


  

Kurdistan Journal of Applied Research (KJAR) 

Print-ISSN: 2411-7684 | Electronic-ISSN: 2411-7706  

 

Website: Kjar.spu.edu.iq | Email: kjar@spu.edu.iq 
  

 

 

 

 

A New Asymmetric Fully 

Homomorphic Encryption Scheme 

for Cloud Banking Data 

 
Zana Thalage Omar Fadhil Salman Abed 
Department of  Computer Department of Information Technology 

College of Science and Technology Kalar Technical Institute 

University of Human Development, Sulaimani Polytechnic University 

Sulaimani, Iraq Kalar,Iraq 

zana.omar@uhd.edu.iq  fadhil.abed@spu.edu.iq 

 

Shaimaa Khamees Ahmed 
Computer Engineering  

College of Engineering 

University of Diyala 

Diyala, Iraq 

shaymaakhamees88@gmail.com 

 

 

Article Info  ABSTRACT 

Volume 5 - Issue 2 -

December 2020 

DOI: 

10.24017/science.2020.2.12 

Article history: 

Received: 24 November 2020 

Accepted: 24 December 2020 

 
Most banks in our time still use the common traditional systems of 

high cost and relatively slow, we are now in the era of speed and 

technology, and these systems do not keep pace with our current 

age, so saving cost and time will be considered a fantastic thing 

for banks. The way to that is to implement cloud computing 

strategies with Considering data security and protection when it 

comes to using the cloud. The best solution to protect data security 

on the cloud is fully homomorphic encryption systems. The time it 

takes to encrypt and decrypt data is one of the main barriers it 

faces. Our current research provides a new algorithm for a 

publicly-keyed encryption system to keep bank data from 

tampering and theft when stored on the cloud computing 

platform, and our new system achieves fully Homomorphic 

Encryption, which allows mathematical operations to be 

performed on the encrypted text without the need for the original 

text. The security of the new system depends on the issue of 

analyzing huge integers, which reach 2048 bits, to their prime 

factors, which are considered almost impossible or unsolvable. A 

banking application has also been created that encrypts the data 

and then stores it on the cloud. The application allows the user to 

create accounts and deposits, transfer and withdraw funds, and 

everything related to banking matters. 

 

Keywords: 

Fully Homomorphic 

Encryption, Cloud computing, 

Asymmetric Encryption, Large 

number, Banking security. 

Copyright © 2020 Kurdistan Journal of Applied Research.  

All rights reserved. 

 

 

 

 

 

mailto:zana.omar@uhd.edu.iq
mailto:fadhil.abed@spu.edu.iq
https://scholar.google.com/citations?view_op=view_org&hl=en&org=18342936164438069611
mailto:shaymaakhamees88@gmail.com


Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 153 

 

1. INTRODUCTION 

The world is witnessing rapid development and prosperity of cloud computing, as cloud 

computing allows the sharing of services such as (applications, storage, processing) with cloud 

users. The focus is on increasing the effectiveness of shared resources[1]. One of the services 

provided by the cloud is to save users 'data on the cloud, hence the challenges and difficulties 

facing the cloud providers begin, as it is their responsibility to protect the security of user data 

on the one hand, On the other hand, the user does not fully trust the cloud providers because 

they can access, modify, and delete user data Intentionally, this issue is an obstacle to cloud 

providers[2]. Another phenomenon is a problem when storing data on the cloud as data 

exchange has become a common phenomenon among cloud providers under the service 

agreement because this phenomenon occurs in the scenes where the data owner is not aware of 

this process and is considered a violation of privacy Security of user data, especially untrusted 

parties may participate in this process [3]. Many believe that the solution lies in the use of 

encryption methods when storing data in the cloud and certainly should not use low-level 

security encryption methods. On the contrary, it must use high-level encryption methods in 

terms of security[4]. Most of the existing encryption systems face two main challenges. The 

first is that The principal distributions face threats in most symmetric key encryption systems 

[5]. The second is that data must be decrypted to make adjustments to it. Therefore, cloud 

providers have the decryption key, and thus the data becomes unsafe[6]. In this paper, we focus 

on the second challenge, where we create an encryption algorithm that allows modifications to 

the encrypted data without the need to decrypt it. This type of encryption is called 

Homomorphic Encryption Systems (HE)[7]. The term "homomorphism" is derived from a 

