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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1087
Secure Cloud Based Centralized Health Improvement through
homomorphism Encryption
Shraddha T. Shelar1, Deepali D. Rane2, Suraj Rasal3 , Shubham Davate4
1,2 Assistant Professor, D. Y. Patil College of Engineering, Pune, Maharashtra, India
3 Assistant Professor, Bharati Vidyapeeth University College of Engineering Pune, India, India
4 Student, D. Y. Patil College of Engineering, Pune, Maharashtra, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract – Every individual on this earth lives with
generation lifestyle irrespective of health concern. Nobody
gives time for their health seriously, doesn’t keeps history
record and avoids healthy environment to survive due to fast
growing life-style. Even he/she visits hospital for minorhealth
issue, later ignores precautions and treatment cause. But due
to ignorance anyone’s health can be possibly reflected into
major serious health issue which further takes anyone
between life and death. Hence, considering these all scenario,
it is very essential for everyone so as to take care of their
health as first priority of their life. This paper represents very
useful medical science application for overcoming such facts.
Here we have presented idea of online scheme for sharing,
transferring, storing and maintaining database related to
person’s health. For this, we have used technique of modern
cryptography specifically a homomorphism encryption
technique and applied for attributes based encrypted data of
every patient. Our scheme will also provide the service for
patient for finding best doctor for best treatment. This uses
third party for storage and authentication scheme for sharing
keys between server and patient. Henceforth, our system will
surely useful for medical science field for providing best
treatment to patients and to give satisfaction for every
individual in view of their health.
Key Words: Attributes, Cryptography, Encryption,
Decryption, Homomorphism, Public Key, Secret key
1. INTRODUCTION
Information security is growing high for providing highly
secure environment on web to store person’s information.
Additionally, most of people don’t want to do their work as
paper based stuffs so as to preserve their previous records.
Online storage is the best way to provide such a services for
users. But as the number of users increases it is very
challenging job for online service providers to give secure
storage servicer. If we consider an example of hospital then
many times, if say patient A consults one doctor say D for
health issue, D will check his previous reports or medical
history. But, sometimes patients misplace his data due to
long gap in consultancy. If that patient has not carried his
data physically with him, then doctor againstartsfrominitial
stage of treatment. Hence it will be very important for that
doctor so as to know the patient’s actual medical history as
well as patient will also face the difficulties in proper
consultancy of getting medicine or health related checkups.
It is obviousthat doctor may consults aspertheirknowledge
and experiencesbut when point comesto check thepatient’s
medical history, doctor may face problems regarding
patients allergenic behavior towards medicine or any
reaction cause due to improper dose of medicine or type of
medicine used. In rare cases, patient may get suffered from
improper or wrong consultancy of doctor. This may creates
very serious health issue for patients due to which many
timespatient may suffer between life and death. Henceforth,
it is very serious issue taken into consideration for every
individual for correct measure of any person’s health and
providing corrective measuresthrough proper consultancy.
It can only be happened by keeping patients previous
medical record safely and showing it to current doctor for
suitable treatments so as to cure with deceases and get
better health.
Fig -1: Cloud based secure system Deployment
This paper is specifically focuses on the issue of medical
health record storage and its awareness for which there
should be standard centralized platform used by all the
doctors before starting with suitable Treatments on that
patient. It will specially used for the purpose of detecting
actual cause of patients and providing corrective measures
based on it through his/her medical history. This approach
based on two aspects. Fist, it include the central online
facility for storing patient’s medical history as patients ID
PID, doctor’s name, medical cause, medicines , reaction
cause, improvement plan and remark. On the other side, it
also includes doctor’s registration number DID,
Specialization, feedback rating report. With these two type
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1088
of data doctor can make specific decision on patient so as to
do a treatment. Additionally, patient will be aware about
which doctor is suitable for him depending on that doctors
rating. Here, in between this, there should be trustworthy
channel provided for maintaining confidentiality in online
storage. Hence, this paper represents a best practice of
efficiently maintaining
Fig -1: Activity for Centralized Medical database system used in Medical Science
secure and long lasting medical database. This will truly
provide patient to get treatment from best doctor as well as
it will help doctor to provide specific and best by looking
into patient’s medical history.
