Ballot-Cancellation Scheme In E-voting System The first Joint - - PowerPoint PPT Presentation

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Ballot-Cancellation Scheme In E-voting System

Kyushu University, Japan Yong-Sork HER

The first Joint Seminar < ISIT-ETRI > 13 May, 2005 , Fukuoka The first Joint Seminar < ISIT-ETRI > 13 May, 2005 , Fukuoka

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• 1. E-voting in JAPAN
• 2. Goals
• 3. The right of casting of the ballot
• 4. Absentee voting
• 5. Overview of [YKDKT03]
• 6. Ballot-cancelable e-voting system
• 7. Proofs
• 8. Conclusion

Contents

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Japan

• Okayama on 23, June (2002)
• Niimi city : A mayoral and a municipal election
• Touch panel method like ATM

(Automated-teller Machine) of BANK.

• General voter
• Absentee voter

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E-voting procedure

Authentication Receive IC-card Inputs the IC card in voting terminal Voting Store the contents of voter 4 4

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Analysis of Japan‘s e-voting

Items Items The existed voting 1994 (Paper-voting) The existed voting 1994 (Paper-voting) The electronic Voting 2002 The electronic Voting 2002 Voting officer (43-voting place) 180-person 178-person Counting officer 85-person 58-person Admission member （ 入会人) 13-person 13-person Counting time

• Major
• Councilman

3 hours 4 hours 25 minutes 25 minutes 25 minutes Invalid ballots

• Major
• Councilman

242 214 Voting ratio 92.06 % 86.82 % Election costs ¥11,630,000 ¥16,460,000 5 5

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Analysis of Japan ‘s e-voting (Cont.)

Candidate Group Candidate Group The ratio of votes obtained The ratio of votes obtained

E-voting < General voter> E-voting < General voter> Existing voting <Absentee voter> Existing voting <Absentee voter> Candidate 1 Candidate 1 78.4 % 78.4 % 69.6 % 69.6 % Candidate 2 Candidate 2 9 % 9 % 11.5 % 11.5 % Candidate 3 Candidate 3 5 % 5 % 13.3 % 13.3 % Candidate 4 Candidate 4 7.6 % 7.6 % 5.6 % 5.6 % Total Total 100% <14,966 persons> 100% <14,966 persons> 100 % <1719 persons> 100 % <1719 persons>

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Goals

• Many e-voting system had been overlooked

ballot-cancellation scheme as well as absentee voting.

• We introduce the reasons why needs the ballot-

cancellation scheme.

• We propose first the ballot-cancellation scheme

based on [YKDKT03] in e-voting system.

If the ballot which be cancelled is found in the existed e-voting system, the e-voting system should be stopped.

7 7 [YKDKT03] Yamaguchi,H., Kitazawa,A., Doi,H., Kurosawa,K., Tsuji,S., ``An Electronic Voting Protocol Preserving Voter's Privacy" IEICE Trans., Vol.E86-D, No.9, 2003.

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The right of casting of the ballot (I)

Election Day Absentee Voter General Voter Ballot counting A term of voting

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The right of casting the ballot Ballot-cancellation Election Day (Japan) Necessary A voting point (Korea) Unnecessary

If the absentee voters lost the right of casting the ballot before election day, the absentee voter's ballot should be cancelled.

The right of casting of the ballot (II)

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Why needs the ballot-cancellation scheme in e-voting system?

• A absentee voter can lost the right of

casting the ballot before election day.

• It can be discovered a substitute vote or

illegal vote by a voter.

• It can be discovered a substitute vote by a

election manager.

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The current state of voting

• The voting ratio is decreased by disadvantages of

used vote method and political apathy of a voter .

• Increasing of the number of absentee voter

It needs the easy voting method for absentee voter.

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Absentee voting

• Early voting or Mail voting
• Accepted reasons for requesting absentee ballots,

by state, 1996 ( U.S)

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No Reason Necessary Absent On Business College Student Disabled Or ill Prevented By Employ- ment Religious Reasons Elderly Out of Jurisdiction For any reason United States 22 States 18 States 23 States 27 States 12 States 18 States 12 States 28 States

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<YKDKT03> Model

Internet

Voter :

1

V

Voter :

2

V

Voter :

k

V

Bulletin board Center 1 Center 2 Eligibility Management Database Passive Observer 13 13 . . .

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Characters of [YKDKT03]

• Overcome the disadvantages of multi-authority

e-voting system

• Much computing resources
• Some fault-tolerant computer system
• Cluster computer system
• To achieve privacy, universal verifiability, and

robustness

• Using Double encryption based on

r-th residue cryptosystem and RSA

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Overview of [YKDKT03]

Center 1 Voter Center 2

①Register a voter

Bulletin Board

③

②

i

m

④

A e i i

N Z E

A mod

≡

⑤

) mod ) ( , , , , (

i i v i i i

v d v v i i v

N H MSG C E ID

⑥ ⑦ ⑧

, mod

1

A d i i

N E Z ≡

⑨

∏ = ∑ = ∏ =

= = = =

l i i l i i B r M l i i

x X m M N X y Z Z

1 1 1

, , mod

B r m l

N x y Z

i

mod = 15 15 mod p G C

i

Z i ≡

A Z Z i j

N G C

i j

mod

) , (

=

) mod ) ( , , , (

1 1 1 1 1

c d c c C

N H MSG Z ID

c

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Decryption in r-th residue encryption

