follow our protocol, which
could refer to the S-CSPs in our system. Their goal is
to extract useful information from user data. The fol-
lowing security requirements, including confidentiality,
integrity, and reliability are considered in our security
model.
Confidentiality. Here, we allow collusion among the S-
CSPs. However, we require that the number of colluded
S-CSPs is not more than a predefined threshold. To
this end, we aim to achieve data confidentiality against
collusion attacks. We require that the data distributed
and stored among the S-CSPs remains secure when they
are unpredictable (i.e., have high min-entropy), even if
the adversary controls a predefined number of S-CSPs.
The goal of the adversary is to retrieve and recover the
files that do not belong to them. This requirement has
recently been formalized in [6] and called the privacy
against chosen distribution attack. This also implies that
the data is secure against the adversary who does not
own the data.
Integrity. Two kinds of integrity, including tag consis-
tency and message authentication, are involved in the
security model. Tag consistency check is run by the cloud
storage server during the file uploading phase, which
is used to prevent the duplicate/ciphertext replacement
attack. If any adversary uploads a maliciously-generated
ciphertext such that its tag is the same with another
honestly-generated ciphertext, the cloud storage server
can detect this dishonest behavior. Thus, the users do
not need to worry about that their data are replaced
and unable to be decrypted. Message authentication
check is run by the users, which is used to detect
if the downloaded and decrypted data are complete
and uncorrupted or not. This security requirement is
introduced to prevent the insider attack from the cloud
storage service providers.
Reliability. The security requirement of reliability in
deduplication means that the storage system can provide
fault tolerance by using the means of redundancy. In
more details, in our system, it can be tolerated even if
a certain number of nodes fail. The system is required
to detect and repair corrupted data and provide correct
output for the users.
3 THE DISTRIBUTED DEDUPLICATION SYS-
TEMS
The distributed deduplication systems’ proposed aim
is to reliably store data in the cloud while achieving
confidentiality and integrity. Its main goal is to enable
deduplication and distributed storage of the data across
multiple storage servers. Instead of encrypting the data
to keep the confidentiality of the data, our new construc-
tions utilize the secret splitting technique to split data
into shards. These shards will then be distributed across
multiple storage servers.
3.1 Building Blocks
Secret Sharing Scheme. There are two algorithms in a
secret sharing scheme, which are Share and Recover.
The secret is divided and shared by using Share. With
enough shares, the secret can be extracted and recovered
with the algorithm of Recover. In our implementation,
we will use the Ramp secret sharing scheme (RSSS) [7],
[8] to secretly split a secret into shards. Specifically, the
(n, k, r)-RSSS (where n > k > r ≥ 0) generates n shares
from a secret so that (i) the secret can be recovered from

4
any k or more shares, and (ii) no information about
the secret can be deduced from any r or less shares.
Two algorithms, Share and Recover, are defined in the
(n, k, r)-RSSS.
• Share divides a secret S into (k − r) pieces of equal
size, generates r random pieces of the same size, and
encodes the k pieces using a non-systematic k-of-n
erasure code into n shares of the same size;
• Recover takes any k out of n shares as inputs and
then outputs the original secret S.
It is known that when r = 0, the (n, k, 0)-RSSS becomes
the (n, k) Rabin’s Information Dispersal Algorithm
(IDA) [9]. When r = k −1, the (n, k, k −1)-RSSS becomes
the (n,k) Shamir’s Secret Sharing Scheme (SSSS) [10].
Tag Generation Algorithm. In our constructions
below, two kinds of tag generation algorithms are
defined, that is, TagGen and TagGen’. TagGen is the tag
generation algorithm that maps the original data copy
F and outputs a tag T(F). This tag will be generated
by the user and applied to perform the duplicate check
with the server. Another tag generation algorithm
TagGen’ takes as input a file F and an index j and
outputs a tag. This tag, generated by users, is used for
the proof of ownership for F.
Message authentication code. A message authentication
code (MAC) is a short piece of information used to
authenticate a message and to provide integrity
and authenticity assurances on the message. In our
construction, the message authentication code is applied
to achieve the integrity of the outsourced stored files. It
can be easily constructed with a keyed (cryptographic)
hash function, which takes input as a secret key and
an arbitrary-length file that needs to be authenticated,
and outputs a MAC. Only users with the same key
generating the MAC can verify the correctness of
the MAC value and detect whether the file has been
changed or not.
3.2 The File-level Distributed Deduplication System
To support efficient duplicate check, tags for each file
will be computed and are sent to S-CSPs. To prevent
a collusion attack launched by the S-CSPs, the tags
stored at different storage servers are computationally
independent and different. We now elaborate on the
details of the construction as follows.
System setup. In our construction, the number of
storage servers S-CSPs is assumed to be n with
identities denoted by id1, id2, · · · , idn, respectively.
