Applying MESE processes to Improve Online E-Voting Prototype System with PTC Web Services

1
Applying MESE processes to Improve Online
E-Voting Prototype System with PTC Web Services

• Master Project Defense
• Hakan Evecek

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Outline of the Talk

• Introduction
• Document overview prepared for this project.
• Related Work
• Paillier Threshold Cryptography (PTC)
• PTC Web Services
• Online E-Voting System
• Suggested Improvement
• Encryption/Decryption Optimization
• User Interface
• Future Directions
• Conclusion

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Introduction

• The online E-Voting system generated within this
  project was based on an idea put forward in the
  Future Suggestions section of the Masters
  Thesis of Mr. Brett Wilson. (http//cs.uccs.edu/g
  sc/pub/master/bswilson/doc/)
• As a result, augmentation of the demo
  application for PTC Web Services was undertaken.

5/29/2007
Hakan Evecek/SE2Evote
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Continued

• Scope of E-Voting
• The world is heading in this direction as
  currently many nations and large companies are
  seeking E-Voting solutions.
• Similar to manual voting - only much faster and
  cheaper, however
• Is the voter confident with the process?
• Can Administrators monitoring verify that one
  vote is recorded for each voter?
• How trustable is the tally process?
• Is it socially acceptable?

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E-Voting Requirements

• 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

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E-Voting Requirements

• 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.

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The categorization of voting system
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MESE Processes Applied for Online E-Voting System

• Project Proposal and Plan
• Software Requirements Document (SRS)
• Software Design Specification (SDS)
• Testing Document
• Defects List
• Project Report

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Related Work

• Some of the Encryption Schemes
• Goldwasser-Micali Scheme (1984)
• It is probabilistic cryptography. Their scheme
  has the ability to encrypt the same text in many
  different ways without changing the modulus. It
  is very slow compared to the other schemes.
• Blum-Goldwasser Scheme (1985)
• This scheme is comparable in speed to another
  public key scheme, RSA. Unfortunately it is not
  as robust as RSA.
• The Paillier cryptosystem (1999)
• a probabilistic asymmetric algorithm for public
  key cryptography. A given cleartext message can
  be encrypted into any one of a very large set of
  possible encryption values
• homomorphic
• deterministic

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Continued

• Uses of Paillier Cryptography
• Electronic Voting
• Anonymous Mix Nets (due to self-blinding
  property)
• Electronic Auctions
• Electronic Lotteries
• Damgard-Jurick Scheme (2000)
• Just a modification of Paillier's scheme. It is
  also called Generalized Paillier System. It
  allows a user to increase the size of the
  encrypted value. Like Paillier it is
  probabilistic and homomorphic.

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Hakan Evecek/SE2Evote
5/29/2007
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Continued

• Homomorphic Encryption
• A special type of cryptography in which the
  sum of two encrypted values is equal to the
  encrypted sum of the values.
• Public Key Cryptography
• Asymmetric cryptography, is a form of
  cryptography in which each user will have a key
  that didnt have to be kept secret.
• Threshold Cryptography
• A cryptographic function can be distributed
  amongst several participants in such a way that
  the operation can be performed only through
  cooperation of a specified subset of the
  participants. In addition, if less than the
  required number of participants attempts to
  perform the action, no useful information can be
  constructed or obtained.

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Cryptographic Techniques Implemented by Brett
Wilson to PTC Web Services

• Paillier CryptoSystem 15
• Trapdoor Discrete Logarithm Scheme
• c gMrn mod n2
• n is an RSA modulus (modulus of 2 safe primes)
• Safe prime - p 2q 1 where q is also prime
• g is an integer of order na mod n2
• r is a random number in Zn
• M L(c?(n) mod n2)/L(g?(n) mod n2) mod n
• L(u) (u-1)/n, ?(n)lcm((p-1)(q-1))
• Important Properties
• Probabilistic (randomness of E(M))
• Homomorphic
• E(M1 M2) E(M1) x E(M2), E(k x M) E(M)k
• Self-blinding
• D(E(M) rn mod n2 ) m

Continued
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Cryptographic Techniques Implemented

• Threshold Encryption 15
• Public key encryption as usual
• Distribute secret key shares among i
  participants
• Decryption can only be accomplished if a
  threshold number t of the i participants
  cooperate
• No information about m can be obtained with less
  than t participants cooperating
• Shamir Secret Sharing
• Lagrange Interpolation formula
• f(X) Sti0 aiXi
• a0 is secret, ai are random, f(X) are secret
  shares
• X is share index (1 to number of servers)
• If enough f(X) available it is possible to
  recover a0

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Operation of E-Voting System 15
2. SOAP/XML Request for PTC Parameters
5. Paillier Public Key
3. SOAP/XML Response containing RSA encrypted
PTC Parameters
6. Paillier Encrypted Vote
8. Partial Decryption Shares of Vote
Tally/Proofs of Correct Decryption
4. RSA Encrypted Secret Key Shares

• Election Authorities
• RSA Public Keys

7. Paillier Encrypted Vote Tally
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Hakan Evecek/SE2Evote
5/29/2007
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User Login Page

