Public Key Cryptography and its applications to Secure Electronic Voting

1
Public Key Cryptography and its applications
toSecure Electronic Voting

• NEC
• Kazue Sako

2
Contents

• A new cryptographic technique
• Public Key Cryptography(PKC)
• Digital Signatures and Public Key Infrastructure
  (PKI)
• Electronic voting system using PKC and PKI

3
Cryptography is indispensable in e-Government
Systems

• Tax declaration What if people know your annual
  income?
• Impersonated applicationWhat if someone else
  applied your passport?
• Contents of public documentWhat if someone else
  altered the document?

4
Conventional CryptosystemSecret-Key cryptosystem

• Sender and Receiver shares a same secret key
  (password).

a same secret key
decryption
encryption
ciphertext
RECEIVER
SENDER
5
New Notion Public Key Cryptography(1970s)

• Encryption using a Public key and Decryption
  using a Private (secret) key

RECEIVER
SENDER
6
Public Key is like a phone number

• If you got a wrong phone number and left a secret
  message in the answering machine your message
  will be heard by the owner of the answering
  machine.
• If you got a wrong public key.. your secret may
  be recovered by an adversary!
• Public key needs to be certified Public Key
  Infrastructure(PKI).

7
The Notion of Digital Signature

• Signing using a Private (secret) Lock
• Verification using a Public key and

A Pair with special properties
A public Key of Signer
A Secret Lock of Signer
RECEIVER
SIGNER
8
Tricks in PKC

• A Mathematically Hard Problems
• Ex Prime factorization It s easy to multiply 2
  numbers. But it is hard to factor a large number,
  even using a supercomputer.
• If you know the prime factors, one can easily do
  inverse function, but otherwise has no clues
  about inversion !

9
The Famous RSA Cryptosystem
Preparation
Generate a tupple (e,d,n) where for all M M
M(mod n) Publish (e,n), d is a private key.
ed
Encryption
e
C M (mod n)
Anyone can encrypt
Decryption
d
M C (mod n)
Require private key
10
Other Fancies using PKC

• Digital Signatures
• Ensures that the originator of the message indeed
  generated the document that no alternation has
  occurred.
• Digital Coin flipping
• Over asynchronous network, one can digitally flip
  coins in a fair manner. Can be used for fair
  lottery system.
• Digital Sealed-bid Auctions
• Can determine the lowest bid without opening all
  the digital envelopes.
• Network Voting
• One can vote from anywhere using network, and yet
  is secure and secret voting.

11
Electronic voting steps of introduction
Network Voting
voting from home
Location-free voting
Internet Voting
Step 3
Voting at a street corner
digital tally
Step 2
E-voting at a polling place
Japan adopted Step-1 type voting since 2002
Paper-based
12
Problem

• Voter verification and vote casting cannot be
  done independentlyvote secrecy?

Im Alice
Im Alice
OK, send vote
Clinton
Clinton
Are you registered?
13
Overview of our voting system

• IDEA current absentees ballot using double
  envelopes

Ballot-counting witness verifies the process
14
Current Status of Network Voting

• No country in the world adopts Network Voting in
  governmental elections.
• We need law amendments to use Network Voting in
  Japan.
• Binding Network Voting is being used in a
  Japanese private organization with 20,000 voters.
  
• The first one in the world using cryptographic
  protocols.
• Saved the cost of printing paper ballots and
  staff cost of counting ballots. Total cost was
  1/10 of paper based one.

15
Summary

• Its been 30 years since the invention of Public
  Key Cryptosystem.
• It improved the life of people by offering
  security and convenience in network society.
• It will continue to be an important technology to
  ensure privacy and fairness that will be needed
  in the services of e-government.