-With the emergence of cloud computing, the concept of trust has become a major issue. Indeed, the key challenge is to ensure to customers that the selected cloud provider may store and process the raw data safely. If this is a storage service, data can be encrypted before sending them to the cloud server; in this case, data confidentiality is assured. However, before performing treatments, these data must be decrypted. It is this step that can be considered a breach of security. Indeed, the fear of seeing sensitive data be processed in crude is a major obstacle in adopting cloud services. To overcome this obstacle and strengthen confidence in the cloud services, in this article we will propose the adoption of Homomorphic Encryption methods that are able to perform operations on encrypted data without knowing the key secret.
INTRODUCTION
Cloud computing is becoming more and more a magic solution, thanks to the gains it presents at the level of cost of software, maintenance computer park and servers maintenance. However, safety concerns, including the fear of seeing confidential information processed in plain, is usually the main obstacle to the adoption of cloud services.
In this article, we will propose to the cloud providers using the homomorphic encryption technique to ensure the confidentiality of confidential data storage and processing in order to overcome the problem with the confidentiality of information and to build confidence in the adoption of cloud services.
The principle of this technique is to encrypt data before sending them to the cloud provider, which allows to perform encrypted data operations without having the secret key, and return a result that is the same as if we had worked directly on the raw data.
The rest of this paper is organized as follows: In Section II, we willl define cloud computing, we will present its service and deployment models, and its essential characteristics. In Section III, we will illustrate some applications of the technique of homomorphic encryption in various areas of the real world. In Section IV, we will define homomorphic encryption and present its operation and the categories that Abderrahim BENI HSSANE
Broad network access: Services are available on the
network and accessible through standard mechanisms
that promote use of client platforms (eg, mobile phones,
tablets, laptops and desktops) [
Resource pooling: The provider’s computing resources
are pooled to serve multiple consumers using a
multitenant model, with different physical and virtual
resources dynamically assigned and reassigned
according to consumer demand. There is a sense of
location independence in that the customer generally has
no control or knowledge over the exact location of the
provided resources but may be able to specify location at
a higher level of abstraction (e.g., country, state, or
datacenter) [
Rapid elasticity: Possibility to change very quickly the
capacity provided, either more or less [
Measured service: Cloud systems automatically control
and optimize resource use by leveraging a metering
capability at some level of abstraction appropriate to the
type of service (e.g., storage, processing, bandwidth,
and active user accounts). Resource usage can be
monitored, controlled, and reported, providing
transparency for both the provider and consumer of
the utilized service [
III.
RELATED WORKS
Applications using the homomorphic encryption technique in the real world are very diverse and numerous. We will present here some.
The cloud private system of storage of electronic medical records of patients, has been proposed. In this system, all data in these files are encrypted by health care providers, before being transferred to the cloud storage system. Secret keys for access to the raw data folders are shared between the patient and the specific suppliers. However, this system does not allow the cloud to perform processing on the data without search by keywords. With the implementation of fully homomorphic encryption, cloud allows to perform operations on encrypted data, and send patient updates, alerts and relevant information based on the received data [2].
In the financial sector, there is a potential application scenario, with the objective of safeguarding confidential data and business customers and functions calculated on the data. Dissemination of relevant information such as data on companies, the stock price etc., are essential in making investment decisions. These data should be disse possible. The functions which make calculations on these data must be owners. They are based on new predictive models of the performance of share prices, which can be the result of costly research carried out by financial analysts. Most companies want to hide these private models to their competitors in order to preserve their investments. With the use of fully homomorphic encryption, some of these functions will be evaluated in private mode. The client will thus transfer an encrypted version of the function to the cloud, for example a program where some of the evaluations are specified encrypted entries. Streaming data is encrypted by the client's public key before being transferred to the cloud. Then the cloud service evaluates the private function on encrypted inputs using the encrypted program description. After the performance of operations on these data, cloud returns a result itself encrypted to the client [2].
Also, Sutar and Patil proposed an authentication framework
in the Cloud, considering three parts, namely: Server Cloud,
the cloud user and third parties. Then, using homomorphic
encryption mechanism, the exchange of information between
the parties mentioned will be preserved. Here, the
authentication process is carried out by a third party after
comparing the information of two other parties (user and the
server cloud). This system has reduced the cloud server
calculations and at the same time has preserved the confidential
information of the user [
IV.
In 1978, Ronald Rivest, Leonard Adleman and Michael
Dertouzos suggested for the first time homomorphic encryption
concept [
Homomorphic encryption systems are capable of
performing operations on encrypted data without knowing the
secret key. These operations generate a result, which is
itself encrypted (i.e. incomprehensible even to cloud provider).