Define the security parameter as 1λ
and initialize a
secret sharing scheme SS = (Share, Recover), and a tag
generation algorithm TagGen. The file storage system
for the storage server is set to be ⊥.
File Upload. To upload a file F, the user interacts
with S-CSPs to perform the deduplication. More
precisely, the user firstly computes and sends the file
tag ϕF = TagGen(F) to S-CSPs for the file duplicate
check.
• If a duplicate is found, the user computes and sends
ϕF,idj = TagGen′
(F, idj) to the j-th server with
identity idj via the secure channel for 1 ≤ j ≤ n
(which could be implemented by a cryptographic
hash function Hj(F) related with index j). The
reason for introducing an index j is to prevent the
server from getting the shares of other S-CSPs for
the same file or block, which will be explained in
detail in the security analysis. If ϕF,idj matches the
metadata stored with ϕF , the user will be provided
a pointer for the shard stored at server idj.
• Otherwise, if no duplicate is found, the user will
proceed as follows. He runs the secret sharing algo-
rithm SS over F to get {cj} = Share(F), where cj
is the j-th shard of F. He also computes ϕF,idj =
TagGen′
(F, idj), which serves as the tag for the j-
th S-CSP. Finally, the user uploads the set of values
{ϕF , cj, ϕF,idj } to the S-CSP with identity idj via a
secure channel. The S-CSP stores these values and
returns a pointer back to the user for local storage.
File Download. To download a file F, the user first
downloads the secret shares {cj} of the file from k out of
n storage servers. Specifically, the user sends the pointer
of F to k out of n S-CSPs. After gathering enough shares,
the user reconstructs file F by using the algorithm of
Recover({cj}).
This approach provides fault tolerance and allows the
user to remain accessible even if any limited subsets of
storage servers fail.
3.3 The Block-level Distributed Deduplication Sys-
tem
In this section, we show how to achieve the fine-grained
block-level distributed deduplication. In a block-level
deduplication system, the user also needs to firstly
perform the file-level deduplication before uploading
his file. If no duplicate is found, the user divides this file
into blocks and performs block-level deduplication. The
system setup is the same as the file-level deduplication
system, except the block size parameter will be defined
additionally. Next, we give the details of the algorithms
of File Upload and File Download.
File Upload. To upload a file F, the user first performs
the file-level deduplication by sending ϕF to the storage
servers. If a duplicate is found, the user will perform
the file-level deduplication, such as that in Section 3.2.
Otherwise, if no duplicate is found, the user performs
the block-level deduplication as follows.
He firstly divides F into a set of fragments {Bi}
(where i = 1, 2, · · · ). For each fragment Bi, the user
will perform a block-level duplicate check by comput-
ing ϕBi = TagGen(Bi), where the data processing and

5
duplicate check of block-level deduplication is the same
as that of file-level deduplication if the file F is replaced
with block Bi.
Upon receiving block tags {ϕBi }, the server with
identity idj computes a block signal vector σBi for each
i.
• i) If σBi =1, the user further computes and sends
ϕBi,j = TagGen′
(Bi, j) to the S-CSP with identity
idj. If it also matches the corresponding tag stored,
S-CSP returns a block pointer of Bi to the user. Then,
the user keeps the block pointer of Bi and does not
need to upload Bi.
• ii) If σBi =0, the user runs the secret sharing al-
gorithm SS over Bi and gets {cij} = Share(Bi),
where cij is the j-th secret share of Bi. The user
also computes ϕBi,j for 1 ≤ j ≤ n and uploads the
set of values {ϕF , ϕF,idj
, cij, ϕBi,j} to the server
idj via a secure channel. The S-CSP returns the
corresponding pointers back to the user.
File Download. To download a file F = {Bi}, the user first
downloads the secret shares {cij} of all the blocks Bi in
F from k out of n S-CSPs. Specifically, the user sends all
the pointers for Bi to k out of n servers. After gathering
all the shares, the user reconstructs all the fragments Bi
using the algorithm of Recover({·}) and gets the file F =
{Bi}.
4 FURTHER ENHANCEMENT
4.1 Distributed Deduplication System with Tag Con-
sistency
In this section, we consider how to prevent a duplicate
faking or maliciously-generated ciphertext replacement
attack. A security notion of tag consistency has been
formalized for this kind of attack [6]. In a deduplication
storage system with tag consistency, it requires that no
adversary is able to obtain the same tag from a pair
of different messages with a non-negligible probability.
