Online e voting prototype with ptc web services v1

Applying MESE processes to Improve Online E-Voting

Prototype System with

Paillier Threshold Cryptosystem

Web Services

Version 1.00

A project submitted to the Faculty of Graduate School, University of Colorado at

Colorado Springs in Partial Fulfillment of the Requirements for the Degree of

Master of Engineering in Software Engineering Department of Computer Science

Prepared by Hakan Evecek

CS701

Dr. Chow

Spring 2007

Online E-Voting Prototype System Evecek / Page 1 of 37

This project for the Masters of Engineering in Software Engineer degree by
Hakan Evecek
has been approved for the
Department of Computer Science
By

_______________________________________________________
Dr. C. Edward Chow, Chair

_______________________________________________________
Dr. Richard Weiner

_______________________________________________________
Dr. Xiaobo Zhou

Date


Table of Contents

Online E-Voting System Project Documentation................................................................4
Abstract................................................................................................................................6
1. Introduction......................................................................................................................7
2. E-Voting System Related Literature................................................................................9
2.1. Public Key Cryptography........................................................................................9
2.2. Homomorphic Encryption.....................................................................................10
2.3. Zero Knowledge Proofs.........................................................................................10
2.5. Cryptographic Voting Protocol..............................................................................11
2.6. Issues in secure e-voting system............................................................................12
2.7. Completely Automated Public Turing test to tell Computers and Humans Apart
(CAPTCHA)..................................................................................................................13
2.8. Chinese Remainder Theorem (CRT)....................................................................14
3. Online E-Voting System Project Description................................................................17
3.1. Paillier Threshold Crytosystem Web Services Architecture and Design..............17
4.1. E-Voting System Overview...................................................................................21
4.1.1 User Login........................................................................................................22
4.1.2. Election Set-Up................................................................................................23
4.1.3. Creating Ballots...............................................................................................24
4.1.4. Vote Format.....................................................................................................25
4.2. Voting....................................................................................................................26
4.2.1. Creating the Vote.............................................................................................26
4.3. Tally the Vote........................................................................................................27
5. PTC Web Services Efficiency Improvement.................................................................28
5.1 Pre-Computation.....................................................................................................28
5.2 Chinese Remainder Theorem (CRT)......................................................................28
5.3 Paillier Scheme Pre-computations for Decryption.................................................29
6. Results ...........................................................................................................................30
6.1 Pre-Computation Performance Evaluations ...........................................................30
6.2. Defects Found .......................................................................................................32
6.3. Conclusion.............................................................................................................34
6.5. Future Suggestions.................................................................................................35
7. References.....................................................................................................................36


Online E-Voting System Project Documentation

The subsequent files are located on the following web site:

http://cs.uccs.edu/~gsc/pub/master/hevecek/doc/

o CS701Proposal_EVotingPrototype.doc : This document describes what the project

would be for the advisory committee. It was submitted in February 2007.

o EVoting_SRS Document.doc: This is the online E-Voting prototype System

Requirements Specification document for the project. The demonstration windows

application created used to get the requirements for the online tool. It also has the use

cases.

o EVoting_SDS Document.doc : This describes the internal design of the project.

This document has both black box and white box designs. Also class diagrams from

the web services are also prepared for documenting although they were developed

previously. It has the main use cases to make it easier to create the SDS. It also

involves database design.

o EVoting_Test Plan.doc: The tests for the project are documented in this document.

Test plans cover all the requirements testing.

o Online E-Voting Prototype with PTC Web Services.doc: This is the project report

document. It is the final report for the project that has discussions about e-voting

system. There are some e-voting related papers researched about the online e-voting

system implementation and I tried to explain why it is so hard to implement, develop

and deploy today by using these papers. Also in this report for the PTC design section

and PTC develop description, [15] is used. Lastly, some efficiency improvements


applied in the code and according to the results that will be explained, it has

improved.

o Paillier ThresholdCryptoService_UserGuide_Updated.doc: This document that is

the user guide for the PTC web services. Source files for the code is placed in the

link below: http://cs.uccs.edu/~gsc/pub/master/hevecek/src/


Abstract

The purpose of this master’s project is to develop an Online E-Voting prototype

system utilizing the Paillier Threshold Cryptosystem (PTC) web services and applying

MESE processes to it in an attempt to find possible solutions to further improve existing

PTC web services.

