A Pairing-Based Blind Signature E-Voting Scheme

1. A Pairing-Based Blind Signature E-Voting Scheme LOURDES LPEZ-GARCA, LUIS J. DOMINGUEZ PEREZ, FRANCISCO RODRGUEZ-HENRQUEZ The Computer Journal July 2013 Presenter:陳昱安 Date:2013/10/14

2. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 2

3. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 3

4. Introduction(1/2) 4

5. Introduction(2/2) • Eligibility • Uniqueness • No-coercion • Accuracy • Receipt-freeness • Variability 5

6. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 6

7. Mathematical Background • Elliptic curves • Bilinear pairings over Barreto-Naehig curves • Security assumptions 7

8. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 8

9. Digital Signatures(1/4) • The Boneh-Lynn-Shacham short signature scheme Let (1 =〈P〉 , 2 =〈Q〉) : additive groups of order r P , Q : points over an elliptic curve r : a prime number H1 : the map-to-point function H1: → 1 9

10. Digital Signatures(2/4) • Key generation Pick a random integer d ∈ r and compute V = dQ. V ∈ 2: public key , d : private key. • Signing Given a private key d, a message m ∈ Compute M= H1(m) and S= dM. The signature of m is S∈ 1. • Verification Given a public key V ∈ 2, a message m ∈ , and a signature S∈ 1. = (V,H1(m)) ? 10

11. Digital Signatures(3/4) • Blind signatures (1, 2, P , Q , r , H1) • Key generation Pick a random integer d ∈ r and compute V = dQ. V ∈ 2 : public key , d : private key. • Blinding (user) Given a message m , calculate M= H1(m) , randomly find b ∈; compute. 11

12. Digital Signatures(4/4) • Signature (signer) Given a blind message; d : private key of the signer, compute • Unblinding(user) Given a blind signatureand a blind factor b, calculate . Then Sis the signature of the message m. • Signature Verification (third party) Given a message m, a signature S ; V : public key of the signer , check = (V,H1(m)) ? 12

13. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 13

14. The Proposed E-Voting Scheme(1/4) 14

15. The Proposed E-Voting Scheme(2/4) • Protocol dataflow Notation Authentication Server (AS) ; Voting Server (VS) {dAS , VAS}: private/public key pair of AS. {dVS, VVS}: private/publickey pair of VS. {IDV , dV , VV}: identifier and private/public key 15

16. The Proposed E-Voting Scheme(3/4) 16

17. The Proposed E-Voting Scheme(4/4) 17

18. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 18

19. Security Analysis (1/6) • Voter privacy The pseudonym private key dtand public key Vt are randomly generated. Knowing themessage m implies finding b in the equation. 19

20. Security Analysis (2/6) • Eligibility The voter requests from the AS a blind signed ballot that will be accepted as legitimate. Before producing the blind signature , the AS must authenticate the voter by reviewing the nominal list, S using the public key of the voter who is requesting the blank ballot. 20

21. Security Analysis (3/6) • Uniqueness During the authentication phase the AS marks the voter record in the nominal list. In the voting phase, the VS checks the ballots, if both signaturesare valid, then the ballot is stored as valid or invalid otherwise. In the counting phase, the VS verifies the signatures with which was generated for the ballot. 21

22. Security Analysis (4/6) • No-coercion ; Receipt-freeness When the results are published after the counting phase, the voter cannot prove who she voted for. This is because of the generation of a random value a that adds randomness to the hash message used as a receipt. The ACK has the goal to show to the voter that the ballot was received by the VS. 22

23. Security Analysis (5/6) • Accuracy To identifya fraudulent ballot means to find a pair that uses the same value for Vt. If when comparing two ballots, both have the same Vt, then the VS discards the second ballot as fraudulent/repeatedand counts only the first one. 23

24. Security Analysis (6/6) • Verifiability The ACK guarantees two things : a. The voter can verify if her ACKis found in the list of valid votes , no chance to extract the value of the vote, due to the random number aand the hash of all values mentioned. b.The VS can prove the accuracy of the results to show that all ACK are unique. 24

25. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 25

26. Implementation Aspects (1/4) 26

27. Implementation Aspects (2/4) 27

28. Implementation Aspects (3/4) 28

29. Implementation Aspects (4/4) 29

30. Outline • Introduction • Mathematical Background • Digital Signatures • The Proposed E-Voting Scheme • Security Analysis • Implementation Aspects • Conclusions 30

31. Conclusions • An electronic voting scheme based on blind signature is proposed which meets the necessary requirements to guarantee a reliable election. • This proposal requires a minimal number of interactions with electoral entities and more efficient than other e-voting schemes based on RSA or DSA crypto schemes. 31