This provides security guarantees against the duplicate
faking attacks in which a message can be undetectably
replaced by a fake one. In the previous related work
on reliable deduplication over encrypted data, the tag
consistency cannot be achieved as the tag is computed by
the data owner from underlying data files, which cannot
be verified by the storage server. As a result, if the data
owner replaces and uploads another file that is different
from the file corresponding to the tag, the following
users who perform the duplicate check cannot detect this
duplicate faking attack and extract the exact files they
want. To solve this security weakness, [6] suggested to
compute the tag directly from the ciphertext by using
a hash function. This solution obviously prevents the
ciphertext replacement attack because the cloud storage
server is able to compute the tag by itself. However, such
a method is unsuitable for the distributed storage system
to realize the tag consistency. The challenge is that tradi-
tional secret sharing schemes are not deterministic. As a
result, the duplicate check for each share stored in differ-
ent storage servers will not be the same for all users. In
[11], though they mentioned the method of deterministic
secret sharing scheme in the implementation, the tag was
still computed from the whole file or ciphertext, which
means the schemes in [11] cannot achieve the security
against duplicate faking and replacement attacks.
4.1.1 Deterministic Secret Sharing Schemes
We formalize and present two new techniques for the
construction of the deterministic secret sharing schemes.
For simplicity, we present an example based on tradi-
tional Shamir’s Secret Sharing scheme. The description
of (k, n)-threshold in Shamir’s secret sharing scheme is
as follows. In the algorithm of Share, given a secret
α ∈ Zp to be shared among n users for a prime p,
choose at random a (k − 1)-degree polynomial function
f(x) = a0 + a1x + a2x2
+ · · · + ak−1xk−1
∈ Zp[X] such
that α = f(0). The value of f(i) mod p for 1 ≤ i ≤ n is
computed as the i-th share. In the algorithm of Recover,
Lagrange interpolation is used to compute α from any
valid k shares.
The deterministic version of Shamir’s secret sharing
scheme is similar to the original one, except all the
random coefficients {ai} are replaced with deterministic
values. We describe two methods to realize the construc-
tions of deterministic secret sharing schemes below.
The First Method
Share. To share a secret α ∈ Zp, it chooses at random
a (k − 1)-degree polynomial function f(x) = a0 + a1x +
a2x2
+ · · · + ak−1xk−1
∈ Zp[X] such that α = f(0), ai =
H(α∥i) and p is a prime, where H(·) is a hash function.
The value of f(i) mod p for 1 ≤ i ≤ n is computed as the
i-th share and distributed to the corresponding owner.
Recover. The description of algorithm Recover is the
same with the traditional Shamir’s secret sharing scheme
by using Lagrange interpolation. The secret α can be
recovered from any valid k shares.
For files or blocks unknown to the adversary, these co-
efficients are also confidential if they are unpredictable.
To show its security, these values can be also viewed
as random coefficients in the random oracle model.
Obviously, these methods can be also applied to the RSSS
to realize deterministic sharing.
The Second Method
Obviously, the first method of deterministic secret shar-
ing cannot prevent brute-force attack if the file is pre-
dictable. Thus, we show how to construct another deter-
ministic secret sharing construction method to prevent
the brute-force attack. Another entity, called key server,
is introduced in this method, who is assumed to be
honest and will not collude with the cloud storage server
and other outside attackers.
System Setup. Apart from the parameters for the first de-
terministic secret sharing scheme, the key server chooses

6
a key pair (pk, sk) which can be initialized as RSA
cryptosystem.
Share. To share a secret α, the user first computes H(α∥i)
for 1 ≤ i ≤ k − 1. Then, he interacts with the key
server in an oblivious way such that the key server
generates a blind signature on each H(α∥i) with the
secret key sk without knowing H(α∥i). For simplicity,
we denote the signature as σi = φ(H(α∥i), sk), where φ
is a signing algorithm. Finally, the owner of the secret
chooses at random a (k − 1)-degree polynomial function
f(x) = a0 + a1x + a2x2
+ · · · + ak−1xk−1
∈ Zp[X] such
that α = f(0) and ai = σi. The value of f(i) mod p for
1 ≤ i ≤ n is computed as the i-th share and distributed
to the corresponding owner.
Recover. It is the same with the traditional Shamir’s
secret sharing scheme.
In the second construction, the secret key sk is applied
to compute the value of σi. Thus, for the cloud storage
server and other outside attackers, they cannot get any
useful information from the short value even if the secret
is predictable [5]. Actually, the signature can be viewed
as a pseudorandom function for α.
4.1.2 The Construction of Distributed Deduplication
System with Tag Consistency
We give a generic construction that achieves tag
consistency below.
System setup. This algorithm is similar to the above
construction except a deterministic secret sharing
scheme SS = (Share, Recover) is given.
File Upload. To upload a file F, the user first performs
the file-level deduplication. Different from the above
constructions, the user needs to compute the secret
shares {Fj}1≤j≤n of the file by using the Share
algorithm. Then, ϕFj = TagGen(Fj) is computed and
sent to the j-th S-CSP for each j. It is the same as above
if there is a duplicate. Otherwise, the user performs
the block-level deduplication as follows. Note that each
server idj also needs to keep ϕFj with the following
information of the blocks.