Greek word-initially composed of two parts. "Homos," which means the same, and "Morphic" 

means the form, this type of encryption (HE) is used in computer science, where it can convert 

plain text into encrypted text and make adjustments to it without the need to decrypt it[7]. This 

type of encryption is done through three stages: the stage of generation of the encryption key, 

the stage of encryption, and the stage of decryption. There are several types of it, one that 

supports multiplication operations, one that supports addition operations, and these two types 

are called (Partial Homomorphic Encryption)[8], [9]. And one that supports multiplication and 

addition operations together and is called (Fully Homomorphic Encryption), which is the type 

that We present in this paper. It supports addition and multiplication operations on encrypted 

data without the need to decrypt the data. The proposed algorithm generates the encryption key 

as described in Section 8, the key generation part, and then the data is encrypted using the 

encryption key through a mathematical algorithm described in the encryption part in Section 8. 

The data is stored on the cloud in an encrypted form and when any modification or addition is 

made to the data, Amendment to it while it is in its encrypted state without the need to decrypt 

it, as the decryption key is owned by the owner of the data only and can decrypt the data 

through the mathematical equation described in the decryption part in Section 8 Encryption is 

an essential and necessary factor when storing data on the cloud where only the owner of the 

data can access the data, so the correct choice of the encryption algorithm is necessary for the 

cloud providers and users also where more efficiency and security accuracy is available [10]. 

 

2. STATEMENT OF THE PROBLEM 

Cloud providers provide many services, including applications and storage many companies 

and users do not trust the providers of these services due to security concerns. Where the user 

does not upload his personal data to the cloud because the cloud providers are able to read and 

modify every bit loaded on the cloud and use it for personal purposes, and this thing does not 

comply with respecting the user’s privacy. Furthermore, some cloud providers still use 

traditional security techniques that are not secure with low-security level to protect user privacy. 

Some of the cloud providers have started to use high-level technologies to protect the privacy of 

users and the security of their data, but there remains a problem that the provider of the cloud 

itself is still able to access user data, and this is not safe for users. This problem can be solved 

when following FHE systems when storing data on the cloud where these systems can encrypt 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 154 

 

the data and store it in the cloud in an encrypted form and thus the cloud provider or others 

cannot see the data and use it, so the privacy of users and the security of their data are protected. 

 

3. RELATED WORK 

A symmetric encryption system was introduced to provide more data security and protect it 

from any serious attack in the year 2019 by [11], And about two years before that, specifically 

in )2017 )data security problems were presented when stored in the cloud and a method was 

proposed to provide complete data security using AES encryption technology with the use of 

standard encryption 128 Bit by [12],in (2018) an encrypting system was introduced based on 

the Pailler algorithm that supports the addition process and on the RSA algorithm that supports 

the multiplication process on the encrypted data by [13], An encrypting scheme based on a 

pattern called asymmetric cipher padding (OAEP)  was introduced with the symmetric cipher 

algorithm that stands for the RSA algorithm in (2018) by [14], and a completely symmetric 

encrypting system based on Euler's theory has been introduced and time complexity has been 

calculated and compared to other methods the size of an encryption key up to bits in (2018) by 

[15], while the size of the encryption key in our algorithm reaches more than 2048 bits and the 

encryption process is accomplished through more complicated and powerful mathematical 

equations, in (2018) a completely symmetric encrypting system was introduced on that relies 

the principle of changing a number from the plain text to another number using a secret key 

without converting On binary format then compare the result with DGHV and SDS systems by 

[16]. Not all banks use online banking services despite the tremendous benefits they enjoy due 

to the attacks they are subject to by cybercriminals. [17], [18] The authors present many attacks 

that occur on different components of online banking services, such as Spy_Eye Malware. 

Fraud and educational phishing are among the most common attacks on banking services, as 

these attacks steal user login confidentiality. [19]–[23] Researchers offer many possible 

solutions to phishing and attacks within browsers and across sites, but without these solutions 

fix the cloud-based environments. Also, risks related to banking services jobs were presented by 

researchers in [24]. 