There are many encryption techniques can be applied for
providing confidentiality in cloud. But traditional schemes
are not long lasting and good enough to providetrustworthy
servers when data is big enough in cloud. Hence, modern
cryptography has been recently joined the field of
cryptography where complete protection package has been
provided even for huge amount of data on web.
In this paper, we have discussed homomorphismencryption
techniques in public key cryptographyforprivacypreserving
secure medical database. We have presented best approach
towards possible outcomes of this skim and shown future
usefulness of this database towards time leading process in
medical science research field.
2. HOMOMORPHISM FOR CLOUD DATA
Cloud is a very large and distributed concept of today’s
online storage scheme, where any type of data in any
quantity has been stored tremendously. This data may be
used as personally or for professionalusewhichisimportant
to keep in safe way. But, any service provider of cloud may
not givea commit wordsabout providing confidentialityand
integrity of data stored on cloud. There are many
cryptographic techniqueshas been applied.Homomorphism
is the best technique to use for internet services where it
plays very important role in cloud computing security [3].
When it is used, original data has been not seen while
applying encryption technique. This is the major role played
by homomorphism that your original data has been not
come into picture at all for encrypting it. When patient
registers and stores data on cloud it is in encrypted form for
safe storage. When other parties wish to explore the
information of that patient, it is operated in encrypted
format.
When patient himself approachesto do sothenonlydatawill
be truly shown in its original form. In this work. When
patient register to network for storage of data, keys are
created for encryption of information and stored on online
cloud into medical database. Basically,homomorphismisthe
technique for already encrypted data which leads to the
double encryption for information. So here there is no right
to third party for accessing bit of original information not
even knows the type of data. The strangeness of this
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1089
technique will truly useful in providing the fruitful services
in medical science field . It also maintainsthe recordsofbest
doctors to approach for getting benefit of best treatment.
Hence this paper is providing possible outcomes for using
this online database technology in medical science field.
3. PROPOSED APPROACH
Life is the most important priority of every individual and
which should be considered first. But due to very busy
schedule no one is ware about if there is not any major
concern about health, if there is no any serious issues
happened regarding health. If it is satisfied through small
and short tablets and oral treatmentsthennotsingleidentity
on earth considers it for granted is very big thing happened
to his/her body. Henceforth considering to all the aspects of
fast going life-style, we have presented a fresh approach of
handling the health of every individuals on earth through
secure medical technology which will positively work in
current aspects of lifestyle.
Figure 2 shown above will explain the architectural view of
how this application will work. This paper is only presenting
the idea for medical science and for involving it into all over
world as government based activity. Because, itwilleffecton
every person’s health. When any individual wants first time
medical health checkup he/she has to register online on the
medical official website. This will generate one PID number
for everyone those who will register. So, when he or she
wants to consult himself/herself. It is will be mandatory for
them to enter PID for knowing medical history ifany so asto
provide specific and best treatment by doctor.Aslikepatient
, every doctor who is doing practice in medical science field
should also register himself/herself for getting their
DID(Doctor’s Identity) which will be used every time when
every patient visits at their place. This will help that doctor
too for their future ratings by patients, for their service
improvement too. When PID and DID hasbeen entered then
only patient’sdata will be shown throughserver’sdatabases.
Hence , for patient also it is necessary to take consultancy
from specific doctor. Thus, following steps will simply
explain the basic model about how this approach can be
implemented for very essential use in medical science.