The file F is firstly divided into a set of fragments
{Bi} (where i = 1, 2, · · · ). For each block, the duplicate
check operation is the same as the file-level check except
file F is replaced with block Bi. Assume that the secret
shares are {Bij} for 1 ≤ j ≤ n and corresponding tags
are ϕBij for block Bi, where 1 ≤ j ≤ n. The tag ϕBij is
sent to the the server with identity idj. A block pointer
of Bi from this server is returned to the user if there is a
match. Otherwise, the user uploads the Bij to the server
idj via a secure channel and a pointer for this block will
also be returned back to the user.
The procedure of the file download is the same as the
previous block-level deduplication scheme in Section 3.3.
In this construction, the security relies on the assump-
tion that there is a secure deterministic secret sharing
scheme.
4.2 Enhanced Deduplication System with Proof of
Ownership
Recently, Halevi [12] pointed out the weakness of the
security in traditional deduplication systems with only
a short hashing value. Halevi showed a number of
attacks that can lead to data leakage in a storage system
supporting client-side deduplication. To overcome this
security issue, they also presented the concept of Proof
of Ownership (PoW) to prevent these attacks. PoW [12]
enables users to prove their ownership of data copies to
the storage server.
Specifically, PoW is implemented as an interactive
algorithm (denoted by PoW) run by a prover (i.e., user)
and a verifier (i.e., storage server). The verifier derives
a short tag value ϕ(F) from a data copy F. To prove
the ownership of the data copy F, the prover needs to
i) compute and send ϕ′
to the verifier, and ii) present
proof to the storage server that he owns F in an inter-
active way with respect to ϕ′
. The PoW is successful if
ϕ′
= ϕ(F) and the proof is correct. The formal security
definition for PoW roughly follows the threat model in
a content distribution network, where an attacker does
not know the entire file, but has accomplices who have
the file. The accomplices follow the “bounded retrieval
model” so they can help the attacker obtain the file,
subject to the constraint they must send fewer bits than
the initial min-entropy of the file to the attacker [12].
Thus, we also introduce Proof of Ownership techniques
in our construction to prevent the deduplication systems
from these attacks.
Furthermore, we also consider how to achieve the
integrity of the data stored in each S-CSP by using the
message authentication code. We now show how to
integrate PoW and the message authentication code in
our deduplication systems. The system setup is similar
to the scheme in Section 3.3 except two PoW notions are
additionally involved. We denote them by POWF and
POWB, where POWF is PoW for file-level deduplication
and POWB is PoW for block-level deduplication,
respectively.
File Upload. To upload a file F, the user performs
a file-level deduplication with the S-CSPs, as in
Section 3.3. If a file duplicate is found, the user
will run the PoW protocol POWF with each S-CSP
to prove the file ownership. More precisely, for the
j-th server with identity idj, the user first computes
ϕF,idj = TagGen′
(F, idj) and runs the PoW proof
algorithm with respect to ϕF,idj . If the proof is passed,
the user will be provided a pointer for the piece of file
stored at j-th S-CSP.
Otherwise, if no duplicate is found, the user will
proceed as follows. He first divides F into a set of
fragments {Bi} (where i = 1, 2, · · · ). For each fragment
Bi, the user will perform a block-level duplicate check,
such as the scheme in Section 3.3.
• If there is a duplicate in S-CSP, the user runs PoWB

7
on input ϕBi,j = TagGen′
(Bi, idj) with the server to
prove that he owns the block Bi. If it is passed, the
server simply returns a block pointer of Bi to the
user. The user then keeps the block pointer of Bi
and does not need to upload Bi.
• Otherwise, the user runs the secret sharing algo-
rithm SS over Bi and gets {cij} = Share(Bi), where
cij is the j-th secret share of Bi. The values of
(cij, ϕBi,j) will be uploaded and stored by the j-th
S-CSP.
Finally, the user also computes the message
authentication code of F as macF = H(kF , F),
where the keys are computed as kF = H0(F) with
a cryptographic hash function H0(·). Then, the user
runs the secret sharing algorithm SS over macF as
{mfj} = Share(macF ), where mfj is the j-th secret
share of macF . The user uploads the set of values
{ϕF , ϕF,idj , mfj} to the S-CSP with identity idj via
a secure channel. The server stores these values and
returns the corresponding pointers back to the user for
local storage.
File Download. To download a file F, the user first
downloads the secret shares {cij, mfj} of the file from k
out of n storage servers. Specifically, the user sends all
the pointers for F to k out of n servers. After gathering
all the shares, the user reconstructs file F, macF by
using the algorithm of Recover({·}). Then, he verifies
the correctness of these tags to check the integrity of
the file stored in S-CSPs.