4. BANK SERVICES IN THE CLOUD 

Because of the limited use of cloud services by companies in various fields and banks, it has 

also created a strong incentive for cloud services providers to develop their services, especially 

security, as researchers in cloud affairs have been stimulated to intensify their research and 

efforts to find appropriate solutions for bank safety and information. The use of cloud services 

for banks is considered a dangerous matter to some extent because to this day storing data on 

the cloud is not considered a safe matter because when the data is uploaded to the cloud, control 

over customer data (such as account numbers, deposits, etc.) is lost, but on the other hand, there 

are many reasons makes banks and other institutions to use cloud services, whether public or 

private, including scalability, agility and saving many costs, but these benefits come with risks 

related to data security, you should consider these risks when using cloud services. This 

problem can be solved if cloud providers use strong encryption algorithms when storing 

customer data in the cloud. This risk is illustrated by US national law [25]. Most cloud service 

providers who use encryption algorithms require their customers to trust them and use their 

decryption keys when making any modification to their previously stored data. This does not fit 

with the principle of respecting the privacy of customer data security. Given the high costs of 

computers, the recent financial crisis, and current health conditions (COVID-19), Banks must 

reduce their information technology costs, but this should not be done at the expense of data 

security and integrity. All these reasons drive banks to use cloud services. This paper offers a 

simplified banking system for storing data on the cloud, this system relies on A New 

Asymmetric Fully Homomorphic Encryption Scheme, as this algorithm relies on data 

encryption, storage on the cloud and modification on request without the need to decrypt data 

and own a private secret key for customers, and thus the privacy of customer data security has 

been respected and therefore customer data (banks) on the cloud is encrypted and cannot be 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 155 

 

viewed Anyone who is not authorized is required. Our new algorithm is explained further in the 

remainder of this paper. 

 

5. HOMOMORPHIC ENCRYPTION CATEGORIES 

There are three main categories of Homomorphic encryption schemes: Partially Homomorphic 

Encryption PHE, Somewhat Homomorphic Encryption SWHE, and Fully Homomorphic 

Encryption FHE schemes. PHE schemes, such as RSA [8], ElGamal [26], Paillier [9], Etc., 

allow to applying either addition or multiplication on encrypted data. G. Kalpana et al. [27], 

allowing unlimited additions and a single multiplication. Construction of scheme supporting 

both operations addition and multiplication simultaneously is possible in 2009 by Gentry [28] 

by using fully homomorphic encryption. 

 

5.1 Partially Homomorphic Encryption (PHE) 

An encryption technique is called a Partially Homomorphic Encryption (PHE) if it applies only 

one operation on encrypted data, i.e., either addition or multiplication but not both [29]. 

 

5.2 Somewhat Homomorphic Encryption (SWHE) 

The scheme that supports a limited number of homomorphic operations known as somewhat 

homomorphic encryption [30]. An encryption technique is called Somewhat Homomorphic 

encryption (SWHE) if it performs a limited number of addition and multiplication operations on 

encrypted data. 

 

5.3 Fully Homomorphic Encryption (FHE) 

An encryption technique is called Fully Homomorphic (FHE) if it performs both addition and 

multiplication simultaneously and can compute any operation [6]. 

 

6. PROPERTIES OF HOMOMORPHIC ENCRYPTION 

6.1 Additive Homomorphic Encryption: 

A homomorphic encryption is additive if: 

𝐸𝑛𝑐 (𝑚1 ⊕  𝑚2)  =  𝐸𝑛𝑐 (𝑚1)  ⊕  𝐸𝑛𝑐 (𝑚2). (1) 

 

6.2 Multiplicative Homomorphic Encryption: 

A homomorphic encryption is multiplicative, if: 

𝐸𝑛𝑐 (𝑚1 ⊗  𝑚2)  =  𝐸𝑛𝑐 (𝑚1)  ⊗  𝐸𝑛𝑐 (𝑚2). (2) 

 

7. FERMAT AND EULER THEOREMS 

Two important theorems presented the first by Pierre de Fermat and the second by Leonhard 

Euler. Both theorems are related to powers in modular arithmetic. 