3.1 Registration Process
This is the initial procedure has to be done by patient/client
as well as doctor. When one patient want to consult by
doctor he/she will register himself/herself through online
scheme. Here it is necessary to check the authorized user by
uploading his/her identity documents so as to avoid the
threats in system. After this, patient will receive PIDnumber
(PIDSk) which is technically secret key generated by server
side. Doctor also has to gain registered ID(DIDSk) before
starting with his/her career in medical science field. In this
step, both doctor’s and patient’s database has been
maintained separately and stored in encrypted formatusing
public keys generated (PIDPk). So, on server data stored is t
in original format and encrypted on server side. It gives the
direct access to third party which is heedfully has to be kept
in encrypted format. Asdata is regarding patient’saswell as
doctor’scredential there should not be anysortofaccessand
rights provided to third party server. Hence, we have came
up with possible solution by using additive and
multiplicative feature of homomorphism encryption. This
hasbeen applied on data as well askey of users. Previouslyit
hasbeen only applied to informationon cloud forstoringthe
data but here keys are also target point for any kind of
attacks likeDoS or Man-in-Middle attacks[1] whichneedsto
overcome also. Hence, Here both will register and will store
their identity on server with keys but in encrypted format.
This processbasically usesattributessets for encryption[2]
3.2 Homo-mechanism for cloud data
This uses EIGmal cryptosystem and Gentry’s cryptosystem
[5][6] to construct the propertieson already encrypteddata.
With this, it is possible to perform the complex calculationof
addition and multiplication on cipher text. When data
encrypted on already encrypted information then there is
only need of approval for itsdecryption by the owner of that
data. Here when homomorphism has been applied on
encrypted data old data get lost automatically which is
stored on third party.
3.3 Access control on personal database
When any patient who is registered for online medical
database initially takes appointment for treatment online.
First best doctors will be displayed as per the ratings given
by previouspatients to them. Patient will select asparticular
doctor asper his/her specialization. For example.Forneural
issues patient will see the list of all neurologists in list asper
the selected information. He or she will take appointment
and will visit that place for consultancy.
When patient will enter his/her PIDSk on platform of
database followed by that doctor’s DIDSk. Initially data will
be in homo-encrypted format on server. When this hasbeen
entered by both side then only all the information of patient
has been displayed to doctor for further consultancy. It is
essential for every individual to keep information most
secure on cloud. Her Information of patient and doctor’s
credentials are stored as well as patient’s complete
information of his/her medical history, previous cause,
allergy medicines, pervious doctor’s information and
consultancy remarks are mentioned in database. The motto
behind this approach is clear towards strongly securing
information aswell asproviding trustworthy access control
for using this platform. Also if this service has been usedasit
is giving solution of double encryption through best feature
of modern cryptography
4. CONCLUSION
This paper presents possible outcomes specifically for
medical science field for maintaining best platform for
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1090
patient doctor relationship. It usesmostsecuretechniquefor
storing and accessing cloud based data for which patient s
well as doctor’sapproval needed. It hasavoidedgivingrights
to third party server for looking into data and applied
technique on cipher text for both keys and data. It will also
save every individual’s time for finding best medical service
for their health by providing highly rated medical specialist
list in very short time. Hence, this all aspectswill trulyuseful
for improvement and enhancement of every body’shealth if
best treatment found which is possible through our
centralized secure communication system.
REFERENCES
[1] M. Abdalla, M. Bellare, P. Rogaway, “DHAES: an
encryption scheme based on the Diffie–Hellman
problem”, IEEE P1363a, 1998.
[2] Shraddha Rasal, “Enhancing Flexibility for ABE through
the Use of Cipher Policy Scheme with Multiple
Mediators”, Springer’s Advances (AISC). November
2014.
[3] Craig Gentry “a fully homomorphic encryption
scheme”, September 2009.
[4] Yi. X. Paulet, R. Bertino .E, “Homomorphic Encryption
and Application,” Springer, Page no 27-46, 2014.
[5] ElGamal, “A Public Key Cryptosystem and a Signature
Scheme based on Discrete Algorithms”,IEEEtransaction
theory, Vol no 4, July 1985.
