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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion A Formal Taxonomy of Privacy in Voting Protocols Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech Universit Grenoble 1, CNRS, Verimag, France First IEEE

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

A Formal Taxonomy of Privacy in Voting Protocols

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech

Université Grenoble 1, CNRS, Verimag, France

First IEEE International Workshop on Security and Forensics in Communication Systems, Ottawa, Canada June 15, 2012

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Electronic voting machines. . .

. . . are used all over the world

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Internet voting

Available in Estonia France Switzerland . . .

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Security Requirements

Eligibility Fairness Robustness Individual Verifiability Universal Verifiability Vote-Independence Privacy Receipt-Freeness Coercion-Resistance

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Security Requirements

Eligibility Fairness Robustness Individual Verifiability Universal Verifiability Vote-Independence Privacy Receipt-Freeness Coercion-Resistance

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

How to secure electronic voting?

Idea: Use formal methods to find bugs and increase confidence Need for formal definitions Lots of related work: [?, ?, ?, ?, ?, ?, ?]... Ideally we need definitions that can be applied on any protocol are comparable include known threats: coercion, vote-buying, vote-copying, forced abstention are suitable for automation

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Four Dimensions

Communication: Vote-Privacy (VP), Receipt-Freeness (RF), Coercion-Resistance (CR) Vote-Independence: Outsider (O), Insider (I) Forced Abstention Attacks: Participation Only (PO), Security against Forced-Abstention-Attacks (FA) Knowledge about honest voters: Exists Behavior (EB), Any Behavior (AB)

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Vote-Privacy (VP)

Main idea: Observational equivalence between two situations. Alice Bob Vote A B

≈l

Vote B A

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

The Applied Pi Calculus [?]

Syntax P, Q, R := processes null process P|Q parallel composition !P replication νn.P restriction (“new”) if M = N then P else Q conditional in(u, x).P message input

ut(u, x).P

message output {M/x} active substitution

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Vote-Privacy: The formal definition

Definition (Vote-Privacy) A voting process respects Vote-Privacy (VP) if for all votes σvA and σvB we have VP′ [V σidAσfAσvA|V σidBσfBσvB] ≈l VP′ [σidAσfAσvB|V σidBσfBσvA]

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Receipt-Freeness (RF)

Again: Observational equivalence between two situations, but Alice tries to create a receipt or a fake. Alice Bob Mallory A B

≈l

B A Secret Data Fake Data

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Receipt-Freeness (RF)

Again: Observational equivalence between two situations, but Alice tries to create a receipt or a fake. Alice Bob Mallory A B

≈l

B A Secret Data Fake Data

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Coercion-Resistance (CR)

Observational equivalence between two situations, but Alice is under control by Mallory or only pretends to be so. Alice Bob Mallory A B

≈l

B A Secret Data Fake Data

Orders Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Coercion-Resistance (CR)

Observational equivalence between two situations, but Alice is under control by Mallory or only pretends to be so. Alice Bob Mallory A B

≈l

B A Secret Data Fake Data

Orders Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Insider (I) vs. Outsider (O)

Main idea: Privacy, but with a voter under control of the attacker. If he can relate his vote to e.g. Alice’s vote, Mallory can distinguish both sides. Alice Bob Mallory Vote A B

≈l

Vote B A Chuck ? ?

O r d e r s Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Insider (I) vs. Outsider (O)

Main idea: Privacy, but with a voter under control of the attacker. If he can relate his vote to e.g. Alice’s vote, Mallory can distinguish both sides. Alice Bob Mallory Vote A B

≈l

Vote B A Chuck ? ?

O r d e r s Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Can we combine Vote-Independence with Receipt-Freeness?

“Receipt-Freeness with Chuck”: Alice Bob Mallory A B

≈l

B A Secret Data Fake Data Chuck ? ?

O r d e r s Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Can we combine Vote-Independence with Receipt-Freeness?

“Receipt-Freeness with Chuck”: Alice Bob Mallory A B

≈l

B A Secret Data Fake Data Chuck ? ?

O r d e r s Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

And with Coercion-Resistance?

“Coercion-Resistance with Chuck”: Alice Bob Mallory A B

≈l

B A Secret Data Fake Data

Orders

Chuck ? ?

O r d e r s Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

And with Coercion-Resistance?

“Coercion-Resistance with Chuck”: Alice Bob Mallory A B

≈l

B A Secret Data Fake Data

Orders

Chuck ? ?

O r d e r s Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Security against Forced Abstention Attacks (FA) vs. Participation Only (PO)

Alice abstains or votes in turn with Bob: Alice Bob Vote B

≈l

Vote B A A

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Security against Forced Abstention Attacks (FA) vs. Participation Only (PO)

Alice abstains or votes in turn with Bob: Alice Bob Vote B

≈l

Vote B

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Introducing Fakes: Exists Behavior (EB) vs. Any Behavior (AB)

Some protocols use fake votes [?] to achieve Receipt-Freeness and Coercion-Restistance. Alice Bob Mallory A B

≈l

A B A Secret Data Fake Data

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion Communication Vote-Independence Forced Abstention Knowledge about honest voters

Introducing Fakes: Exists Behavior (EB) vs. Any Behavior (AB)

Some protocols use fake votes [?] to achieve Receipt-Freeness and Coercion-Restistance. Alice Bob Mallory A A B