5 SECURITY ANALYSIS
In this section, we will only give the security analysis for
the distributed deduplication system in Section 4. The
security analysis for the other constructions is similar
and thus omitted here. Some basic cryptographic tools
have been applied into our construction to achieve se-
cure deduplication. To show the security of this protocol,
we assume that the underlying building blocks are se-
cure, including the secret sharing scheme and the PoW
scheme. Thus, the security will be analyzed based on the
above security assumptions.
In our constructions, S-CSPs are assumed to follow the
protocols. If the data file has been successfully uploaded
and stored at servers, then the user who owns the file
can convince the servers based on the correctness of the
PoW. Furthermore, the data is distributedly stored at
servers with the secret sharing method. Based on the
completeness of the underlying secret sharing scheme,
the file will be recovered by the user with enough correct
shares. The integrity can be also obtained because the
utilization of secure message authentication code.
Next, we consider the confidentiality against two types
of adversaries. The first type of adversary is defined as
dishonest users who aims to retrieve files stored at S-
CSPs they do not own. The second type of adversary is
defined as a group of S-CSPs and users. Their goal is
to get the useful information of file content they do not
own individually by launching the collusion attack. The
attacks launched by these two types of adversaries are
denoted by Type-I attack and Type-II attack, respectively.
Because the RSSS is used in our construction, the differ-
ent level of confidentiality is achieved in terms of the
parameter r given in the RSSS scheme, which increases
with the number of r. Thus, in the following security
analysis, we will not explain this furthermore.
Confidentiality against a Type-I Attack
This type of adversary tries to convince the S-CSPs with
some auxiliary information to get the content of the file
stored at S-CSPs. To get one piece of share stored in a
S-CSP, the user needs to perform a correct PoW protocol
for the corresponding share stored at the S-CSP. In this
way, if the adversary wants to get the k-th piece of a
share he does not own, he has to convince the k-th S-
CSP by correctly running a PoW protocol. However, the
user cannot get the auxiliary value used to perform PoW
if he does not own the file. Thus, based on the security
of PoW, the security against a Type-I attack is easily
derived.
Confidentiality against a Type-II Attack
As shown in the construction, the data is processed
before being outsourced to cloud servers. A secure secret
sharing scheme has been applied to split each file into
pieces, where each piece is distributedly stored in a S-
CSP. Because the underlying RSSS secret sharing scheme
is semantically secure, the data can not be recovered
from pieces of shares that are less than a predefined
threshold number. This means the confidentiality of the
data stored at the S-CSPs is guaranteed even if some
S-CSPs collude. Note that in the RSSS secret sharing
scheme, no information will be leaked even if any r of
n shares collude. Thus, the data in our scheme remains
secure even if any r S-CSPs collude.
We also need to consider the security against a col-
luding attack for PoW protocol because the adversary
may also get the data if he successfully convinces the
S-CSPs with correct proof in PoW. There are two kinds
of PoW utilized in our constructions. These are block-
level and file-level proof of ownership. Recently, the
formal security definition of PoW was formally given in
[12]. However, there was one tradeoff security definition.
This definition relaxes the restriction that the proof fails
unless the accomplices of the adversary send more than a
threshold or more bits to the adversary, regardless of the
file entropy. Next, we will present a security analysis of
the proposed PoW in distributed deduplication systems.
Assume there are t S-CSPs that would collude and try
to extract a user’s sensitive file F, where t < k. We will
only present the analysis for file because the security
analysis for block is the same. From this assumption,
we can model it by providing an adversary with a set
of tags {ϕF,idi1 , · · · , ϕF,idit }, where idi1, · · · , idit are the
identities of the servers. Furthermore, the interactive

8
values in the proof algorithm between the users and
servers with respect to these tags are available to the
adversary. Then, the proof of PoW cannot be passed to
convince a server with respect to another different tag
ϕF,id∗ , where id∗
̸∈ {idi1, · · · , idik}. Such a PoW scheme
with a secure proof algorithm can be easily constructed
based on previously known PoW methods. For example,
the tag generation TagGen(F, idi) algorithm could be
computed from the independent Merkle-hash tree with
the different cryptographic hash function Hi(·) [12]. Us-
ing the proof algorithm in the PoW scheme with respect
to ϕF,idi , we can then easily obtain a secure proof of
ownership scheme with the above security requirement.
Finally, based on such a secure PoW scheme and
secure secret sharing scheme, we can get the following
security result for our distributed deduplication system
from the above analysis.
Theorem 1: The proposed distributed deduplication
system achieves privacy against the chosen distribution
attack under the assumptions that the secret sharing
scheme and PoW scheme are secure.
The security analysis of reliability is simple because
of the utilization of RSSS, which is determined by pa-
rameters of n and k. Based on the RSSS, the data can
be recovered from any k shares. More specifically, this
reliability level depends on n − k.
6 EXPERIMENT
We describe the implementation details of the proposed
distributed deduplication systems in this section. The
main tool for our new deduplication systems is the Ramp
secret sharing scheme (RSSS) [7], [8]. The shares of a
file are shared across multiple cloud storage servers in a
secure way.