[6] Van Dijk, M., Gentry, C., Halevi, S., & Vaikuntanathan, V.
“Fully homomorphic encryption over the integers”
EUROCRYPT2010pp.24–43.Berlin:Springer.
doi:10.1007/978-3-642-13190-5_2,2010

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Secure Cloud Based Centralized Health Improvement through homomorphism Encryption

  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1087 Secure Cloud Based Centralized Health Improvement through homomorphism Encryption Shraddha T. Shelar1, Deepali D. Rane2, Suraj Rasal3 , Shubham Davate4 1,2 Assistant Professor, D. Y. Patil College of Engineering, Pune, Maharashtra, India 3 Assistant Professor, Bharati Vidyapeeth University College of Engineering Pune, India, India 4 Student, D. Y. Patil College of Engineering, Pune, Maharashtra, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract – Every individual on this earth lives with generation lifestyle irrespective of health concern. Nobody gives time for their health seriously, doesn’t keeps history record and avoids healthy environment to survive due to fast growing life-style. Even he/she visits hospital for minorhealth issue, later ignores precautions and treatment cause. But due to ignorance anyone’s health can be possibly reflected into major serious health issue which further takes anyone between life and death. Hence, considering these all scenario, it is very essential for everyone so as to take care of their health as first priority of their life. This paper represents very useful medical science application for overcoming such facts. Here we have presented idea of online scheme for sharing, transferring, storing and maintaining database related to person’s health. For this, we have used technique of modern cryptography specifically a homomorphism encryption technique and applied for attributes based encrypted data of every patient. Our scheme will also provide the service for patient for finding best doctor for best treatment. This uses third party for storage and authentication scheme for sharing keys between server and patient. Henceforth, our system will surely useful for medical science field for providing best treatment to patients and to give satisfaction for every individual in view of their health. Key Words: Attributes, Cryptography, Encryption, Decryption, Homomorphism, Public Key, Secret key 1. INTRODUCTION Information security is growing high for providing highly secure environment on web to store person’s information. Additionally, most of people don’t want to do their work as paper based stuffs so as to preserve their previous records. Online storage is the best way to provide such a services for users. But as the number of users increases it is very challenging job for online service providers to give secure storage servicer. If we consider an example of hospital then many times, if say patient A consults one doctor say D for health issue, D will check his previous reports or medical history. But, sometimes patients misplace his data due to long gap in consultancy. If that patient has not carried his data physically with him, then doctor againstartsfrominitial stage of treatment. Hence it will be very important for that doctor so as to know the patient’s actual medical history as well as patient will also face the difficulties in proper consultancy of getting medicine or health related checkups. It is obviousthat doctor may consults aspertheirknowledge and experiencesbut when point comesto check thepatient’s medical history, doctor may face problems regarding patients allergenic behavior towards medicine or any reaction cause due to improper dose of medicine or type of medicine used. In rare cases, patient may get suffered from improper or wrong consultancy of doctor. This may creates very serious health issue for patients due to which many timespatient may suffer between life and death. Henceforth, it is very serious issue taken into consideration for every individual for correct measure of any person’s health and providing corrective measuresthrough proper consultancy. It can only be happened by keeping patients previous medical record safely and showing it to current doctor for suitable treatments so as to cure with deceases and get better health. Fig -1: Cloud based secure system Deployment This paper is specifically focuses on the issue of medical health record storage and its awareness for which there should be standard centralized platform used by all the doctors before starting with suitable Treatments on that patient. It will specially used for the purpose of detecting actual cause of patients and providing corrective measures based on it through his/her medical history. This approach based on two aspects. Fist, it include the central online facility for storing patient’s medical history as patients ID PID, doctor’s name, medical cause, medicines , reaction cause, improvement plan and remark. On the other side, it also includes doctor’s registration number DID, Specialization, feedback rating report. With these two type