(Secret key) Two large prime numbers, and (Public key) and (Plain text) (Encryption) , where is a random number.

p q ) ( pq N = y ) ( r m m < ≤ N x y Z

r m

mod = x

Conditions of the parameters < Case 1> is odd < Case 1> is odd

r j r B y e e e e r e r q e r p

N j

< ≤ ∉ = = = − = − 1 ), ( 1 ) , gcd( ) , 1 gcd( ) , 1 gcd(

2 1 2 1 2 1

} , mod | { ) (

* N r N

Z x N x w w r B ∈ = =

< Case 2> is even < Case 2> is even

) 1 / ( 1 ), ( 2 ) , gcd( 2 ) , 1 gcd( ) , 1 gcd(

2 1 2 1 2 1

= < ≤ ∉ = = = − = − N y r j r B y e e e e r e r q e r p

N j

r r y satisfies the above condition “a basic element”

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Ballot –Cancellation scheme for Yes-No Voting

MODEL

Bulletin Board Center 1 Center 2 Voter CC Database Voting Authentication Ballot-cancellation Counting CC: Cancellation Center 17 17

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Extended homomorphism property based on r-th residue encryption

) ( , mod )) ( / ) ( ( ) ( m n N x n E m E n m E

r

< = −

) ( mod ) ( , mod ) ( m n N x y n E N x y m E

r n r m

< = =

Then,

N x y N x y N x y n E m E N x y n m E

r n m r n r m r n m

mod ) mod /( ) mod ( ) ( / ) ( , mod ) (

− −

= = = −

Therefore, 18 18

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Bulletin Board

Ballots

Voter’s

• wn

designated section

Commitment data for multiplication Final tally in encrypted form Final tally

Accepted Mark

Center1’s own Designated section

Voter’s

• wn

designated section Accepted Mark Voter’s

• wn

designated section Accepted Mark

Ballots Voter’s

• wn

designated section Commitment data for multiplication Final tally in encrypted form Final tally Accepted Mark Center1’s own Designated section Center 1’s

• wn

designated section Accepted Mark Center 2’s

• wn

designated section Accepted Mark Ballot-cancellation

• r not?

CC’s own Designated section

BB of [YKDKT03] Extended BB 19 19

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Ballot-cancel e-voting system

Center 1 Absenter Voter Center 2

①Register a voter

Bulletin Board

③

② C a s t i n g i

m

④

A e i i

N Z E

A mod

≡

⑤

) mod ) ( , , , , (

i i v i i i

v d v v i i v

N H MSG C E ID

⑥ ⑦ ⑧

, mod

1

A d i i

N E Z ≡

⑨Compute and

b a b a

M M M Z Z Z − = = /

B r m l

N x y Z

i

mod = 20 20 mod p G C

i

Z i ≡

A Z Z i j

N G C

i j

mod

) , (

= Checking the right

• f casting of the ballot

CC a

Z

b

Z ⑩

Final tally of total ballots Final tally of cancelled ballots

b a

M M

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Prover P Verifier V

] mod , mod [ p h y p g x

α α

≡ ≡ Proof of Knowledge for mod log log p y x

h g

≡

*

2

N R Z

∈ ω mod p g a

ω

≡ mod ' p h a

ω

≡ ' , a a

α

Z b

R

∈

2

mod N ab r + = ω mod ? p ax g

b r

mod ' ? p y a h

b r

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Prover P Verifier V

})] 1 , { , mod ( mod [

2

∈ ≡ ≡

i r i m i Z i

m N x y Z where p G C

i i

Proof of Validity of ballot

*

2

,

N R Z

t s ∈

2 1 2

mod ~ , mod mod ~ , mod p G T N t y T p G S N s S

T r S r

≡ ≡ ≡ ≡

−

2 2 2 2

mod , mod )) , , ~ ( 2 Pr , , ( ) 1 ( mod , mod )) , , ~ ( 2 Pr , , ( ) ( ) 1 ( , ) ( N TZ W N tx V where W C T

• of

W V send m N SZ W N sx V where W C S

• of

W V send m b t s send b

i T i T T i T T i i S i S S i S S i

≡ ≡ = ≡ ≡ = = =

T S ~ , ~ } 1 , { ∈ b

(in random order) (in random)

2 2

mod ? ) , , ~ ( 2 ) 1 ( mod ? ) , , ~ ( 2 ) ( ) 1 ( mod ? ~ , mod ? ~ ) (

1

N W V and W C T proof check m N W V and W C S proof check m b p G T p G S check b

T r T T i i S r S S i i t y S

r r

≡ = ≡ = = =

−

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Prover P Verifier V

] mod / [

2

N X y Z

r M ≡

Proof of Validity for decryption

*

2

N R Z

R ∈

2

mod ~ N R Z

r

≡

Z ~

r R Z

b ∈ b a

2

mod N RX a

b

≡

accepts if

V

2

mod ) / /( ~ N y Z a Z

b M r

≡

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Conclusions

• Propose the necessary of ballot-

cancellation scheme in e-voting scheme Propose ballot-cancelable e-voting system based on Double encryption

• Apply the e-voting system based on

ElGamal encryption to ballot-cancelable e- voting system

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