The efficiency of the proposed distributed systems are
mainly determined by the following three parameters
of n, k, and r in RSSS. In this experiment, we choose
4KB as the default data block size, which has been
widely adopted for block-level deduplication systems.
We choose the hash function SHA-256 with an output
size of 32 bytes. We implement the RSSS based on the
Jerasure Version 1.2 [13]. We choose the erasure code in
the (n, k, r)-RSSS whose generator matrix is a Cauchy
matrix [14] for the data encoding and decoding. The
storage blowup is determined by the parameters n, k,
r. In more details, this value is n
k−r in theory.
All our experiments were performed on an Intel
Xeon E5530 (2.40GHz) server with Linux 3.2.0-23-
generic OS. In the deduplication systems, the (n, k, r)-
RSSS has been used. For practice consideration, we test
four cases:
• case 1: r = 1, k = 2, and 3 ≤ n ≤ 8 (Figure 3(a));
• case 2: r = 1, k = 3 and 4 ≤ n ≤ 8 (Figure 3(b));
• case 3: r = 2, k = 3, and 4 ≤ n ≤ 8 (Figure 3(c));
• case 4: r = 2, k = 4, and 5 ≤ n ≤ 8 (Figure 3(d)).
As shown in Figure 1, the encoding and decoding
times of our deduplication systems for each block (per
4KB data block) are always in the order of microseconds,
and hence are negligible compared to the data transfer
performance in the Internet setting. We can also observe
that the encoding time is higher than the decoding time.
The reason for this result is that the encoding operation
always involves all n shares, while the decoding opera-
tion only involves a subset of k < n shares.
The performance of several basic modules in our con-
structions is tested in our experiment. First, The average
time for generating a hash function with 32-byte output
from a 4KB data block is 25.196 usec. The average time
is 30 ms for generating a hash function with the same
output length from a 4MB file, which only needs to be
computed by the user for each file.
Next, we focus on the evaluation with respect to some
critical factors in the (n, k, r)-RSSS. First, we evaluate the
efficiency between the computation and the number of S-
CSPs. The results are given in Figure 2, which shows the
encoding/decoding times versus the number of S-CSPs
n. In this experiment, r is set to be 2 and the reliability
level n−k = 2 are also fixed. From Figure 2, the encoding
time increases with the number of n since more shares
are involved in the encoding algorithm.
We also test the relation between the computational
time and the parameter r. More specifically, in Figure 3,
it shows the encoding/decoding times versus the con-
fidentiality level r. To realize this test, the number of
S-CSPs n = 6 and the reliability level n − k = 2 are
fixed. From the figure, it can be easily found that the
encoding/decoding time increases with r. Actually, this
observation could also be derived from the theoretical
result. If we recall that a secret is divided into k−r equal-
size pieces in the Share function of the RSSS. As a result,
the size of each piece will increase with the size of r,
which increases the encoding/decoding computational
overhead. From this experiment, we can also conclude
it will require much higher computational overhead in
order to achieve higher confidentiality. In Figure 4, the
relation of the factor of n − k and the computational
time is given, where the number of S-CSPs and the
confidentiality level are fixed as n = 6 and r = 2. From
the figure, we can see that with the increase of n−k, the
encoding/decoding time decreases. The reason for this
result is based on the RSSS, where fewer pieces (i.e., k)
will be required with the increase of n − k.
7 RELATED WORK
Reliable Deduplication systems Data deduplication tech-
niques are very interesting techniques that are widely
employed for data backup in enterprise environments
to minimize network and storage overhead by detecting
and eliminating redundancy among data blocks. There
are many deduplication schemes proposed by the re-
search community. The reliability in deduplication has
also been addressed by [15], [11], [16]. However, they
only focused on traditional files without encryption,
without considering the reliable deduplication over ci-
phertext. Li et al. [11] showed how to achieve reliable key

9
100
150
200
250
300
350
400
450
3 4 5 6 7 8
TimeCost(usec)
Number of S-CSPs
Encoding
Decoding
(a) Impact on Encoding/Decoding time: case 1.
200
250
300
350
400
450
500
550
4 5 6 7 8
TimeCost(usec)
Number of S-CSPs
Encoding
Decoding
(b) Impact on Encoding/Decoding time: case 2.
250
300
350
400
450
500
550
600
650
700
750
4 5 6 7 8
TimeCost(usec)
Number of S-CSPs
Encoding
Decoding
(c) Impact on Encoding/Decoding time: case 3.
450
500
550
600
650
700
750
800
5 6 7 8
TimeCost(usec) Number of S-CSPs
Encoding
Decoding
(d) Impact on Encoding/Decoding time: case 4.
Fig. 1. The Encoding and Decoding time for different RSSS parameters.