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1088 of data doctor can make specific decision on patient so as to do a treatment. Additionally, patient will be aware about which doctor is suitable for him depending on that doctors rating. Here, in between this, there should be trustworthy channel provided for maintaining confidentiality in online storage. Hence, this paper represents a best practice of efficiently maintaining Fig -1: Activity for Centralized Medical database system used in Medical Science secure and long lasting medical database. This will truly provide patient to get treatment from best doctor as well as it will help doctor to provide specific and best by looking into patient’s medical history. There are many encryption techniques can be applied for providing confidentiality in cloud. But traditional schemes are not long lasting and good enough to providetrustworthy servers when data is big enough in cloud. Hence, modern cryptography has been recently joined the field of cryptography where complete protection package has been provided even for huge amount of data on web. In this paper, we have discussed homomorphismencryption techniques in public key cryptographyforprivacypreserving secure medical database. We have presented best approach towards possible outcomes of this skim and shown future usefulness of this database towards time leading process in medical science research field. 2. HOMOMORPHISM FOR CLOUD DATA Cloud is a very large and distributed concept of today’s online storage scheme, where any type of data in any quantity has been stored tremendously. This data may be used as personally or for professionalusewhichisimportant to keep in safe way. But, any service provider of cloud may not givea commit wordsabout providing confidentialityand integrity of data stored on cloud. There are many cryptographic techniqueshas been applied.Homomorphism is the best technique to use for internet services where it plays very important role in cloud computing security [3]. When it is used, original data has been not seen while applying encryption technique. This is the major role played by homomorphism that your original data has been not come into picture at all for encrypting it. When patient registers and stores data on cloud it is in encrypted form for safe storage. When other parties wish to explore the information of that patient, it is operated in encrypted format. When patient himself approachesto do sothenonlydatawill be truly shown in its original form. In this work. When patient register to network for storage of data, keys are created for encryption of information and stored on online cloud into medical database. Basically,homomorphismisthe technique for already encrypted data which leads to the double encryption for information. So here there is no right to third party for accessing bit of original information not even knows the type of data. The strangeness of this
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1089 technique will truly useful in providing the fruitful services in medical science field . It also maintainsthe recordsofbest doctors to approach for getting benefit of best treatment. Hence this paper is providing possible outcomes for using this online database technology in medical science field. 3. PROPOSED APPROACH Life is the most important priority of every individual and which should be considered first. But due to very busy schedule no one is ware about if there is not any major concern about health, if there is no any serious issues happened regarding health. If it is satisfied through small and short tablets and oral treatmentsthennotsingleidentity on earth considers it for granted is very big thing happened to his/her body. Henceforth considering to all the aspects of fast going life-style, we have presented a fresh approach of handling the health of every individuals on earth through secure medical technology which will positively work in current aspects of lifestyle. Figure 2 shown above will explain the architectural view of how this application will work. This paper is only presenting the idea for medical science and for involving it into all over world as government based activity. Because, itwilleffecton every person’s health. When any individual wants first time medical health checkup he/she has to register online on the medical official website. This will generate one PID number for everyone those who will register. So, when he or she wants to consult himself/herself. It is will be mandatory for them to enter PID for knowing medical history ifany so asto provide specific and best treatment by doctor.Aslikepatient , every doctor who is doing practice in medical science field should also register himself/herself for getting their DID(Doctor’s Identity) which will be used every time when every patient visits at their place. This will help that doctor too for their future ratings by patients, for their service improvement too. When PID and DID hasbeen entered then only patient’sdata will be shown throughserver’sdatabases. Hence , for patient also it is necessary to take consultancy from specific doctor. Thus, following steps will simply explain the basic model about how this approach can be implemented for very essential use in medical science. 