KYUSHU UNIV. 1 1 Ballot-Cancellation Scheme In E-voting System The first Joint Seminar The first Joint Seminar < ISIT-ETRI > < ISIT-ETRI > 13 May, 2005 , Fukuoka 13 May, 2005 , Fukuoka SAKURAI LABORATORY Kyushu University, Japan Yong-Sork HER SAKURAI LABORATORY
KYUSHU UNIV. 2 2 Contents 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 SAKURAI LABORATORY 8. Conclusion SAKURAI LABORATORY
KYUSHU UNIV. 3 3 Japan • Okayama on 23, June (2002) • Niimi city : A mayoral and a municipal election • General voter SAKURAI LABORATORY • Absentee voter • Touch panel method like ATM (Automated-teller Machine) of BANK. SAKURAI LABORATORY
KYUSHU UNIV. 4 4 E-voting procedure Inputs the IC card Receive IC-card in voting terminal SAKURAI LABORATORY Authentication Voting Store the contents of voter SAKURAI LABORATORY
KYUSHU UNIV. 5 5 Analysis of Japan‘s e-voting The existed voting The electronic Voting The existed voting The electronic Voting Items Items 1994 (Paper-voting) 2002 1994 (Paper-voting) 2002 Voting officer 180-person 178-person (43-voting place) Counting officer 85-person 58-person Admission member 13-person 13-person （ 入会人 ) Counting time - Major 3 hours 25 minutes SAKURAI LABORATORY - Councilman 4 hours 25 minutes 25 minutes Invalid ballots - Major 242 0 - Councilman 214 0 Voting ratio 92.06 % 86.82 % Election costs ¥11,630,000 ¥16,460,000 SAKURAI LABORATORY
KYUSHU UNIV. 7 7 Analysis of Japan ‘s e-voting (Cont.) The ratio of votes obtained The ratio of votes obtained Candidate Candidate Group E-voting Existing voting Group E-voting Existing voting < General voter> <Absentee voter> < General voter> <Absentee voter> Candidate 1 78.4 % 69.6 % Candidate 1 78.4 % 69.6 % Candidate 2 9 % 11.5 % Candidate 2 9 % 11.5 % Candidate 3 5 % 13.3 % Candidate 3 5 % 13.3 % SAKURAI LABORATORY Candidate 4 7.6 % 5.6 % Candidate 4 7.6 % 5.6 % 100% 100 % 100% 100 % Total Total <14,966 persons> <1719 persons> <14,966 persons> <1719 persons> SAKURAI LABORATORY
KYUSHU UNIV. 7 7 Goals • Many e-voting system had been overlooked ballot-cancellation scheme as well as absentee voting . If the ballot which be cancelled is • We introduce the reasons why needs the ballot- found in the existed e-voting system, cancellation scheme. the e-voting system should be stopped. SAKURAI LABORATORY • We propose first the ballot-cancellation scheme based on [YKDKT03] in e-voting system. [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. SAKURAI LABORATORY
KYUSHU UNIV. 8 8 The right of casting of the ballot (I) Ballot counting A term of voting Election Day G eneral A bsentee V oter V oter SAKURAI LABORATORY SAKURAI LABORATORY
KYUSHU UNIV. 9 9 The right of casting of the ballot (II) If the absentee voters lost The right of casting the ballot Ballot-cancellation the right of casting the ballot before election day, Election Day (Japan) Necessary the absentee voter's ballot should be cancelled. SAKURAI LABORATORY A voting point (Korea) Unnecessary SAKURAI LABORATORY
KYUSHU UNIV. 10 10 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 SAKURAI LABORATORY election manager. SAKURAI LABORATORY
KYUSHU UNIV. 11 11 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 SAKURAI LABORATORY It needs the easy voting method for absentee voter. SAKURAI LABORATORY
KYUSHU UNIV. 12 12 Absentee voting • Early voting or Mail voting • Accepted reasons for requesting absentee ballots, by state, 1996 ( U.S) Prevented Out of No Absent Disabled Religious College By Jurisdiction Reason On Or Elderly Student Employ- For any Necessary Business ill Reasons ment reason SAKURAI LABORATORY United 22 18 23 27 12 18 12 28 States States States States States States States States States SAKURAI LABORATORY