0
500
1000
1500
2000
2500
3000
5 6 7 8 9 10
TimeCost(usec)
Number of S-CSPs
Encoding
Decoding
Fig. 2. Impact of number of
S-CSPs n on encoding/decoding
times, where r = 2 and n − k = 2.
0
200
400
600
800
1000
0 1 2 3
TimeCost(usec)
Confidentiality Level
Encoding
Decoding
Fig. 3. Impact of confidentiality
level r on the encoding/decoding
times where n = 6 and n − k = 2.
0
200
400
600
800
1000
1 2 3
TimeCost(usec)
Reliability Level
Encoding
Decoding
Fig. 4. Impact of reliability level
n−k on encoding/decoding times,
where n = 6 and r = 2.
management in deduplication. However, they did not
mention about the application of reliable deduplication
for encrypted files. Later, in [16], they showed how to
extend the method in [11] for the construction of reliable
deduplication for user files. However, all of these works
have not considered and achieved the tag consistency
and integrity in the construction.
Convergent encryption. Convergent encryption [4]
ensures data privacy in deduplication. Bellare et
al. [6] formalized this primitive as message-locked
encryption, and explored its application in space-
efficient secure outsourced storage. There are also
several implementations of convergent implementations
of different convergent encryption variants for secure
deduplication (e.g., [17], [18], [19], [20]). It is known
that some commercial cloud storage providers, such
as Bitcasa, also deploy convergent encryption [6]. Li
et al. [11] addressed the key-management issue in
block-level deduplication by distributing these keys
across multiple servers after encrypting the files. Bellare
et al. [5] showed how to protect data confidentiality
by transforming the predicatable message into a
unpredicatable message. In their system, another third
party called the key server was introduced to generate
the file tag for the duplicate check. Stanek et al. [21]
presented a novel encryption scheme that provided
differential security for popular and unpopular data.
For popular data that are not particularly sensitive,
the traditional conventional encryption is performed.
Another two-layered encryption scheme with stronger
security while supporting deduplication was proposed
for unpopular data. In this way, they achieved better
tradeoff between the efficiency and security of the
outsourced data.

10
Proof of ownership. Harnik et al. [22] presented a number
of attacks that can lead to data leakage in a cloud storage
system supporting client-side deduplication. To prevent
these attacks, Halevi et al. [12] proposed the notion of
“proofs of ownership” (PoW) for deduplication systems,
so that a client can efficiently prove to the cloud storage
server that he/she owns a file without uploading the
file itself. Several PoW constructions based on the
Merkle Hash Tree are proposed [12] to enable client-side
deduplication, which includes the bounded leakage
setting. Pietro and Sorniotti [23] proposed another
efficient PoW scheme by choosing the projection of a
file onto some randomly selected bit-positions as the
file proof. Note that all of the above schemes do not
consider data privacy. Recently, Xu et al. [24] presented
a PoW scheme that allows client-side deduplication in
a bounded leakage setting with security in the random
oracle model. Ng et al. [25] extended PoW for encrypted
file, but they did not address how to minimize the key
management overhead.
PoR/PDP. Ateniese et al. [26] introduced the concept
of proof of data possession (PDP). This notion was
introduced to allow a cloud client to verify the integrity
of its data outsourced to the cloud in a very efficient
way. Juels et al. [27] proposed the concept of proof of
retrievability (PoR). Compared with PDP, PoR allows
the cloud client to recover his outsourced data through
the interactive proof with the server. This scheme was
later improved by Shacham and Waters [28]. The main
difference between the two notions is that PoR uses
Error Correction/Erasure Codes to tolerate the damage
to portions of the outsourced data.
8 CONCLUSIONS
We proposed the distributed deduplication systems to
improve the reliability of data while achieving the con-
fidentiality of the users’ outsourced data without an
encryption mechanism. Four constructions were pro-
posed to support file-level and fine-grained block-level
data deduplication. The security of tag consistency and
integrity were achieved. We implemented our deduplica-
tion systems using the Ramp secret sharing scheme and
demonstrated that it incurs small encoding/decoding
overhead compared to the network transmission over-
head in regular upload/download operations.
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ACKNOWLEDGEMENTS
This work was supported by National Natural Sci-
ence Foundation of China (No. 61472091, 61272455 and
U1135004), 973 Program (No. 2014CB360501), Natural
Science Foundation of Guangdong Province (Grant No.
S2013010013671).
Jin Li received his B.S. (2002) in Mathemat-
ics from Southwest University. He got his Ph.D
degree in information security from Sun Yat-
sen University at 2007. Currently, he works at
Guangzhou University as a professor. He has
been selected as one of science and technology
new stars in Guangdong province. His research
interests include Cloud Computing Security and
Applied Cryptography. He has published over 70
research papers in refereed international con-
ferences and journals. His work has been cited
more than 2400 times at Google Scholar. He also has served as the
program chair or program committee member in many international
conferences.
