The main dominant force to democratic governance is elections. Elections enable voters to choose leaders and to hold them answerable for their performance in office and reinforce the stability and legitimacy of the political community. The electoral process becomes challenging for individuals who cannot visit the polling stall for casting their votes. With the integration of data innovation, electronic voting system framework is all the more intriguing and too helpful for ensuring mass participation in the elections as people have the priviledge to vote anywhere. Nevertheless, security bridges stand as the main worry for using electronic voting system. Electronic voting system has been proven to be exploited by simulated hack attacks. The proposed authentication algorithm guarantees security prerequisites and solves the deficiencies in the RSA and Message Digest Method 5 Algorithm. The system can compute the sum of votes in ciphertext form without revealing the choice of the voters using its homomorphic property. The resulting ciphertext form without revealing the choice of the voters. The resultant ciphertext values will not be the same even though the same plaintext is encrypted, with a size of 4 times larger than the plaintext size. The success ratio for the system is 100% with the maximum number of messages that can be processed is 3.287.937.778 messages. Therefore, the proposed authentication algorithm for electronic voting system is effective, robust and simple and provide users with availability, confidentiality and integrity than the RSA and MD 5 algorithms.

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AKENTEN APPIAH- MENKA UNIVERSITY OF SKILL TRAINING AND
ENTREPRENEURIAL DEVELOPMENT
APPLICATION OF HOMOMORPHIC ENCRYPTION ALGORITHM IN
ELECTRONIC VOTING SYSTEM
BY
PRINCE DUAH MENSAH
MIT 821 INFORMATION SECURITY

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ABSTRACT
The main dominant force to democratic governance is elections. Elections enable voters to
choose leaders and to hold them answerable for their performance in office and reinforce
the stability and legitimacy of the political community. The electoral process becomes
challenging for individuals who cannot visit the polling stall for casting their votes. With
the integration of data innovation, electronic voting system framework is all the more
intriguing and too helpful for ensuring mass participation in the elections as people have
the priviledge to vote anywhere. Nevertheless, security bridges stand as the main worry for
using electronic voting system. Electronic voting system has been proven to be exploited
by simulated hack attacks. The proposed authentication algorithm guarantees security
prerequisites and solves the deficiencies in the RSA and Message Digest Method 5
Algorithm. The system can compute the sum of votes in ciphertext form without revealing
the choice of the voters using its homomorphic property. The resulting ciphertext form
without revealing the choice of the voters. The resultant ciphertext values will not be the
same even though the same plaintext is encrypted, with a size of 4 times larger than the
plaintext size. The success ratio for the system is 100% with the maximum number of
messages that can be processed is 3.287.937.778 messages. Therefore, the proposed
authentication algorithm for electronic voting system is effective, robust and simple and
provide users with availability, confidentiality and integrity than the RSA and MD 5
algorithms.

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CHAPTER ONE
INTRODUCTION
Elections are expected to free and free because it is the back bone of a democracy. Elections
are a standardized process by which adult citizens cast votes and elect leaders and members
to different government positions. Elections provide us with a peaceful transition of power
from one form of government to another; people may always nominate a party to form
government if they are dissatisfied with the current government, its policies and the way
its operates. The way to select representatives or leaders is by voting. In traditional voting
system, voters have to reach polling station and cast their votes and this is sometimes
difficult for the aged and the people who are living far from their home and voting centers.
Voting through the internet therefore allows voters to give their votes to their
representatives from anywhere as it ensures efficient and secured way of casting and
calculating the votes.
Electronic voting is often seen as a tool for making the electoral process more efficient and
for increasing trust in its management. Properly implemented, e-voting solutions can
increase the security of the ballot, speed up the processing of results and make voting
easier. Electronic voting system is associated with the strength of faster vote count and
tabulation, more accurate results as human error is excluded, efficient handling of
complicated electoral systems formulae that require laborious counting procedures,
improved presentation of complicated ballot papers, increased convenience for voters and
prevention of fraud in polling stations and during the transmission and tabulation of results
by reducing human intervention. Nevertheless, there are some loopholes associated with
the electronic voting system which includes lack of transparency, risk of manipulation by
insiders with privileged access to the system or by hackers from outside. If not carefully
planned and designed, especially with its security concerns, electronic voting can
undermine the confidence in the whole electoral process. Therefore, our proposal uses