3.1 Registration Process This is the initial procedure has to be done by patient/client as well as doctor. When one patient want to consult by doctor he/she will register himself/herself through online scheme. Here it is necessary to check the authorized user by uploading his/her identity documents so as to avoid the threats in system. After this, patient will receive PIDnumber (PIDSk) which is technically secret key generated by server side. Doctor also has to gain registered ID(DIDSk) before starting with his/her career in medical science field. In this step, both doctor’s and patient’s database has been maintained separately and stored in encrypted formatusing public keys generated (PIDPk). So, on server data stored is t in original format and encrypted on server side. It gives the direct access to third party which is heedfully has to be kept in encrypted format. Asdata is regarding patient’saswell as doctor’scredential there should not be anysortofaccessand rights provided to third party server. Hence, we have came up with possible solution by using additive and multiplicative feature of homomorphism encryption. This hasbeen applied on data as well askey of users. Previouslyit hasbeen only applied to informationon cloud forstoringthe data but here keys are also target point for any kind of attacks likeDoS or Man-in-Middle attacks[1] whichneedsto overcome also. Hence, Here both will register and will store their identity on server with keys but in encrypted format. This processbasically usesattributessets for encryption[2] 3.2 Homo-mechanism for cloud data This uses EIGmal cryptosystem and Gentry’s cryptosystem [5][6] to construct the propertieson already encrypteddata. With this, it is possible to perform the complex calculationof addition and multiplication on cipher text. When data encrypted on already encrypted information then there is only need of approval for itsdecryption by the owner of that data. Here when homomorphism has been applied on encrypted data old data get lost automatically which is stored on third party. 3.3 Access control on personal database When any patient who is registered for online medical database initially takes appointment for treatment online. First best doctors will be displayed as per the ratings given by previouspatients to them. Patient will select asparticular doctor asper his/her specialization. For example.Forneural issues patient will see the list of all neurologists in list asper the selected information. He or she will take appointment and will visit that place for consultancy. When patient will enter his/her PIDSk on platform of database followed by that doctor’s DIDSk. Initially data will be in homo-encrypted format on server. When this hasbeen entered by both side then only all the information of patient has been displayed to doctor for further consultancy. It is essential for every individual to keep information most secure on cloud. Her Information of patient and doctor’s credentials are stored as well as patient’s complete information of his/her medical history, previous cause, allergy medicines, pervious doctor’s information and consultancy remarks are mentioned in database. The motto behind this approach is clear towards strongly securing information aswell asproviding trustworthy access control for using this platform. Also if this service has been usedasit is giving solution of double encryption through best feature of modern cryptography 4. CONCLUSION This paper presents possible outcomes specifically for medical science field for maintaining best platform for
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 12 | Dec-2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1090 patient doctor relationship. It usesmostsecuretechniquefor storing and accessing cloud based data for which patient s well as doctor’sapproval needed. It hasavoidedgivingrights to third party server for looking into data and applied technique on cipher text for both keys and data. It will also save every individual’s time for finding best medical service for their health by providing highly rated medical specialist list in very short time. Hence, this all aspectswill trulyuseful for improvement and enhancement of every body’shealth if best treatment found which is possible through our centralized secure communication system. REFERENCES [1] M. Abdalla, M. Bellare, P. Rogaway, “DHAES: an encryption scheme based on the Diffie–Hellman problem”, IEEE P1363a, 1998. [2] Shraddha Rasal, “Enhancing Flexibility for ABE through the Use of Cipher Policy Scheme with Multiple Mediators”, Springer’s Advances (AISC). November 2014. [3] Craig Gentry “a fully homomorphic encryption scheme”, September 2009. [4] Yi. X. Paulet, R. Bertino .E, “Homomorphic Encryption and Application,” Springer, Page no 27-46, 2014. [5] ElGamal, “A Public Key Cryptosystem and a Signature Scheme based on Discrete Algorithms”,IEEEtransaction theory, Vol no 4, July 1985. [6] Van Dijk, M., Gentry, C., Halevi, S., & Vaikuntanathan, V. “Fully homomorphic encryption over the integers” EUROCRYPT2010pp.24–43.Berlin:Springer. doi:10.1007/978-3-642-13190-5_2,2010