Fermat’s Little Theorem 

Suppose that p is prime and gcd (a, p) = 1 (or a and p are relatively prime or p does not divide, 

then 

M p-1 ≡ 1 (mod p)  (3) 

 

7.1 Euler’s Theorem 

Euler’s Theorem is a generalize of Fermat’s Little Theorem. Suppose n be an arbitrary positive 

integer, ø(n) denote the number of integers 1 =< a <= n such that if gcd(a, n) = 1, 

then: M ø (n) ≡ 1 (mod n) (4) 

So that: 

M r* ø (n) +1 ≡ M (mod n), when r is an integer, M<n   and n=p*q where p and q are two primes 

number. 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 156 

 

8. PROPOSED FULLY HOMOMORPHIC ENCRYPTION SYSTEM 

8.1 The proposed scheme works as follows: 

Generating the encryption key and then encrypting the numbers and texts and storing them in 

encrypted form on the cloud. In our work, we use a local cloud and experiment with the 

proposed scheme on it. The purpose of this process is to save the data encrypted on the cloud so 

that no one can view the data and use it for personal purposes, Therefore, when the data owner 

needs to perform an amendment of the encrypted data on the cloud, an encrypted request is sent 

to the server and the server performs mathematical operations on the encrypted data and returns 

an encrypted result where this encrypted result can only be decrypted through the private 

encryption key which is with the owner of Data only so that he can decrypt the encrypted result 

and see his data. In this way, we have maintained the privacy and security of the data when 

stored in the cloud. These procedures go through three stages. Generation the encryption key 

stage, the encryption stage, and the decryption stage. 

 

8.2 Algorithm of A New Asymmetric Fully Homomorphic Encryption 

 Key Generation: 

Generate two large Prime number p, q  

Select two big random integer z and w 

Compute 𝑛 =  𝑝 ∗ 𝑞 and ø (𝑛)  = (𝑝 − 1) ∗ (𝑞 − 1) 
Calculate = 𝑛 ∗ 𝑧 , 𝑒𝑘 = 𝑤 ∗  ø (𝑛) and 𝑃𝑢𝑏𝑘𝑒𝑦 = 𝑃𝑘 ∗ 𝑒𝑘 
The public key is (Pubkey,ek) and private key is (p, q) 

 Messages Encryption: 

The message M will always be less than pk, that   (m1&m2), (m1+m2) and (m1*m2) < 

Pk 

The schema of message encryption is: 

𝑪 = 𝑷𝒖𝒃𝒌𝒆𝒚 + 𝒎
𝒆𝒌+𝟏  𝒎𝒐𝒅  𝑷𝒌  (5) 

Which depended only public-key (Pubkey, ek,  Pk)  to send the message                 

Where  

 M: Plain-text(Message), C: cipher-text 

 Message Decryption: 

The schema of cipher decryption is: 

              𝑀 = 𝐶 𝑚𝑜𝑑 𝑛  (6) 
 

8.3 Evaluate of fully Homomorphic Encryption Properties 

 

8.3.1 To Proof correctness of the scheme: 

C = Pubkey + M
ek+1 mod Pk  

M=C mod n = Pubkey + M
ek+1 mod Pk (mod n) 

                    = Pubkey( mod n)  + M
ek+1  mod n (mod Pk) 

                    =0+ Mek+1  mod n (mod Pk)= M
  mod Pk=M (since M< Pk)  

 

8.3.2 The Proof of Additive Homomorphic 

If the following condition is fulfilled, it becomes clear to us that the proposed scheme Additive 

Homomorphic: 

𝒎𝟏 + 𝒎𝟐 = 𝒅𝒆𝒄 [𝒆𝒏𝒄 (𝒎𝟏) + 𝒆𝒏𝒄 (𝒎𝟐)]  
Where dec is the decryption function and enc is the encryption function 

Proof: 

𝑐1 = 𝑃𝑢𝑏𝑘𝑒𝑦 + 𝑚1
𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) = 𝑃𝑘 ∗ 𝑒𝑘 + 𝑚1

𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) 

𝑐2 = 𝑃𝑢𝑏𝑘𝑒𝑦 + 𝑚2
𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) = 𝑃𝑘 ∗ 𝑒𝑘 + 𝑀2

𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) 

𝑐1 + 𝑐2=[𝑃𝑘 ∗ 𝑒𝑘 + 𝑚1
𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 )+ 𝑃𝑘 ∗ 𝑒𝑘 + 𝑚2

𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 )] mod n 
 =𝑃𝑘 ∗ 𝑒𝑘  (𝑚𝑜𝑑 𝑛)+ 𝑚1