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Homomorphic encryption to overcome these security issues and ensure the effectiveness
and efficiency of the electronic voting system.
1.2 Purpose of the Study
The main purpose of the article is to propose an authentication protocol, namely
Homomorphic encryption to address the deficiencies in the RSA and MD 5 algorithm in
securing an electronic voting system. The article specifically looks at:
i. Application of the Homomorphic Encryption
ii. Attack or collision resistance of Homomorphic Encryption
iii. The performance and time complexity of Homomorphic Encryption

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CHAPTER TWO
LITERATURE REVIEW
The literature review involves identifying gaps in the literature and seeking new lines of
inquiry with regards to the topic. The literature review encompasses electronic voting
system, homomorphic encryption and its properties with palier cryptosystem.
2.1 Electronic Voting System
Electronic Voting System, also known as e- voting, is voting that uses electronic means to
either aid or take care of casting and counting ballots. Depending on the particular
implementation, electronic voting may use standalone electronic voting machines (EVM)
or computers connected to the internet (online voting).
Electronic Voting may encompass a range of internet services, from basic transmission of
tabulated results to full- function online voting through common connectable household
devices. The degree of automation may be limited to marking a paper ballot, or may be a
comprehensive system of vote input, vote recording, data encryption and transmission to
servers and consolidation and tabulation of election results.
A worthy electronic voting system must perform most of these tasks while complying with
a set of standards established by regulatory bodies, and must also be capable to deal
successfully with strong requirements associated with security, accuracy, integrity,
swiftness, privacy, auditability, accessibility, cost- effectiveness, scalability and ecological
sustainability

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2.2 Homomorphic Encryption
R. Rivest, M. Dertouzos and Leo. Adleman presented the idea of Homomorphic
cryptosystem, long after the development of RSA. Homomorphic encryption is a type of
encryption method that allows computations to be performed on encrypted data without
decrypting it. The results of the computations are also encrypted and can only be revealed
by the owner of the secret key. It enables one to operate on encrypted data
Let E be an encryption function used to encrypt plaintext, x as plaintext and f() as operation
to implement , So homomorphic encryption is defined as :
f(E(x1), E(x2) ....E(xn)) = E(f(x1,x2....xn)) Additive Homomorphism :
Binary operation is denoted by +, so additive homomorphic is described as
E(x2) + E(x1) = E (x2 + x1)
Pallier Cryptography supports additive homomorphic property
2.3 Types of Homomorphic Encryption
Homomorphic encryption comes in different types and they include:
i. Partially Homomorphic Encryption (PHE): PHE only allows selected
mathematical functions to be performed on encrypted data.
ii. Somewhat Homomorphic Encryption (SHE): SHE allows a limited number of
mathematical operations up to a certain complexity to be performed, for a limited
number of times.
iii. Fully Homomorphic Encryption (FHE): FHE allows any kind of mathematical
operation to be performed for an unlimited number of times.

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2.4 Advantages of Homomorphic Encryption
i. Establishing a higher standard of data security
ii. Analyzing data without infringing on users’ privacy
iii. Generating measurable economic benefits by allowing big data analytics
on encrypted data while maintaining privacy and compliance controls
iv. Processing encrypted data in public and private clouds and third-party
environments while maintaining confidentiality controls
v. Allowing secure and efficient cloud use
2.5 Disadvantages of Homomorphic Encryption
i. Computationally expensive, as it introduces significant overheads compared to
performing the operations on non-encrypted data.
ii. Homomorphic encryption requires either application modifications or dedicated
and specialized client-server applications in order to make it work functionally.
2.6 Paillier Cryptosystem
One of the well- known schemes for homomorphic cryptography is Paillier. It was invented
by Pascal Paillier in 1999. It can encrypt many bits in single operation with a constant
factor of expansion and also an efficient decryption. Pallier cryptosystem is defined by four
terms: key generation, encryption, decryption and homomorphic operation.

