Enhancing PTC based Secure E-Voting System (note: modification of Brett Wilson

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Enhancing PTC based Secure E-Voting System(note
modification of Brett Wilsons Paillier Threshold
Cryptography Web Service view graph)

• by
• Justin Pohlmann
• Allen Liu

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Outline of the Talk

• Introduction/Motivation
• Related Work
• Paillier Threshold Cryptography
• Suggested Improvement
• Encryption/Decryption Optimization
• User Interface
• Future Direction
• Conclusion

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Introduction/Motivation

• E-voting Requirements
• Privacy/Anonymity, Completeness, Soundness,
  Un-reusability, Eligibility, Fairness
• Robustness, Universal Verifiability,
  Receipt-Freeness, Incoercibility

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Introduction/Motivation

• Many new Secure Voting protocols
• Mathematical algorithms presented in literature
• Unable to identify/locate implementations of
  these algorithms
• UCCS effort to develop a secure e-voting
  application
• Using the concept of Paillier Threshold
  Cryptosystem to implement a voting system
• Find areas of improvement
• Encryption Optimization
• User Interface

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Related Work

• Basis for Implementation
• Sharing Decryption in the context of Voting or
  Lotteries (Fouque, Poupard, Stern)
• Closely related research
• A Generalization of Pailliers Public Key
  Cryptosystem with Applications to Electronic
  Voting (Damgard, Jurik, Nielson)
• Encryption and Decryption Optimization

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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

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Uses of Paillier Cryptography

• Electronic Voting
• Anonymous Mix Nets (due to self-blinding
  property)
• Electronic Auctions
• Electronic Lotteries

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Cryptographic Techniques Implemented

• Paillier CryptoSystem
• 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

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Suggested Encryption/Decryption Optimization
Current Paillier System Suggested Paillier System
Key Generation g na mod n2 Key Generation gn1
Encryption C gMxnmodn2 Encryption C gMxnsmodns1
Decryption M L(c?(n) mod n2)/L(g?(n) mod n2) mod n Decryption cdmodns1 ? (1n)jMdmodns gdmodns1 ? (1n)jdmodns (jMd)(jd)-1 Mmodns
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Suggested Encryption/Decryption Optimization

• .
• From O(ns) ? O(s)

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Cryptographic Techniques Implemented

• Threshold Encryption
• 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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Voting Application PTC Use
9. Vote Tally
2. SOAP/XML Request for PTC Parameters
Election Admin
5. Paillier Public Key
PTC Web Service
PTC CSP
6. Paillier-Encrypted Vote
3. SOAP/XML Response containing RSA encrypted
PTC Parameters
PTC CSP
Voter
1. Election Authorities RSA Public Keys
PTC CSP
8. Partial Decryption Shares of Vote
Tally/Proofs of Correct Decryption
Election Authorities
4. RSA Encrypted Secret Key Shares
Voters Vote
PTC CSP
7. Paillier Encrypted Vote Tally
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Preliminary Website Layout
Election Creation
Admin Page
Login Page
Encrypt/ Decrypt
Voter Page
Vote Page
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Admin Page

• Election Creation
• Add User(s)/Group(s) allowed to vote
• Add Election Admins
• Encryption/Decryption
• Via Email
• Add group

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Voter Page

• Elections users can vote on
• Brings up voting page
• Allows vote, then doesnt allow user to vote again

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Database Schema
Candidate
Ballots
Encryptors
Users
Elections
Votes
Encryption Status
Eligibility
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Future Direction

• Implement the suggested Improvement
• Integrate other cryptosystem protocols (i.e.
  Receipt-Freeness and Zero Knowledge Proofs)

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Questions?