Online voting (e-voting) would be more convenient, relatively secure and utilize

fewer resources. To be able to access e-voting system from a personal, business or even a

public library computer may be more convenient for many people needing to vote. This

could potentially be a solution for the low voter turnout at the polls. However, it is still

questionable whether elections can be conducted online or over the internet due to the

high level of concern over security.

Systems considered to be apart of e-voting are Machine readable (create, read,

count) ballot systems, Direct Recording Electronic (DRE) systems, voting using mobile

devices and internet voting [1]. As part of this project, an online e-voting prototype

system has been constructed using the demonstration windows application tool created

for PTC web services. A pre-computation process is applied due to efficiency

improvements. The details of this optimization and improvement in the web services

process will be explained in the subsequent sections.

In addition to the application of the pre-computation to the process, the Chinese

Remainder Theorem can be applied during the decryption process. This change might not

be as noticeable as the pre-computation, however it will make it more efficient as the

calculation gets easier.


1. Introduction

In traditional elections, a voter usually goes to the voting stations. After direct

person-person verification with some IDs, the voter is allowed to vote. The voter is then

given a ballot which allows a single vote. Once the ballot is used, it cannot be used again.

However, this ballot must also be anonymous. The ballot must identify the voter as being

permitted to vote, but not reveal their actual identity, and the voter must also be given

assurances of this. Traditional polling methods trust a lot of parties during the election.

The current methods require an attacker interact directly with the voting process to

disrupt it. There is a greater chance of getting caught as there will be physical evidence in

the traditional polling.

On the other end, internet is harder to control and manage the security as Network

and internet related attacks are more difficult to trace. In the traditional polling, you know

who is in the election room. Also with the internet or network related voting, from all

around the world you will have attackers, not only by the few people in the room [3].

Figure 1 shows the hierarchy of the voting schemes just discussed [17].


Figure 1: The categorization of the voting schemes [17].

Another issue with e-voting is educating the voters. We can not consider that all

the users are computer gurus and they will use the e-voting systems easily. When e-

voting is designed it needs to be easy to use. We should consider the fact that a large

portion of the voting public has a very little knowledge about the computers. According

to some of the research done by the Public Policy Institute of California over 50% of 18-

44 years of age voters prefers Internet voting [3].

Some recent studies have focused on e-voting, its security concerns and making it

more secure. Below is the list of related literature about e-voting:


2. E-Voting System Related Literature

2.1. Public Key Cryptography

Public key cryptography, also known as asymmetric cryptography, is a form of

cryptography in which each user will have a key that didn’t have to be kept secret.

Having this public key will not inhibit the system’s secrecy as a message encrypted with

the public key can be decrypted only with the corresponding private key. The private key

is kept secret, while the public key may be widely distributed. The public and private

keys are related mathematically. The private key cannot be practically derived from the

public key [4]. The two main branches of public key cryptography are:

Public key encryption — a message encrypted with a recipient's public key cannot

be decrypted by anyone except the recipient possessing the corresponding private key.

This is used to ensure confidentiality [4].

The problem with the public key encryption is the intruder can easily replace the

private key with his when the sender requests the public key. This means the newly

received public key will have the intruder’s private key and he can easily decrypt the

message. To avoid this issue digital signature can be used.

Digital Signatures — a message signed with a sender's private key can be verified

by anyone who has access to the sender's public key, thereby proving that the sender

signed it and that the message has not been tampered with. This is used to ensure

authenticity [4].

Conversely, Secret key cryptography, also known as symmetric cryptography

uses a single secret key for both encryption and decryption. It is also known as one-key

or private-key encryption. The requirement is the shared secret that both parties should


have a copy. In this e-voting prototype shared keys will be used for the users’ encryption

in our tests.

2.2. Homomorphic Encryption

The encryption algorithm E ( ) is homomorphic if given E(x) and E(y), one can

obtain E(x Φ y) without decrypting x; y for some operation Φ.

In that case, homomorphic encryption is a special type of cryptography in which

the sum of two encrypted values is equal to the encrypted sum of the values. In simple

mathematics, this is equivalent to the communicative property of multiplication. For a

majority of cryptographic algorithms, this does not hold true.