The result obtained is the same as if we performed these
operations on the raw data [
Mathematically speaking, we say that a system is
homomorphic encryption if: from Enc(x) and Enc(y), it is
possible to calculate Enc(f(x, y)), where f can be : +, ×, ⊕
[
The principles of the operation of the Homomorphic
Encryption are as follows, and as shown in Figure 3[
Among the homomorphic encryption systems are distinguished, depending on the operations that evaluates raw data, multiplicative homomorphic encryption and additive homomorphic encryption.
homomorphic encryption is multiplicative, if there is an
algorithm that can calculate Enc (x × y) from Enc (x)
and Enc (y) without knowing x and y [
encryption is additive, if there is an algorithm that can
calculate Enc (x + y) from Enc (x) and Enc (y) without
knowing x and y [
Among Homomorphic Encryption systems, we distinguish three categories, depending on the operations performed on the data :
Partially Homomorphic Encryption (PHE) : allows
to perform operations on encrypted data, let
multiplication or addition, but not both [
Somewhat Homomorphic Encryption (SWHE) :
allows to perform more than one operation, but a
limited number of multiplication and addition
operations [
Fully Homomorphic Encryption (FHE): This is a
cryptographic system that supports an unlimited
number of both additions and multiplications [
BGN
Let x, y ∈ Zp, pk = (n) and sk =(p, q)
Enc (x y) ≡ (Enc (x) Enc (y)) ( mod n), or x y = Dec (Enc (x) Enc (y))
≡ (Enc (x) Enc (y)) (mod p)
Enc (x + y) ≡ Enc (x) + Enc (y) ( mod n), or x + y = Dec (Enc (x) + Enc (y)) ≡ (Enc (x) + Enc (y)) (mod p) V.
TRUST ISSUES IN CLOUD COMPUTING
With the services offered by the cloud providers,
companies can increase their productivity in the shortest
possible time, with fewer staff and reduced costs. However, the
adoption of such a service can only be done if security is
ensured. Indeed, the major challenge is to strengthen the trust
of customers by assuring them that the cloud providers may
store and process data securely [
Indeed, ensuring optimum level of security has become a necessity to preserve the integrity, confidentiality and availability of services associated with the Cloud. for strengthen the trust of customers. We will classify this trust into two levels, according to the requirements of customers (businesses, consumers, etc.):
At this level, customers can trust the cloud service
providers if privacy, data integrity and service availability are
ensured. The following figure shows level one of the trust.
Availability: is the property of information to be
accessible and usable upon demand by an authorized
entity[
Integrity: is the property of information not to be altered.
This means that the system must prevent undue
modification of information (i.e, of a modification by
unauthorized users or incorrect modification by
authorized users) [
Privacy: refers to the will of a user to control the
disclosure of private information (authentication,
authorization and access control) communication of
encrypted data, and management of user identity [
Even security associated with level one of the trust is
assured, in the case of confidential data, customers require to
ensure the confidentiality of storing and processing data.
Figure 5 presents level two of the trust.
Confidentiality: ensures that data remains confidential
and invisible to the cloud provider, and even if the
provider data centers have been attacked, customer data
can neither be stolen nor reused [
In an unreliable environment , like in the public cloud , the confidentiality of the storage of confidential data and their treatment must be ensured. Thus, researchers noted a useful encryption method in this type of environment: homomorphic encryption. Homomorphic encryption methods are able to perform operations on encrypted data without decrypting them and to give us results that are the same as if we had performed these operations on the raw data. This would allow us to outsource the calculation and storage of confidential data to the cloud, while keeping the secret keys that are essential to decrypting the results of operations performed on encrypted data.
VI.
LIMITS OF HE CRYPTOSYSTEMS
Today, HE technique appears as the most effective and the safest for outsourcing the calculation and storage of confidential data to the cloud. However, HE systems have certain limitations. In the following we will present the limits of the ElGamal and EHES algorithms.
The table below presents the limits of cryptosystems: ElGamal and EHES. Π mi < p , with i={1,2,...,k}. pk=(n), sk=(d), et x1, x2,..., xk ∊ ℤp
Π xi < p , with i={1,2,...,k}.
∑ xi < p , with i={1,2,...,k}.
In some cases the encrypted message by EHES algorithm is itself that the clear message.
As indicated in Figure 3, the EHES encryption algorithm is as follows:
Enc(x) = x + r×pq (mod n), with pk=(n) and sk=(p, q). if r×pq = α×n, with α ∊ ℕ* therefore, Enc(x) = x
if r×pq = α×n = α×pq ⇔ r×pq-1 = α ×q we get: p, q ∊ ℙ so now, q divides r.
Therefore, ∃ r ∊ ℕ* such that r×pq = α×n
We improved EHES encryption algorithm, in in a way that the encrypted message is always different from the clear message. The new encryption algorithm of Enhanced EHES is as followings:
Enc(x) = x + prq (mod n)
If prq = α×n = α×pq ⇔ p r(q-1) = α ×q we get: p, q ∊ ℙ so now, ∄ α ∊ ℕ* such that p rq = α×n
In this article, we discussed the importance of adopting the homomorphic encryption technology for cloud providers. This technique allows them to preserve the confidentiality of sensitive data in order to strengthen the trust of their clients. Also, we have presented the limits of the ElGamal and EHES cryptosystems and we proposed an improved version of the EHES algorithm.
In our future work, we will focus on the analysis and improvement of homomorphic encryption algorithms of different systems, and we will determine their limits and performance.
I would like to thank my supervisor Mr. Abdellah EZZATI and my framing Mr. Abderrahim BENI HSSANE for the help, encouragement and guidance they have given me, in order to achieve this modest work.