𝑒𝑘+1 (𝑚𝑜𝑑  𝑛) mod 𝑃𝑘 +𝑃𝑘 ∗ 𝑒𝑘  (𝑚𝑜𝑑 𝑛)+ 
𝑚2

𝑒𝑘+1 (𝑚𝑜𝑑  𝑛) mod 𝑃𝑘  = m1+m2 
[𝑚1

𝑒𝑘+1 (𝑚𝑜𝑑  𝑛)mod 𝑃𝑘  =m1 mod 𝑃𝑘 = [𝑚1] ,by Fermat’s Little Theorem 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 157 

 

(m1 
r* 𝜭 (n) +1 mod n ≡ m1) 

[𝑃𝑘 ∗ 𝑒𝑘  (𝑚𝑜𝑑 𝑛) = 0], since 𝑃𝑘  =n *z, which is multiple of n modular n equal to zero. 
And so on the same for other terms. 

 

8.3.3 The Proof of Multiplicative Homomorphic 

If the following condition is fulfilled, it becomes clear to us that the proposed scheme 

Multiplicative Homomorphic: 

m1*m2=dec [enc (m1) * enc (m2)]       

Where dec is the decryption function and enc is the encryption function  

Proof: 

m1*m2=dec [enc (m1) * enc (m2)]       

𝑐1 = 𝑃𝑢𝑏𝑘𝑒𝑦 + 𝑚1
𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) = 𝑃𝑘 ∗ 𝑒𝑘 + 𝑚1

𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) 

𝑐2 = 𝑃𝑢𝑏𝑘𝑒𝑦 + 𝑚2
𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) = 𝑃𝑘 ∗ 𝑒𝑘 + 𝑀2

𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 ) 

𝑐1 ∗ 𝑐2 = [𝑃𝑘
2

∗ 𝑒𝑘
2+𝑃𝑘 ∗ 𝑒𝑘 ∗ 𝑚2

𝑒𝑘+1 ( 𝑚𝑜𝑑   𝑃𝑘 )+ 
 𝑃𝑘 ∗ 𝑒𝑘 ∗ 𝑚1

𝑒𝑘+1 ( 𝑚𝑜𝑑   𝑃𝑘 )+ 𝑚1
𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 )* 𝑚2

𝑒𝑘+1 (𝑚𝑜𝑑  𝑃𝑘 )] mod n 

=𝑃𝑘
2 ∗ 𝑒𝑘

2(𝑚𝑜𝑑 𝑛)𝑚𝑜𝑑  𝑃𝑘 + 𝑃𝑘 ∗ 𝑒𝑘 ∗ 𝑚2
𝑒𝑘+1 ( 𝑚𝑜𝑑   𝑛) mod 𝑃𝑘  

+𝑃𝑘 ∗ 𝑒𝑘 ∗ 𝑚1
𝑒𝑘+1 ( 𝑚𝑜𝑑   𝑛) mod 𝑃𝑘  

 +𝑚1
𝑒𝑘+1 (𝑚𝑜𝑑   𝑛) mod  𝑃𝑘 ∗  𝑚2

𝑒𝑘+1 (𝑚𝑜𝑑  𝑛) mod  𝑃𝑘  =m1*m2 
[𝑚1

𝑒𝑘+1 (𝑚𝑜𝑑  𝑛)mod 𝑃𝑘  =m1 mod 𝑃𝑘 = [𝑚1] ,by Fermat’s Little Theorem(m1 
r* 𝜭 (n) +1 ≡ m1) 

[𝑃𝑘 ∗ 𝑒𝑘  (𝑚𝑜𝑑 𝑛) = 0], since 𝑃𝑘  =n *z, which is multiple of n modular n equal to zero. 
And so on the same for other terms. 

 

9. RESULTS AND DISCUSSION 

Our proposed method has been applied in Java Language on a laptop that has these 

characteristics Intel (R) core (TM) i7-8550U CPU @1.80GHz 2.00GHz, 8 GB Ram, 64-bit 

Operating System, x64-based processor, Windows 10 and Big Integer library of java is used. 