It is one of the schemes that can be used in e-voting especially to be able to tally

the votes even though the results are encrypted. There are few cryptosystems which uses

homographic encryption. They will be discussed in the next section.

2.3. Zero Knowledge Proofs

In cryptography it is often needed to prove some statement to someone without

giving extra information. This is accomplished by Zero Knowledge Proofs. Especially for

the authentication systems Zero Knowledge Proofs can be used. For example, a party

might want to prove his identity with secret information and does not want the other party

to learn anything about this secret. In other words, second party can only know the

correctness of the statement or identity of the first party and no more information.

2.4. Threshold Cryptography

Threshold Cryptography is a term used to describe a cryptosystem in which the

ability to perform a cryptographic function can be distributed amongst several


participants in such a way that only through cooperation of a specified subset of the

participants can the operation be performed. In addition, if less than the required number

of participants’ attempts to perform the action, no useful information can be constructed

or obtained. The threshold value is typically denoted by the letter t. In a threshold

system as defined here, only t+1 cooperating authorities can perform the desired

cryptographic operation.

The essential components of a threshold cryptography system are a key

generation algorithm, an encryption algorithm, a share decryption algorithm, and a

combining algorithm [5]. First, the key generation algorithm generates the public key

parameters, a set of secret key “shares”, and a set of “verifier keys”. The secret key

shares are distributed to the participants in a secure manner. The encryption algorithm

provides encryption services for an appropriately-sized message m by applying the public

key parameters and an encryption algorithm to generate the ciphertext c. The share

decryption algorithm is used by each participant with a secret key share to “partially

decrypt” the encrypted message c. Each participant also uses the verifier key

corresponding to the secret key share to generate a proof of correct encryption. The

combining algorithm takes all of the “partial decryptions” or “decryption shares”, verifies

their corresponding proofs, and combines the decryption shares to reveal the original

message m. The combining step only succeeds if t+1 valid decryption shares are used.

2.5. Cryptographic Voting Protocol

Basic requirements for electronic voting

• Privacy – All votes should be kept secret


• Completeness – All valid votes should be counted correctly

• Soundness – Any invalid vote should not be counted

• Unreusability – No voter can vote twice

• Eligibility – Only authorized voters can cast a vote

• Fairness – Nothing can affect the voting

Extended Requirements for electronic voting

• Robustness – faulty behavior of any reasonably sized coalition of

participants can be tolerated. In other words, the system must be able to tolerate to certain

faulty conditions and must be able to manage these situations.

• Universal Verifiability – any party can verify the result of the voting

• Receipt-freeness – Voters are unable to prove the content of his/her vote

• Incoercibility – Voter cannot be coerced into casting a particular vote by a

coercer.

There are four main approaches to efficient and fully secure elections:

• Schemes based on homomorphic encryption

• Schemes based on mixnets

• Heterodox schemes

• Schemes based on secret sharing among several mutually distrustful

election authorities.

2.6. Issues in secure e-voting system


The issues behind e-voting need to be examined conservatively before such

potentially dangerous moves are made. In a voting system, privacy and security are

desired, but are not always simultaneously achievable at a reasonable cost. In online

voting systems, verification is very difficult to do accurately, and anonymity is difficult

to ensure. This document shows some of the many problems with practical e-voting and

why public elections are too important to trust to it [3].

When e-voting system scheme is considered there are different modules involved

to consider the security and design. Three important phases of having a secure system

are considered as design, development and deployment. In other words, it is important tp

have the foundation in designing a secure and practical e-voting scheme to produce a

secure, efficient and publicly acceptable implementation of voting schemes in the real

world.

2.7. Completely Automated Public Turing test to tell Computers and Humans Apart
(CAPTCHA)
Any additional check for the security or spam will decrease the security concerns

users have today for the e-voting systems. A CAPTCHA is a program that can generate

and grade tests that humans can pass but current computer programs cannot. In our

project this is used to confirm that users are trying to vote instead of the automated

computer systems. CAPTCHAs have several applications for practical security like

preventing comment spam in blogs, protecting web registrations, online polls where you

want to make sure that humans are voting not the programs, preventing dictionary

attacks, search engine bots, worms and spasm etc. Official Captcha site has published

some guidelines for it [6].