Xiaofeng Chen received his B.S. and M.S. on
Mathematics in Northwest University, China. He
got his Ph.D degree in Cryptography from Xidian
University at 2003. Currently, he works at Xidian
University as a professor. His research interests
include applied cryptography and cloud comput-
ing security. He has published over 80 research
papers in refereed international conferences and
journals. His work has been cited more than
1000 times at Google Scholar. He has served as
the program/general chair or program committee
member in over 20 international conferences.
Xinyi Huang received his Ph.D. degree from the
School of Computer Science and Software En-
gineering, University of Wollongong, Australia,
in 2009. He is currently a Professor at the Fu-
jian Provincial Key Laboratory of Network Secu-
rity and Cryptology, School of Mathematics and
Computer Science, Fujian Normal University,
China. His research interests include cryptogra-
phy and information security. He has published
over 60 research papers in refereed international
conferences and journals. His work has been
cited more than 1000 times at Google Scholar. He is in the Editorial
Board of International Journal of Information Security (IJIS, Springer)
and has served as the program/general chair or program committee
member in over 40 international conferences.
Shaohua Tang received the B.Sc. and M.Sc.
Degrees in applied mathematics, and the Ph.D.
Degree in communication and information sys-
tem all from the South China University of Tech-
nology, in 1991, 1994, and 1998, respectively.
He was a visiting scholar with North Carolina
State University, and a visiting professor with the
University of Cincinnati, Ohio. He has been a
full professor with the School of Computer Sci-
ence and Engineering, South China University
of Technology since 2004. His current research
interests include information security, networking, and information pro-
cessing. He has published more than 80 research papers in referred
international conferences and journals. He has been authorized over 20
patents from US, UK, Germany, and China. He is on the Final Evaluation
Panel of the National Natural Science Foundation of China. He is a
member of the IEEE and the IEEE Computer Society.
Yang Xiang received his PhD in Computer Sci-
ence from Deakin University, Australia. He is
currently a full professor at School of Information
Technology, Deakin University. He is the Director
of the Network Security and Computing Lab
(NSCLab). His research interests include net-
work and system security, distributed systems,
and networking. In particular, he is currently
leading his team developing active defense sys-
tems against large-scale distributed network at-
tacks. He is the Chief Investigator of several
projects in network and system security, funded by the Australian Re-
search Council (ARC). He has published more than 130 research papers
in many international journals and conferences, such as IEEE Trans-
actions on Computers, IEEE Transactions on Parallel and Distributed
Systems, IEEE Transactions on Information Security and Forensics, and
IEEE Journal on Selected Areas in Communications. Two of his papers
were selected as the featured articles in the April 2009 and the July 2013
issues of IEEE Transactions on Parallel and Distributed Systems. He has
published two books, Software Similarity and Classiﬁcation (Springer)
and Dynamic and Advanced Data Mining for Progressing Technological
Development (IGI-Global). He has served as the Program/General Chair
for many international conferences such as ICA3PP 12/11, IEEE/IFIP
EUC 11, IEEE TrustCom 13/11, IEEE HPCC 10/09, IEEE ICPADS
08, NSS 11/10/09/08/07. He has been the PC member for more than
60 international conferences in distributed systems, networking, and
security. He serves as the Associate Editor of IEEE Transactions on
Computers, IEEE Transactions on Parallel and Distributed Systems,
Security and Communication Networks (Wiley), and the Editor of Journal
of Network and Computer Applications. He is the Coordinator, Asia for
IEEE Computer Society Technical Committee on Distributed Processing
(TCDP). He is a Senior Member of the IEEE.
Mohammad Mehedi Hassan is an Assistant
Professor of Information Systems Department in
the College of Computer and Information Sci-
ences, King Saud University, Riyadh, Kingdom
of Saudi Arabia. He received his Ph.D. degree
in Computer Engineering from Kyung Hee Uni-
versity, South Korea in February 2011. He has
authored and co-authored more than 80 pub-
lications including refereed IEEE/ACM/Springer
journals, conference papers, books, and book
chapters. His research interests include cloud
collaboration, media cloud, sensor-cloud, mobile Cloud, IPTV, and wir-
less sensor network.

12
Abdulhameed Alelaiwi is an Assistant Pro-
fessor of Software Engg. Department, at the
College of Computer and Information Sciences,
King Saud University. Riyadh, Saudi Arabia. He
is currently the Vice Dean for Deanshhip of Sci-
entiﬁc Research at King Saud University. He re-
ceived his PhD degree in Software Engineering
from the College of Engineering, Florida Institute
of Technology-Melbourne, USA in 2002. He has
authored and co-authored many publications in-
cluding refereed IEEE/ACM/Springer journals,
conference papers, books, and book chapters. His research interest
includes software testing analysis and design, cloud computing, and
multimedia.

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