 

9.1. Case studies  

In this section, several studies will be presented that we conducted to test our system to prove 

the creation of the secret key and its use for encryption and decryption 

 

Case study 1: 

Let us choose two different number m1= 4, m2 = 8, select prime numbers p=467, q=307, select 

random number r=401, z=271 and w=449 and compute n, ø (n) =(p-1) *(q-1), pk,ek and Pubkey 

where n = p*q , pk=n*z, ek=w* µ(n) and  Pubkey = pk*ek, as in figure 1, so n = 57490969 ,  

ø (n) = 57038400, pk=15580052599, ek=25610241600 and Pubkey = 399008911201097918400  

now we will compute c1, c2 where 

c1= Pubkey +m1 
ek+1 mod pk  

c1= 399008911201097918400+4
25610241600+1 mod 15580052599 

c1= 399008911209721563754 

c2= Pubkey +m2 
ek+1 mod pk 

c2= 399008911201097918400+8
25610241600+1 mod 15580052599 

c2= 399008911201097918408 

 

A. Check the Additive Homomorphism  

Let us define C3 is the result of c1+c2  

c3= c1+c2  

c3= 399008911209721563754+ 399008911201097918408 

c3= 798017822410819482162  

m3= c3 mod p 

m3= 798017822410819482162 mod 467 

m3= 12, which is the same of m1+m2 = 4 + 8 =12 

 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 158 

 

B. Check the Multiplication Homomorphism  

Let us define C4 is the result of C1*C2  

c4= c1*c2  

c4= 399008911209721563754* 399008911201097918408 

c4= 159208111221326555237218115498200062183632 

m4= C4 mod p 

m4= 159208111221326555237218115498200062183632 mod 467 

m4= 32, which is the same of m1*m2 = 4 * 8 =32 

 

Case study 2: 

We took as an example of 2048 bit A message containing several languages: English, Kurdish, 

Arabic and Chinese, to indicate that our scheme works in all languages. The message was: 

Fully Homomorphic encryption system is the best solution when storing data in the cloud 

 التشفير التماثلي التام يعد افضل حل عند تخزين البيانات على السحابة

全同态加密系统是在云中存储数据时的最佳解决方案 

 هومومورفيك ئينكريپشن باشترين ڕێگايه بۆ ههڵگرتنی زانياری له كاڵودا

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58551018895584377087249191335724085433447024543185504758455631650550492203454

64241056074079024109166204002367569192042605346490577631743669656928602593119

87269878821499594667240449799539516699641411229698173419572164662026446722542

45842179370658749263407810196728233031159967134374914299433764943853524262950

10248374434570101830938140507177653834149747566763219105733110623512036996321

94535963913255933743321718394914382531286601992742907837501385111059060019874

77588021055291849648949570048628664064077590484738933338889181212587636009178

3321 

q=27479324216009061896292077972720073521672478547125991911969838200015924859

13445493592485385233195477049349741424361315108262249184165808418072920022405

32191240404858029386958419842799686682471795353968158406182041332189135779311

42268145416491773923591539609233733196404783888133066336919076387688113196684

53317377733188135302564932982125876956345691771505946023899771659248597752163

70450129344735564036443811888747396621308549176665800328009187819795087471726

72324090656507275368384213216100552615957975944972170017248687813245723168819

51160642892464178663003766675944121364487852226241867052819190294856408013991

2399 

r=221704313573415863159846363027780946932749477453300762390358010519665644221

87140855682320560549672999017524704999360401622672733792707046542939076114622

71294645777433048961662607368834573356607007276968285901809569193575593361195

95183592425870109416627348226330225417095167338356961355353440978586915860732

25295416801346356644268401349085223233791565552540400714669486000596164658328

53354843569032953795841177317760938909217583755697157793455522895018625285194

62537280823951426545206331004884970981539080382288397414773455434023413361954

47440852503074070578011632695922887511174829871285336692705513320415788577077

679 

z=275249857110002837815800172710466356018329806961099866732193189637794181023

63701442691287193897733121259027100064136824329301210609187447135330014261476

50949829649323789524585055409208200878901235351905015521587034028332528553850

11614529987564845152327785052325832471682154173508783558623331252252968152219

16027089844912780553832369867433821093674360804418144757102515585490143240810

04911834111030009876069187484163346362681914347253110719669693609577828580519

55506648516062732533087705315351585063502912220372815271233309365462638783981

32239648469349585337867535450178014597005244053675435612025992973391019104165

051 

w=27970928086245618554130758033009128606102344747844162488872725298013994846

66750703759209951503644756559344326593436488713439727941370882474185729394202



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 159 

 