Accessibility: It should be easily accessible for reading the text. If it is a problem

due to legal reasons audio CAPTCHA can also be used.

Image Security: Images should be distorted randomly. Without random

distortion, application will be open to the attacks.

Script Security: By using this, systems are closed to any computer attacks.

However we also need to make sure that scripts used are not easily accessible so that

attacker will find the easy way around them to use the systems.

Security Even After Wide Spread Adoption: Some of the sites might be using the

sites that have CAPTCHAs setup. It is important that the security level kept the same and

these sites are still secure even after a significant number of sites adopt them [6].

2.8. Chinese Remainder Theorem (CRT)

On several papers for improving the efficiency, CRT is recommended to use both

on encryption and encryption process [16], [21]. As described below CRT is not affecting

to the multiplication. In other words, multiplying two big prime numbers and processing

the multiplication will be the same as processing them first and then multiplying. This

way the process will be done with smaller numbers and will be faster. Then

multiplication can be done.

Theorem Statement:

Suppose n1, n2, …, nk are integers which are pairwise coprime. Then, for any

given integers a1,a2, …, ak, there exists an integer x solving the system of simultaneous

congruences


Furthermore, all solutions x to this system are congruent modulo the product

N = n1n2…nk.

Sometimes, the simultaneous congruences can be solved even if the ni's are not

pairwise coprime. A solution x exists if and only if:

All solutions x are then congruent modulo the least common multiple of the ni.

In that case,

We can perform 2 operations mod p and mod q like below.

x ≡ a mod p,

x ≡ b mod q,

The Chinese Remainder Theorem can be used to efficiently reduce the decryption

workload of the cryptosystems [21]. To see this, one has to employ the functions Lp and

Lq defined over

By


Decryption can therefore be made faster by separately computing the message

mod p and mod q and recombining modular residues afterwards:

With pre-computations

Where p - 1 and q - 1 have to be replaced by α in the fast variant.


3. Online E-Voting System Project Description

In this project, PTC Web services are used. In this section, I will explain how the

PTC web services work. Efficiency improvement that will be applied to the PTC web

services required some changes on some of the classes used. Applying more

improvements will need more changes on the classes where calculations applied. Details

will be explained in the following sections of this report.

3.1. Paillier Threshold Crytosystem Web Services Architecture and Design

The Paillier cryptosystem is a probabilistic asymmetric algorithm for public key

cryptography, first published by Pascal Paillier in 1999. This probabilistic scheme has

generated a good amount of interest and further study since it was discovered.

The problem of computing n-th residue classes is believed to be computationally

difficult to compute. This is known as the Composite Residuosity (CR). The scheme is an

additive homomorphic cryptosystem; this means that, given only the public-key and the

encryption of m1 and m2, one can compute the encryption of m1 + m2.

One of the properties of Paillier as mentioned above is the homomorphic property

which can allow this cryptosystem to do simple addition operations on several encrypted

values and obtain the encrypted sum. The encrypted sum can later be decrypted without

ever knowing the encrypted values that made up the sum. Due to these useful

characteristics of Paillier, the scheme has been suggested for use in threshold

cryptosystems, secret sharing schemes and the design of voting protocols especially the

e-voting systems.

Another property of Paillier cryptosystem is self-blinding. This property is

essential as it means a ciphertext can be re-encrypted with a random parameter without


changing the underlying cleartext and without changing the ability to decrypt the

ciphertext using the original keypair[15]. Probabilistic property of Paillier will help to

protect voter’s privacy since none of the votes will be encrypted to the same ciphertext.

Paillier has described three different methods in his research. PTC Web services

that will be used in this project are using one of these three methods. Below are the

schemes invented by Pascal Paillier [21] and

Scheme 1: Scheme 1 is probabilistic encryption scheme based on composite

residuosity. According to theorem mentioned in his paper [21] Scheme 1 is one-way if

an only if the Computational Composite Residuosity Assumption holds. It is also

semantically secure if and only if the Decisional Composite Residuosity Assumption

hold. n is the multiplication of two prime numbers, n = pq. g is randomly selected base.