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CHAPTER THREE
METHODOLOGY
The methodology comprises of the specific procedures or techniques used to identify,
select, process and analyze information about the homomorphic encryption. It further
discusses the various methods that makes the Homomorphic Encryption an efficient choice
over the other algorithms, including the sources of data collection, Homomorphic
Encryption Design Architecture and Research Instruments.
3.1 Sources of Data Collection
Information for this report was sourced from various secondary sources, all listed in the
reference list. Data from publications by International Journal of Applied Engineering
Research ISSN 0973-4562 Volume 13, Number 11 (2018) also proved valuable. This
report is not comprehensive analysis of the available literature but provides a broad
overview of the algorithm.
3.2 Stages in the Electronic Voting System using Homomorphic Encryption
In today’s competitive world, most of a lot of things are created on online platform.
Similarly, in internet voting system, people can cast their votes without visiting the election
booth. Internet voting system utilizes homomorphic encryption to count votes. The final
outcome is taken from encrypted collection of votes without decrypting them. So it remains
unknown who voted for whom. In this system, integrity and anonymity of the voter remains
hidden.
The voter should have to create their own account on this portal by verified government
documents. The several stages for online voting system are given below.

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Figure 1: A Flow Diagram
3.2.1 Registration stage
In this stage we can add new voter in electronic voting system by authenticating
voter through Election authority. The eligibility of the individual voter is verified by
collecting required details about them. User will enter their basic details and will add
their voter id which will be crossed checked with the electoral commission database.
After successful registration, user will able to cast a vote through electronic voting
system.

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3.2.2Authentication stage
This stage comes after registration stage. In this stage, user will authenticate themselves
using login id (which will be their voter id) and password that was set by the user in
registration phase. Thus using user id and password users can get uniquely authenticated.
3.2.3Voting stage
In this stage voter can give their vote. They can give vote to their selected candidate. The
vote given by voters to their selected candidates are then encrypted using Paillier
encryption. The encrypted votes are stored in database which will be then tallied in tally
stage.
3.2.4 Calculation stage
In this phase Votes that are stored in encrypted (using homomorphic encryption) form in
database are added to get total no of votes received by the respective parties. Consider we
have two numbers 10 and 20, we have to perform the addition on encrypted numbers using
pailliar algorithm.
3.4 Diagram of Homomorphic Encryption Scheme
A widely esteemed application of homomorphic encryption schemes is cloud computing.
Presently, the need for cloud computing is increasing fast, as the data we are processing
and computing on is getting bigger and bigger every day, with the effect that a single
person’s computation power does not suffice anymore. Hence, it is favorable to use
someone else’s power without losing the privacy we seek.
Say, Alice wants to store a sensitive file m ∈ {0, 1} n on Bob’s server. So she sends Bob
Enc(m1), ..., Enc(mn). Assume that the file is a database (a list of people with specific
information about them) and Alice wants to find out how many of them are 25 years old.
Instead of retrieving the data from Bob, decrypting it and searching for the wanted

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information, she will ask Bob to do the computations, without him knowing what or who
he is computing on. The answer from Bob comes in form of a ciphertext which only she
can decrypt with her secret key.
3.4 Research Instruments
Research instruments are tools used for data collection and analysis of the study. The
following tools were used in analyzing RSA Algorithm: flow chart, pseudocode and python
(programming language).
3.4.1 Flow Chart
A flowchart is a generic tool that is used to separate steps of a process in sequential order.
It has been adapted for a wide variety of purposes and can be used to describe various
processes.
3.4.2 Pseudocode
Pseudocode is meant only as a tool to help expedite the development process and defining
all inputs, outputs and interactions needed to effectively solve a problem. It should not add
another layer of complexity to the process.
3.4.3 Python
Python is the most efficient cross- platform tool, specifically programming language used
for artificial intelligence and machine learning solutions.

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CHAPTER FOUR
RESULTS AND DISCUSSION
This section of the article presents the findings of the study whose main purpose is to
propose a novel authentication algorithm to resolve the deficiencies in RSA and Message
Digest Method 5. The presentation of findings aligns with the objectives of the article of
the proposed Homomorphic encryption.
Analyzing Algorithm means to study the specification of the Algorithm and come to a
conclusion about how the implementation of that algorithm will perform in general. Here,
the amount of resources necessary to execute the algorithm is determined and its equivalent
running time (time complexity) or efficiency of the algorithm.
4.1 Application of the Electronic Voting System Using the Homomorphic Encryption
Algorithm
Based on the stages of the electronic voting system, users would have to follow strict
instructions to be able to cast their votes successfully as discussed in chapter 3. Here, we
shall consider the process a user must go through to cast his or her vote.
In the first place, voter will register themselves on the portal by giving some basic details
as their Full name, password, voter id, gender and region. After, fill the details user’s voter
id will be authenticated with government database of voter id.
Figure 4.1: Registration Form