• Assumed that users has registered previously and
  has secure login credentials provided.
• Admin Users
• Voters
• Completely Automated Public Turing test to tell
  Computers and Humans Apart (CAPTCHA)

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Admin Page

• Election Creation
• Ballot Creation
• Tally Vote
• Encryption/Decryption
• Generate Safe Prime Numbers

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Election Form
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5/29/2007
Hakan Evecek/SE2Evote
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Continued
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Hakan Evecek/SE2Evote
5/29/2007
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Ballots Form
5/29/2007
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Hakan Evecek/SE2Evote
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Voter Page

• Voter can access to the elections and complete
  the voting process.
• Automatically loads the voting page.
• Allows vote, then doesnt allow user to vote
  again

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Database Schema
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Suggested Key Generation, Encryption/Decryption
Optimization

• Safe Prime Numbers Pre-Computation Process.
• Chinese Remainder Theorem to calculate p,q
  separately and then multiply for n.
• Paillier Scheme Pre-Computation for decryption.

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Results

• 128 bit Encryption
• 256 bit Encryption

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Lessons Learned

• The SE processes applied in this project has set
  precedence which can be used for the future
  projects.
• Ensure that the SRS, SDS and test documents can
  be easily modified and any future enhancements
  can be made with ease.
• Security issues involved in E-voting systems.
• CRT is a very useful theorem that can be applied
  on other theorems to improve the efficiency and
  increase the speed of the computations.
• Pre-computation is always an improvement to the
  systems as long as they are designed and
  architected properly like running a thread on the
  background to generate prime numbers in this
  case.
• Setting up read/write access permissions for the
  folders is important in ASP .Net. It is very
  important to follow the processes on this setup.
• Certificate registration and confirmation
  requires additional processes for the internet
  solutions.

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Future Direction

• Implement the suggested CRT improvement into the
  code.
• Implement constant value pre-computation for
  decryption process.
• Fix XML solution in the code.
• Add more web application security protocols and
  processes.
• Implement registration and voter identity
  verification process.
• Authenticity of election parameters/ballots not
  currently guaranteed
• Implement signing of election parameters/ballots
  by admin

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Conclusion

• Encryption parameters creation process
  improvements with the application of
  pre-computation to the web services.
• Alternate processes are also available to improve
  the efficiency further, such as CRT Theorem,
  applying pre-computation to other constants in
  the Pailliers scheme and also using 3rd scheme
  instead of the 1st scheme as explained in many
  researches.
• The online E-Voting system with Paillier
  Cryptosystem Web Services implemented in this
  project brings a more secure e-voting environment
  one step closer.
• Online E-Voting systems need to be considered as
  an enterprise solution when security, from the
  registration till the end of the Tally process,
  is to be considered.

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References

• 1 http//cris.joongbu.ac.kr/publication/evoting_
  implementation-APIEMS2004.pdf
• Implementation issues in a secure e-voting
  schemes, Riza Aditya, Byoungcheon Lee, Colin Boyd
  and Ed Dawson.
• 3 http//www.cs.virginia.edu/pev5b/writing/aca
  demic/thesis/thesis.html
• Vote Early, Vote Often, and VoteHere A Security
  Analysis of VoteHere, Philip E. Varner, May 11,
  2001.
• 5 http//www.trustycom.fr/pdf/FoPoSt00.pdf P.
  Fouque, G. Poupard, J.Stern, Sharing Decryption
  in the Context of Voting or Lotteries, Financial
  Cryptography 2000 Proceedings.
• 6 http//www.captcha.net/ , the Official
  CAPTCHA web site.
• 7 http//www.vote.caltech.edu/reports/alv-nag_lo
  yola.pdf R. Michael Alvarez, Jonathan Nagler, The
  Likely consequences of Internet Voting for
  Political Representations.
• 15 B. Wilson, C. E. Chow, Paillier Threshold
  Cryptography Web Service Users Guide,
  University of Colorado Colorado Springs
  Masters Project, 2006.
• 16http//www.cs.rit.edu8080/ms/static/spr/2005/
  4/kar1141/report.pdf , Progress on Probabilistic
  Encryption Schemes, Kert Richardson, July 2006.
• 17 http//www.cs.umd.edu/jkatz/THESES/staub.pdf
  .gz An Analysis of Chaums voter-verifiable
  election scheme, Julie Ann Staub, 2005
• 18 http//www.brics.dk/RS/00/45/BRICS-RS-00-45.p
  df Ivan Damgard and Mads J. Jurik, A
  Generalization, a Simplification and Some
  Applications of Pailliers Probabilistic
  Public-Key System, PKC 2001.
• 20 http//www.rsa.com/rsalabs/cryptobytes/Cryp
  toBytes_January_2002_final.pdf CryptoBytes, Dan
  Boneh, Hovav Shacham, Spring 2002.
• 21 http//www.gemplus.com/smart/rd/publications/
  pdf/Pai99pai.pdf Public-Key CryptoSystems Based
  on Composite Degree Residuosity Classes, Pascal
  Paillier, 1999
• 22 http//en.wikipedia.org/wiki/Paillier_cryptos
  ystem , Paillier Crytosystem from Wikipedia, the
  free encyclopedia.