This can be done by checking whether . This is done on the

PTC web services used. n and g are public parameters and (p, q) or λ remains private.

Encryption:
plaintext m < n
randomly select r < n
ciphertext c =
Decryption:
ciphertext c < n2

Table 3.1 Paillier’s Scheme 1 [21]


Scheme 2: Scheme 2 is a trapdoor permutation based on composite residuosity.

As described above n is the product of two prime numbers. From the table below, there

are steps explained for decryption. To be able to retrieve m, all these steps will be

required. Scheme 2 is one-way if and only if RSA [n,a] is hard [21].

Encryption:
plaintext m < n2
split m into m1, m2 such that m = m1 + nm2
ciphertext c =
Decryption:
ciphertext c < n2

plaintext m = m1 + n m2

Scheme 3: Third scheme is the variant with fast decryption. As this is a fast

decryption, this scheme can be applied to improve the efficiency. In the following

sections this scheme will be re-visited and it will be recommended for efficiency

improvements in the current web services.

Encryption:
plaintext m < n
randomly select r < n
ciphertext =
Decryption:
ciphertext c < n2


It is assumed that g Є for some 1 ≤ α ≤ λ. In other words α and λ are not the

same secret keys.


Below are the steps for the key generation, encryption and decryption used [22].

Key generation

1. Choose two large prime numbers p and q randomly.

2. Compute n = pq and λ = lcm(p − 1, q − 1)

3. Select random integer g where

4. Ensure n divides the order of g by checking the existence of the following

multiplicative inverse:

where function L is defined as

The public (encryption) key is (n,g).

The private (decryption) key is (λ,μ).

Encryption

1. Let m be a message to be encrypted where

2. Select random r where

3. Compute ciphertext as:

Decryption

1. Ciphertext

2. Compute message:

It is the same as the scheme 1 described above. This computation takes some time

due to the large prime numbers used. The secret key is SK = λ(n) = lcm((p-1),(q-1)).


4. Online E-Voting Prototype System

The capabilities of the Paillier Threshold Cryptography system has been

demonstrated on an Online E-Voting Prototype system created for this project. This is a

prototype and should not be used in the real world scenarios. It shows the use of the

Paillier Threshold Cryptography Web Service. It also has some additional security

features like Completely Automated Public Turing test to tell Computers and Humans

Apart (CAPTCHA) added to decrease the security concerns. This prototype system SRS

and SDS document are all created and they can be downloaded from

http://www.cs.uccs.edu/~gsc/pub/master/hevecek/doc/ folder.

4.1. E-Voting System Overview

The e-voting system allows for 1 out of L candidate ballots. No options are

provided for n out of L ballots or write-in ballots. An “election” may consist of more

than one ballot. An election administrator creates the ballots and other election

parameters. The administrator requests the Paillier threshold encryption parameters from

the PTC Web Service during the initial election set-up. The administrator submits the

election parameters to a VotingService web service, and saves the election parameters

(including the cryptosystem parameters) to an XML file. Voters then load the election

parameters by opening the XML file, make their selection(s), and cast their encrypted

vote(s) to the VotingService web service. During the tally phase, the votes are multiplied

together, and, due to the homomorphic properties of the Paillier cryptosystem, the

product can be decrypted to reveal the sum total of all the votes [15].


4.1.1 User Login

User Login is the first form users connected when the voting page is loaded from

the internet. It will have a connection to the database to validate the user credentials. User

types are either voters or Administrators. It is assumed that users have used another

interface or form to register for voting. In the same login page there will be Completely

Automated Public Turing test to tell Computers and Humans Apart (CAPTCHA)

validation with random numbers. Six digit random numbers will be created each time the

page is loaded to be able to stop any kind of computer attacks to the voting site.

Figure 4.1 User Login Form


4.1.2. Election Set-Up

The election administrator uses the Election Builder form to create or modify an

election (before the election is posted to the voting web service). To create a new

election, the administrator clicks on the “New Election” button. A new election is

created and a unique election id is assigned. The administrator must then enter his/her

name and a descriptive title for the election. Election page is the most important

Administrator page as it has all the functionality setup for the election.