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After successful registration stage, user can login with their voter id as username and
password that is set by them. Thus, voters will be authenticated uniquely with the
combination of voter id and password.
Figure 4.2: Homepage Figure 4.3: Login Page
This is where voters will cast their votes to choose their choice of candidate. Candidates
are denoted using the party’s symbol. Voter just needs to tap on the button indicated below
the party’s symbol.
Figure 4.4: Voting Page Figure 4.5: Polling Result
In existing system, Voter cast their votes online through electronic voting system and the
vote is stored in encrypted form using Paillier algorithm. The ballots are shuffled and apply
the rotational method on votes for storing votes in database which increase the time and

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space complexity so the overall cost of the system will not increase. The proposed system
allows voters to cast the votes and store it in encrypted form using Paillier cryptosystem
form maintaining the integrity of data. When vote casted for specific candidate, votes of
that candidate are stored in encrypted form and null value is in encrypted form
automatically set to the remaining candidates in database. This will provide more security
as the vote in encrypted form is updated in database for all candidates.
The attacker as well as the administrator or the employees who have access to the database
will not be able to distinguish between the ballot stored for the candidate is a vote cast by
the voter or a null value. The final county of votes for each candidate is calculated using
homomorpnic addition property of Paillier cryptosystem. The proposed system is faster
and provide more security as all votes are stored in encrypted form and this will help in
maintaining the three traids of the cybersecurity and thus, availability, confidentiality, and
integrity of the system.
4.2: Collision Resistance of Homomorphic Encryption
The figure below shows the security performance or collision resistance of homomorphic
encryption with Paillier algorithm.
Figure 4.6: Security Performance of Homomorphic Encryption

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From the above table, it can be indicated that the security performance with regards to the
key size increases with asymmetric encryption and decreases with symmetric encryption.
This shows that homomorphic encryption with paillier algorithm are semantically secure
and strong against collision resistance.
4.3 Performance and time complexity of Homomorphic Encryption
The performance, efficiency and time complexity of the above encryption algorithm is
calculated using the size of the key, given in bits as against time, also given in ms.
Figure 4.7: Encryption time for Paillier and Elgamal

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Table 4.1: Encryption time for Paillier Algorithm
The above table shows a rise in the encryption time as the length of the key increases. So
the combination of homomorphic encryption using Paillier cryptosystem can significantly
improve the storage and processing performance in the electronic voting scheme.
Therefore, homomorphic encryption can be considered much faster than many other
algorithms.

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CHAPTER FIVE
SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATIONS
The purpose of this article was to propose authentication algorithm to resolve the
deficiencies in RSA and Message Digest Method 5 Algorithms. This section presents the
summary of the major findings from the analyses of data, and then, make recommendations
and conclusion.
5.1 Summary of Major Findings
In the first place, it was revealed that the application of the electronic voting system using
homomorphic encryption undergoes four processes which includes registration stage,
authentication stage, voting stage and calculation stage where we get to know the results
of the election.
Secondly, the study indicated that the security performance with regards to the key size
increases with asymmetric encryption and decreases with symmetric encryption. This
shows that homomorphic encryption with paillier algorithm are semantically secure and
strong against collision resistance.
Furthermore, the study shows that the combination of homomorphic encryption using
Paillier cryptosystem can significantly improve the storage and processing performance in
the electronic voting scheme. Therefore, homomorphic encryption can be considered much
faster than many other algorithms.
5.2 Recommendation
Based on the various findings, I will recommend the proposed Homomorphic Paillier
Algorithm as an authentication encryption for electronic voting system rather than RSA
and MD 5.

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5.3 Conclusion
Voting through the internet has attracted many people specifically people living far from
their homes than traditional system of voting. From past few years, a lot of researchers
have started seeking interest in this field due to transparency and security concern. This
research paper describes the internet voting system using Paillier algorithm and its
homomorphic characteristics. This system gives assurance of data confidentiality and data
integrity in which it will use homomorphic properties for calculation of votes in the
encrypted form and then decrypting them to get it totally secure.
The homomorphic encryption algorithm is semantically secure, stronger collision
resistance and much faster processing performance than RSA and MD 5.

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