Applying MESE processes to Improve Online E-Voting Prototype System with PTC Web Services Master Project Defense Hakan Evecek 1 5/29/2007Hakan Evecek/SE2Evote

Outline of the Talk Introduction Document overview prepared for this project. Related Work Paillier Threshold Cryptography (PTC) PTC Web Services Suggested Improvement ◦ Encryption/Decryption Optimization ◦ User Interface Online E-Voting System Future Directions Conclusion 2 5/29/2007Hakan Evecek/SE2Evote

Introduction General idea behind Electronic Voting: ◦ Similar to the 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 the tally process?  Is it socially acceptable? Many countries are looking for E-Voting solutions. In other words, what are the e-voting requirements: 3 5/29/2007Hakan Evecek/SE2Evote

E-Voting Requirements 4 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 5/29/2007Hakan Evecek/SE2Evote

E-Voting Requirements 5 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. 5/29/2007Hakan Evecek/SE2Evote

The categorization of voting system 6 5/29/2007Hakan Evecek/SE2Evote

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 7 5/29/2007Hakan Evecek/SE2Evote

Related Work Other Techniques Used In E-voting Protocols ◦ A Secure and Optimally Efficient Multi-Authority Election Scheme (Cramer, Gennaro, Schoenmakers)  Receipt-free: protocols where vote-buying or coercing is not possible because voters cannot prove to others how they voted. ◦ Non-Interactive Zero Knowledge Proofs  Proof does not require interaction  Proof does not reveal any other information  Prove vote is valid without revealing content of vote  Prove two encryptions encrypt the same message without revealing message 8 5/29/2007Hakan Evecek/SE2Evote

Cryptographic Techniques Implemented by Bret Wilson Paillier CryptoSystem [15] ◦ Trapdoor Discrete Logarithm Scheme ◦ c = g M r n mod n 2  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 n α mod n 2  r is a random number in Z n * ◦ M = L(c λ (n) mod n 2 )/L(g λ (n) mod n 2 ) mod n ◦ L(u) = (u-1)/n, λ (n)=lcm((p-1)(q-1)) ◦ Important Properties  Probabilistic (randomness of E(M))  Homomorphic  E(M 1 + M 2 ) = E(M 1 ) x E(M 2 ), E(k x M) = E(M) k  Self-blinding  D(E(M) r n mod n 2 ) = m 9 5/29/2007Hakan Evecek/SE2Evote

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) = Σ ti=0 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 10 5/29/2007Hakan Evecek/SE2Evote

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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) 13 5/29/2007Hakan Evecek/SE2Evote

Admin Page Election Creation Encryption/Decryption Tally Vote Generate Safe Prime Numbers Ballot Creation 14 5/29/2007Hakan Evecek/SE2Evote

Voter Page Voter can access to the elections and complete the voting process. Automatically loads the voting page. ◦ Allows vote, then doesn’t allow user to vote again 15 5/29/2007Hakan Evecek/SE2Evote

Database Schema 16 5/29/2007Hakan Evecek/SE2Evote

Suggested Key Generation, Encryption/Decryption Optimization 17 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. 5/29/2007Hakan Evecek/SE2Evote

Results 128 bit Encryption 256 bit Encryption 18 5/29/2007Hakan Evecek/SE2Evote

Lessons Learned Add problems encountered and how you solve them. Mistakes made and how you discovered them. Tell story. 19 5/29/2007Hakan Evecek/SE2Evote

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 20 5/29/2007Hakan Evecek/SE2Evote

Conclusion 21 Summarize/itemize what you have achieved. 5/29/2007Hakan Evecek/SE2Evote

References [1] [1] Implementation issues in a secure e-voting schemes, Riza Aditya, Byoungcheon Lee, Colin Boyd and Ed Dawson. Implementation issues in a secure e-voting schemes, Riza Aditya, Byoungcheon Lee, Colin Boyd and Ed Dawson. [3] [3] Vote Early, Vote Often, and VoteHere: A Security Analysis of VoteHere, Philip E. Varner, May 11, Vote Early, Vote Often, and VoteHere: A Security Analysis of VoteHere, Philip E. Varner, May 11, [5] P. Fouque, G. Poupard, J.Stern, Sharing Decryption in the Context of Voting or Lotteries, Financial Cryptography 2000 Proceedings. [5] P. Fouque, G. Poupard, J.Stern, Sharing Decryption in the Context of Voting or Lotteries, Financial Cryptography 2000 Proceedings. [6] the Official CAPTCHA web site. [6] the Official CAPTCHA web site. [7] R. Michael Alvarez, Jonathan Nagler, The Likely consequences of Internet Voting for Political Representations. [7] R. Michael Alvarez, Jonathan Nagler, The Likely consequences of Internet Voting for Political Representations. [10] I. Damgard, M. Jurik, J. Nielson, A Generalization of Paillier’s Public-Key System with Applications to Electronic Voting, Aarhus University, Dept. of Computer Science. [10] I. Damgard, M. Jurik, J. Nielson, A Generalization of Paillier’s Public-Key System with Applications to Electronic Voting, Aarhus University, Dept. of Computer Science.A Generalization of Paillier’s Public-Key System with Applications to Electronic VotingA Generalization of Paillier’s Public-Key System with Applications to Electronic Voting [15] B. Wilson, C. E. Chow, Paillier Threshold Cryptography Web Service User’s Guide, University of Colorado – Colorado Springs Master’s Project, [15] B. Wilson, C. E. Chow, Paillier Threshold Cryptography Web Service User’s Guide, University of Colorado – Colorado Springs Master’s Project, [16] Progress on Probabilistic Encryption Schemes, Kert Richardson, July [16] Progress on Probabilistic Encryption Schemes, Kert Richardson, July [17] An Analysis of Chaum’s voter-verifiable election scheme, Julie Ann Staub, 2005 [17] An Analysis of Chaum’s voter-verifiable election scheme, Julie Ann Staub, 2005http:// [18] Ivan Damgard and Mads J. Jurik, A Generalization, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System, PKC [18] Ivan Damgard and Mads J. Jurik, A Generalization, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System, PKC [19] Implementing Perfect Questionable Encryptions, Adam L. Young and Moti M. Yung. [19] Implementing Perfect Questionable Encryptions, Adam L. Young and Moti M. Yung. [20] CryptoBytes, Dan Boneh, Hovav Shacham, Spring [20] CryptoBytes, Dan Boneh, Hovav Shacham, Spring [21] Public-Key CryptoSystems Based on Composite Degree Residuosity Classes, Pascal Paillier, 1999 [21] Public-Key CryptoSystems Based on Composite Degree Residuosity Classes, Pascal Paillier, 1999http:// [22] Paillier Crytosystem from Wikipedia, the free encyclopedia. [22] Paillier Crytosystem from Wikipedia, the free encyclopedia /29/2007Hakan Evecek/SE2Evote