Before ballots can be added to the election, the encryption parameters must be

specified and retrieved from the web service. This must occur before the ballots are

added or created, since the vote format is dependent on the specified key size. The

administrator clicks to the “Encryption Parameters” . This button will be available after

the Administrator details are entered. Once this button is clicked, the administrator

specifies the key size and whether or not to encrypt the returned key shares. The

administrator can then add the key share owner information for each owner that is to

receive a secret key share. If the key shares will be encrypted, the administrator will be

required to enter the owner’s username which is the same as the users login and

certificate name to be able to choose automatically. Once all owners have been added, the

administrator selects the cryptosystem threshold value and then clicks “Send Request”,

which sends the request to the web service. In the current configuration, a key size of

larger than 256 and sometimes 512 bits will result in such a delay that a “timeout” error is

caused, so it is not recommended that key sizes greater than 256 be used for the web

application. The web service will generate the requested parameters, encrypt the key

shares (if specified), and return them [15]. The Encryption Parameter Request form will


transfer the returned parameters to the Election Builder form and close automatically.

The election crypto parameters are displayed at the bottom of the Election Builder form.

Lastly, on the same election page ballots can be added for the election. If the

ballots are created prior to the election creation page, the list will appear in the window

for administrator to choose from the list. They can be added to any election by

highlighting from the list and clicking to the”Add Ballots” button. If the ballot is valid, it

will be imported into the election and displayed in the Election Summary textbox in the

form.

After all the users, ballots and Administrator details loaded from the election

form, the Administrator will need to save and post the election to be able to initialize

election voting. The election will be saved as an XML file. First save the election by

clicking to the “Save Election” button. It will be saved in the web server

“App_Data/XMLFiles Folder”. Details of the folder structures are documented in the

Software Design Specification document. Posting the election to the voting web service

is a non-reversible operation in the application unless the details are manually deleted

from the database. Post Election button will be enabled after saving the election. To post

the election, click to “Post Election” button. A web service call will be made that posts

the election data to the web service, which then creates the appropriate database entries

that are used to manage the election [15].

4.1.3. Creating Ballots

Existing ballots can now be added to the election or new ballots can be created

using the options from the Election form. To create a new ballot, the administrator will

need to click to the “New Ballot” link from the elections page. It will open the Ballot


Builder form. A new ballot will be created and the random ballot id displayed in the

form. Administrator will need to put ballot issue/ problem, and then enter all of the

available choices, one at a time by using the “Add Choices” button and the text box.

Each choice is entered by typing the appropriate text. A choice can be deleted by

selecting the choice in the list, and clicking “Delete Candidate” button. When the ballot

is complete, the ballot should be saved by clicking “Save ballot” button. This button will

get all the details entered and save the ballot in XML format in the web server

“App_DataXML FilesBallots” folder. The Ballot Builder Form must be closed and then

re-opened in order to create another ballot. Ballot creation page is also accessible from

the Administrator menu.

4.1.4. Vote Format

When a ballot is added to an election, the format of the vote for that ballot is

derived from the key size chosen for the election and the number of “candidate” choices

on the ballot. These two values determine the maximum number of voters allowed. The

total size of the vote is limited to the key size k (in bits). The vote is split into c bit fields

where c is the number of candidates. The size of the bit fields vc= k/c. However, vc is

limited to 32 bits so that each candidate’s field will fit into a 32-bit integer (for ease of

extraction only). Therefore, if k/c > 32, vc=32 and only the first 32*c bits of the vote will

be used. To cast a vote, a voter votes the value 2^(ic*vc) where ic is the desired candidates

ballot index (0,…,c-1). By using votes of this format, the tally can be computed by

multiplying all of the votes together and decrypting the product. Due to the

homomorphic property of the Paillier cryptosystem, the multiplication carried out in the

ciphertext space corresponds to addition in the cleartext space, and thus the decryption of


the product will contain the summed votes for each candidate. Each candidate’s bit field

can then be extracted and evaluated to determine the total number of votes for that

candidate [15].