26568930125038906366151005406608696506059925021656511039066192720032347527969

16825734793075507607756350581033260197597066561939143858829691043997062844545

31619047315794357733653339906082961824373494521550887529988893790465408818017

14334723034181238734693852986203812112960241219323273443674522837689161421055

48731309980467698859425343574740941094513723675441376882831853221735200060302

65054894069344437565316320341105324384528818788195486201847329573292754450278

3547 

n=10769580094727002503471943187166493982427611244942262080176583144009934659

81143042618421771243562508741529558462567496164974218162794828070090102743116

14675744981617706981159659278840348642493533661619004418505278308630146273559

49776532784746004292342193106772858086635741189742878628382470222788825482078

61943946691808699382242542777997373518125113923399713103380525808288086413349

19212781469514351491835805699434775073115335471855882883646035920190250024882

58963291569442031252109254395186706720792585518142909784365241155548844983342

83189320986270780236136127138605362150211782152865745381504375705543553816512

21080065655104503709942786890696056308249476633106547878851299305806005512585

83541393276463237096719409790300468531918013125461699424164364113733499007492

38417041896555095544181828755557265971346981037514011439434062675852888528243

74771452124934839087438528317526026501724778542161519207350378280716665713992

33093893068896685065293401056907219377231430933622052700439764141956013176800

08441865070124950005050281952689339441458657533442962099842432475896256930594

04126544402701922750498619154017022505738530444115173928551210212914269478804

12860202143331118919677011230626375006094163641104605963225042768615177326418

04068211108887647811534025697434933102079051297094993378106248264111141798110

06075632477579241815254478917115784613782075604252933691662961011635444393974

09530862792837844730182746315230788913885544817429507257108778271967617395803

69155228561187843144824186591120699659377823199894425771268810353616296436945

83356611341470626782237814429171429730166442379827572105352396392849523835926

02752329293726120327361136868710322352784471970286028331332376113647464712430

52579019338540424638344553771108463500791094165293405274249922836843857047119

94952998965052165507568745669931336591389786290832307146403761468886675257507

99641 

 

The Message after encryption (Cipher Text): 

89295900219191118519022931543915293570526367958119369756690615872509965393822

31001740321331646477256733520778478120002484749463886513532178306089038239543

02840563285267128770795997132212844773626461847056101966474470314533455350620

35961583853467335353692058643877483368839024324323253148702413976549021747125

84267662290418187689873676027208635786466580431611882199972233892265537394995

11808792503513297027206315025447067373256990258810928316926704967052369318515

39123933129291735790734203167224718452036002934602397499396928658480040019814

48753794055536037412565397913390978373800211854455912862135884453189535416422

48643350177392070083256386839997606638372180955482018837827049995130280291737

80477854749578970665250919555137362702387050753022510647671078135904779199076

99613784625827003099595182929464504486913045408507958278445397409776501583072

08218365845189684157830888068028334654562249806532825451487522249699122205996

68854356943638262766852210468449630191908418239367807625716544138399309127329

81414556161366337124764581505287880141762366994590146327071125276854185469427

99348536482500412527825762989106752138717310011092660740968429827301331409068

42543259406882786575288370599930117936612945953571324798139866765622746682555

71132508113770654369759346831687920038271029897667892423374810263220958410482

11999897930106631362581295255946251804804094917660182672337363831278103290372

31174843643462187324258096511620171705278849528849072515299421288789465771681



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 160 

 

0

500

1000

1500

2000

2500

3000

8 kilobyte 12 kilobyte 20 kilobyte 28 kilobyte 40 kilobyte

Encryption and Decryption time measured in miliseconds

Encryption time (ms) Decryption time (ms)

43248593387968474598670964355373653052749795427143289149329468840372409439550

54849884901788502012854967911585319237252603534567463085636877395614784177845

96965108486808004477401942768168047222903019793219239964275477699956509410684

52328268610784830191025845961252703855535813829958762877983640392413802255355

46428135007324080259252467858536957855977571160173001816724564278149168611602

45823522934535900592968120713467599445675667134123013501889780848602863778123

26326135402160036272556155249730667204639551120185330579724202900318999797435

42879664943985365924734927922050496995004574143976224500409164715995045548258

80591841522178517562068523430265973738052677570728032144342485814823604886324

50637171202401642868793240782799510215265259095894494535471354049093275530862

39224260691868986164678833953163322689297576670114211557653732496694098293514

17825457316748989715570095449667266994555193687741260632502600000910540602742

76914747724897228602651401673101955313890555932552792140290794613348372108415

57663927723446685822998162225135864218539770247362377169461300200659677780338

82526148523095531246278362277516264723046543270412030208182692229566558800145

51506581473160603366883980285215638955963339387612200134501841503508805535949

21185510472589502996007692047569736831254613398327847474835174479696247965785

6968471415060827235319400271780….etc Due to the length of the encrypted text (Cipher 