≈l

A B A Secret Data Fake Data

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Relations among the notions

CRO,FA,AB

CRI,FA,AB
CRO,FA,EB
CRI,FA,EB
CRO,PO,AB
CRI,PO,AB
CRO,PO,EB
CRI,PO,EB
RF O,FA,AB
RF I,FA,AB
RF O,FA,EB
RF I,FA,EB
RF O,PO,EB
RF I,PO,EB
RF O,PO,AB
RF I,PO,AB
VPO,FA,AB
VPI,FA,AB
VPO,FA,EB
VPI,FA,EB
VPO,PO,EB

VPI,PO,EB

VPO,PO,AB
VPI,PO,AB
Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech

A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Plan

1 Introduction 2 Definitions: Four Dimensions

Communication Vote-Independence Forced Abstention Knowledge about honest voters

3 Analysis and Case Studies 4 Conclusion

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Conclusion

Generalized model New modular definition Includes known threats Hierarchy of notions Allows fine-grained comparison of different types of protocols Can be automatically verified using existing tools (within certain complexity limits)

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Future Work

Automate and/or automatically verify more of the proofs Computational definition

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Introduction Definitions: Four Dimensions Analysis and Case Studies Conclusion

Thank you for your attention!

Questions?

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Existing definitions

[?, ?]: Tailored to a specific protocol [?, ?]: Unsuitable for protocol by Juels/Civitas [?, ?]: Vote-Independence based on definitions by [?, ?] [?]: Coercion Resistance, very fine-grained → difficult to compare [?]: Privacy as unlinkability, unsuitable for automated verification . . .

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Case Studies

Protocol

Priv. Notion

Comments Juels et al. [?] CRI,FA,EB Requires fakes to achieve CR Bingo Voting [?] CRI,PO,AB Trusted voting machine

variant

CRI,FA,AB Secure against forced abstention Lee et al. [?] CRO,PO,AB Vulnerable to vote-copying Okamoto [?] RF I,PO,AB Based on trap-door commitments

variant

RF I,FA,AB Private channel to administrator Fujioka et al. [?] VPI,PO,AB Based on blind signatures

variant

VPI,PO,AB Permits multiple votes

Simp. Voting Prot.

VPO,PO,AB Vulnerable to vote-copying

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Modeling a voting protocol

Definition (Voting Protocol) A voting protocol is a tuple of processes (V , A1, . . . , Am) where V is the process that is executed by the voter, and the Aj’s are the processes executed by the election authorities. Definition (Voting Process) A voting process of a voting protocol (V , A1, . . . , Am) is a closed plain process VP = ν ˜ n.(V σid1σf1σv1| . . . |V σidnσfnσvn|A1| . . . |Al) We define an evaluation context VP′ which is like VP, but has a hole instead of two V σi.

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Definition (Process Pch [?]) Let P be a process and ch be a channel. We define Pch as follows: 0ch ˆ = 0, (P|Q)ch ˆ = Pch|Qch, (νn.P)ch ˆ = νn.out(ch, n).Pch when n is a name of base type, (νn.P)ch ˆ = νn.Pch otherwise, (in(u, x).P)ch ˆ = in(u, x).out(ch, x).Pch when x is a variable

f base type,

(in(u, x).P)ch ˆ = in(u, x).Pch otherwise, (out(u, M).P)ch ˆ = out(u, M).Pch, (!P)ch ˆ = !Pch, (if M = N then P else Q)ch ˆ = if M = N then Pch else Qch.

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Definition (Process Pc1,c2 [?]) Let P be a process, c1, c2 channels. We define Pc1,c2 as follows: 0c1,c2 ˆ = 0, (P|Q)c1,c2 ˆ = Pc1,c2|Qc1,c2, (νn.P)c1,c2 ˆ = νn.out(c1, n).Pc1,c2 if n is a name of base type, (νn.P)c1,c2 ˆ = νn.Pc1,c2 otherwise, (in(u, x).P)c1,c2 ˆ = in(u, x).out(c1, x).Pc1,c2 if x is a variable

f base type & x is a fresh variable,

(in(u, x).P)c1,c2 ˆ = in(u, x).Pc1,c2 otherwise, (out(u, M).P)c1,c2 ˆ = in(c2, x).out(u, x).Pc1,c2, (!P)c1,c2 ˆ = !Pc1,c2, (if M = N then P else Q)c1,c2 ˆ = in(c2, x).if x = true then Pc1,c2 else Qc1,c2 where x is a fresh variable and true is a constant.

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Definition (Process A\out(ch,·) [?]) Let A be an extended process. We define the process A\out(ch,·) as νch.(A|!in(ch, x)).

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Definition (Equivalence in a Frame) Two terms M and N are equal in the frame φ, written (M = N)φ, if and only if φ ≡ ν ˜ n.σ, Mσ = Nσ, and {˜ n} ∩ (fn(M) ∪ fn(N)) = ∅ for some names ˜ n and some substitution σ. Definition (Static Equivalence (≈s)) Two closed frames φ and ψ are statically equivalent, written φ ≈s ψ, when dom(φ) =dom(ψ) and when for all terms M and N (M = N)φ if and only if (M = N)ψ. Two extended processes A and B are statically equivalent (A ≈s B) if their frames are statically equivalent.

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols

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Definition (Labelled Bisimilarity (≈l)) Labelled bisimilarity is the largest symmetric relation R on closed extended processes, such that A R B implies

1 A ≈s B, 2 if A → A′, then B → B′ and A′ R B′ for some B′, 3 if A α

− → A′ and fv(α) ⊆ dom(A) and bn(α) ∩ fn(B) = ∅, then B →∗ α − →→∗ B′ and A′ R B′ for some B′.

Jannik Dreier, Pascal Lafourcade, Yassine Lakhnech A Formal Taxonomy of Privacy in Voting Protocols