4.2. Voting

4.2.1. Creating the Vote

Once an election has been created, saved, and posted to the election web service,

voters can create and cast votes. After the user login page user logs in either as an

Administrator or a voter. If the user logs in as an Administrator, he will have a link from

the menu for the voting page. If the user has logged in with voter credentials, then he will

be connected to the voting page automatically. When connected to the voting page, a list

box will have all the elections available for the voters. This list is the list of the elections

in the elections folder. After highlighting the election and clicking to the button to load

the election, election details will be loaded for voters to vote. The ballots from the

election will be loaded, with each issue being loaded into the issue text box, and it’s

corresponding choices loaded into the textbox to the right (the choices textbox). The

voter can make his/her choice simply by clicking on the desired choice. That issue’s

choices will then be displayed in the choices textbox. Again, select the desired choice by

clicking on it in the choices textbox. Once a choice has been selected, the ballot issue

and the selected choice will appear in the “Current Votes” textbox. To the right of the

issue question and the selected choice is the hex value of the vote to be cast. Once all

choices have been made, the voter can submit his/her vote by selecting “Submit Vote”

button at the bottom of the page. This button will cal the web services and save the vote

into the database. Once the vote is submitted, no changes can be made.


At any time after submitting his/her vote, a voter can check the posted values of

his/her vote by selecting “Check Submitted Vote” button. This invokes a web service call

to the voting web service which retrieves the encrypted vote values posted for that

election [15].

4.3. Tally the Vote

Administrator will have access to use the Tall Vote option during the election

process to tally the vote. Administrator will need to click the “Tally/Decrypt Vote”

button on the menu. The Tally form will open. In a list box elections list will appear for

Administrator to choose and tall the vote. If the secret key shares were encrypted, the

program will automatically get the certificates according to the issued names of the users

to decrypt the owner’s Paillier secret key share. That’s why it is important for

Administrator to collect all the registration details from the user to be able to create the

users. He/she will assign the right certificates so that there won’t be any issues in the

future process like tally / decrypt vote process. The product of the votes for each ballot

is then calculated and displayed both encrypted and decrypted, and the candidate’s tallies

are extracted from the decrypted bit field and displayed.


5. PTC Web Services Efficiency Improvement
This can be done in three different ways.

5.1 Pre-Computation
This change will be done for the key generation where the prime numbers will be

calculated prior. Any real-time computations will slow down the process on cryptography

application. Any pre-computation will improve the efficiency of the application. This

pre-computation can be done via background thread setup in the application.

<setting name="ServerPath" serializeAs="String">
<value>c:inetpubwwwrootEVotingPreComputation</value
>
</setting>
<setting name="PrimeNumberCalculationType"
serializeAs="String">
<value>DB</value>
</setting>

This pre-computation is applied to the SafePrimeNumbers generator function.

This function is used for the pre-computation.

5.2 Chinese Remainder Theorem (CRT)

Chinese Remainder Theorem is one of the most useful theorems of number theory

as it says it is possible to reconstruct the integers in a certain range from their residues

module a set of pair wise relatively prime module. Details of CRT is explained in the

previous sections. Paillier has suggested to use CRT for especially key generation and

decryption processes [21]. Also CRT has become standard today in many RSA

applications as it increases the decryption up to 4 times [16]. Decryptions can be made

faster by separately computing the messages mod p and mod q instead of mod n and

recombining modular residues later.


With pre-computations:

where p-1 and q-1 have to be placed by α

5.3 Paillier Scheme Pre-computations for Decryption

Scheme 1 used in this project is not the most efficient one especially for

decryption as it is also mentioned in Pascal papers study [21]. Scheme 3 improves the

performance of decryption and he suggested in the same paper to pre-compute the

constant instead of only p and q values applied in this project. Also

another constant parameter below can be pre-computed [21].

These constant pre-computations can be done with the same methods used in this project.


6. Results

6.1 Pre-Computation Performance Evaluations

Pre-computations results are put into both the text file and the Pre-Computation

tables created in the SQL Server. Both the text file and the database solutions have

increased the performance in other words response time more than 80% in average for

both 256 and 128 bit key sizes. Unfortunately this test failed with 1024 and 512 bit key

sizes due to time out issues.

There is a parameter setup in the settings to use the random prime number

generator either real time or text file or database. As a default it will set to the real time.

XML solution also needs some improvements and this will be suggested in the future

improvements section of the project.


Online e voting prototype with ptc web services v1

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