Text), which reaches more than 530 pages, it has been truncated. Where the encrypted time was 

151225 ms and the decrypted time was 157 ms. we have also tested it on text with 8KB in its 

size and several different Keys in terms of size, and we compared the results with the planners 

from in terms of velocity, we obtained the following results as shown in table 1 and figure 1 

 
Table 1:  Performance of small file size encryption and decryption measured in a millisecond with 64bit 

key length. 

File size Encryption time (ms) Decryption time (ms) 

8 kilobyte 444 ms 54 ms 

12 kilobyte 517 ms 56 ms 

20 kilobyte 1262 ms 209 ms 

28 kilobyte 1705 ms 385 ms 

40 kilobyte 2504 ms 818 ms 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

Figure 1:  Computation encryption and decryption time of our schema 
  

 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 161 

 

.9.2 Our Asymmetric Fully Homomorphic Encryption Scheme Applied to Banking Data in 

the cloud:  
The Bank Application work as shown in figure 2 

9.3 Cloud and banking app experiences: 

As for our banking application, we created two accounts and encrypted them with a 2048-bit 

encryption key using our previously mentioned algorithm which required 1264 milliseconds as 

encryption time and stored it on a local private cloud as shown in figures 3 and 4. And also 

requests 65 milliseconds as the decryption time as is shown in figures 5 and 6 

9.4 Results of NIST Statistical Tests on the Generated Secret Keys: 

The randomness of this novel proposal is evaluated by the well-known NIST test suite[31]. 

Table 2 shows the test results of the proposed algorithm from the NIST statistical tests, 

demonstrating that the best statistical performance was obtained with this algorithm. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

Figure 2:  Scheme Representing the Link between the Bank and its Data Hosted in a Cloud 

Provider Server 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3:  Create a new account and encrypt it at Bank Application Level then send to the cloud server 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 162 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4:  User login data in encrypted form at Cloud Server leve 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

Figure 5:  User Data in encrypted form at Cloud Server 

 

 

 

 

 

 

 
 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 163 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

Figure 6:  User Data at Bank Application Level after decrypting it 

 

 

 

Table 2:  NIST test results for the proposed algorithm 

 

 

Tests P-value Result 

Frequency (Monobits) 0.969730 SUCCESS 

   

Block Frequency 0.934397 SUCCESS 

   

Cumulative Sums (Cusum) 0.955178 SUCCESS 

   

Runs 0.791649 SUCCESS 

   

Longest Run of Ones 0.812369 SUCCESS 

   

Rank 0.828802 SUCCESS 

   

Discrete Fourier Transform 0.749568 SUCCESS 

   

Non-Overlapping Template Matching 0.865923 SUCCESS 

   

Overlapping Template Matching 0.667917 SUCCESS 

   

Approximate Entropy 0.879027 SUCCESS 

   

Random Excursions 0.919402 SUCCESS 

   

Random Excursions Variant 0.942381 SUCCESS 

   

Serial 0.842202 SUCCESS 

   

Linear Complexity 0.909160 SUCCESS 



Kurdistan Journal of Applied Research | Volume 5 – Issue 2 – December 2020 | 164 

 

 

 

10. CONCLUSION 

In this paper, a new encryption technology based on Asymmetric(public key) Fully 

Homomorphic Encryption Scheme  has been proposed to ensure the security of user data when 

stored on the cloud and respect their privacy at rest that support all languages like(English, 

Arabic, Kurdi and Chinese) and others, Very large prime numbers (up to 617 digits, 2048 bit) 

represent the strength for attack of our scheme because the proposed system depends on the 

problem of Factorization to the primary factors, which are considered mathematical issues 

under discussion at the present time and the user data is encrypted with different keys  and thus 

provides effective security which prevents attackers from analyzing it and using it for personal 

purposes that ensure the security measures of the proposed technology it is resistance For any 

kind of brute force, mathematics, and time attacks, it explains that it can protect user data even 

if it is leaked to unauthorized parties, thus the proposed scheme ensures data security when it is 

stored in the cloud. 

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