KYUSHU UNIV. 13 13 <YKDKT03> Model Bulletin board V Voter : 1 Center 1 V Voter : 2 Internet . Eligibility . Management . SAKURAI LABORATORY Database V Voter : k Center 2 Passive Observer SAKURAI LABORATORY
KYUSHU UNIV. 14 14 Characters of [YKDKT03] • Overcome the disadvantages of multi-authority e-voting system - Much computing resources - Some fault-tolerant computer system - Cluster computer system SAKURAI LABORATORY • To achieve privacy, universal verifiability, and robustness - Using Double encryption based on r-th residue cryptosystem and RSA SAKURAI LABORATORY
KYUSHU UNIV. 15 15 Overview of [YKDKT03] Z Z Z ≡ d = ⑦ mod , j i mod 1 E N C G N ( , ) i i A j i A d ⑧ ( , , , ( ) c mod ) ID Z MSG H 1 N Center 1 C c c c 1 1 1 1 Bulletin Board ① Register a voter ⑨ l = = M r ∏ mod , d Z Z y X N v i B ( , , , , ( ) mod ) ⑥ ID E C MSG H i N = v i i v v v 1 i i i i i ② m SAKURAI LABORATORY l l i = = ∑ ∏ , M m X x i i = = 1 1 i i = m r ③ mod Z y i x N l B A mod ≡ e ④ E Z N i i A Voter i ≡ Z ⑤ mod p C G i 0 Center 2 SAKURAI LABORATORY
KYUSHU UNIV. 16 16 Decryption in r- th residue encryption p q (Secret key) Two large prime numbers, and N = ( ) y pq (Public key) and ≤ < ( 0 ) m m r (Plain text) = m r x (Encryption) , where is a random number. mod Z y x N Conditions of the parameters < Case 1> is odd < Case 2> is even r < Case 1> is odd < Case 2> is even r − = − = gcd( 1 , ) p r e gcd( 1 , ) p r e 1 1 − = − = gcd( 1 , ) q r e gcd( 1 , ) q r e 2 2 SAKURAI LABORATORY = = 2 r e e r e e 1 2 1 2 = = gcd( , ) 2 e e gcd( , ) 1 e e 1 2 1 2 ∉ ≤ < j j ∉ ≤ < ( ), 1 y B r j r ( ), 1 y B r j r N N = = = ∈ * r ( / 1 ) y N ( ) { | mod , } B r w w x N x Z N N y satisfies the above condition “a basic element” SAKURAI LABORATORY
KYUSHU UNIV. 17 17 Ballot –Cancellation scheme for Yes-No Voting MODEL Voting Voter Authentication Ballot-cancellation Center 1 CC Bulletin Board SAKURAI LABORATORY Database Center 2 Counting CC : Cancellation Center SAKURAI LABORATORY
KYUSHU UNIV. 18 18 Extended homomorphism property based on r-th residue encryption = = < m r n r ( ) mod , ( ) mod ( ) E m y x N E n y x N n m Then, − − = m n r ( ) mod , E m n y x N = m r n r ( ) / ( ) ( mod ) /( mod ) E m E n y x N y x N − = m n r mod y x N SAKURAI LABORATORY Therefore, − = r < ( ) ( ( ) / ( )) mod , ( ) E m n E m E n x N n m SAKURAI LABORATORY
KYUSHU UNIV. 19 19 Bulletin Board BB of [YKDKT03] Commitment data Final tally Ballots Final tally for multiplication in encrypted form Voter’s Voter’s Voter’s Center1’s own own Accepted own Accepted own Accepted Designated designated Mark designated Mark designated Mark section section section section Extended BB SAKURAI LABORATORY Commitment data Ballot-cancellation Final tally Ballots Final tally for multiplication or not? in encrypted form Voter’s Center 1’s Center 2’s Center1’s own CC’s own own Accepted own Accepted own Accepted Designated Designated designated Mark designated Mark designated Mark section section section section section SAKURAI LABORATORY
KYUSHU UNIV. 20 20 Ballot-cancel e-voting system Z Z Z ≡ d = ⑧ mod , j i mod 1 E N C G N ( , ) i i A j i A ⑨ Compute and Z Z a b Center 1 ① Register a voter Bulletin Board d ⑥ v ( , , , , ( ) mod ) ID E C MSG H i N ② C a s t i n g i v i i v v v m i i i i ⑩ = / Z Z Z a b = − Absenter Voter M M M a b SAKURAI LABORATORY = m r ③ mod Z y x N i l B ⑦ Checking the right ≡ e A mod ④ E Z N i i A of casting of the ballot i ≡ Z ⑤ mod p C G i 0 M Final tally of total ballots a M Center 2 Final tally of cancelled ballots CC b SAKURAI LABORATORY
KYUSHU UNIV. 21 21 ≡ log log mod x y p Proof of Knowledge for 0 g h Prover P Verifier V α α ≡ ≡ [ mod , mod ] x g p y h p 0 0 * ω ∈ R Z N 2 ω ≡ mod p a g 0 a , ' a ω ≡ ' mod a h p 0 ∈ b Z α SAKURAI LABORATORY R = ω + mod N r ab 2 r b ? mod g ax p 0 r b ? ' mod h a y p 0 SAKURAI LABORATORY
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