Electronic Voting Protocol Analysis with the Inductive Method
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1 Electronic Voting Protocol Analysis with the Inductive Method
2 Introduction E-voting use is spreading quickly in the EU and elsewhere Sensitive, need for formal guarantees Inductive Method: protocol verification through theorem proving + mathematical induction Toolbox being built with as dummy protocol Goal: make all properties rigourously verifiable
3
4 Motivation Analysis of e-voting dominated by ProVerif automatic verifier Powerful, but sometimes limited Motivation to fill in the gaps with complementary, alternative approach
5 E-voting protocols: primitives Often require modelling new crypto primitives Blind signatures Bit commitment Proxy re-encryption...
6 Related Work Ryan / Kremer / Delaune: applied pi calculus, partially mechanized through ProVerif Observational equivalence: traces in which two voters swap their votes are equivalent in a sense Parts of the proof done by hand
7 Method: the Inductive approach Mathematical induction on protocol steps Dolev-Yao threat model Tool support: Isabelle/HOL interactive theorem prover
8 92 A practical secret voting scheme for large scale elections, AUSCRYPT 1992 By Fujioka, Okamoto and Ohta Claims four classical properties
9 Properties of Fairness: Partial results confidential as long as the voting phase is ongoing Eligibility: Only registered voters can vote, and only once Individual verifiability: Voters can check their vote was counted Privacy: How a particular voter voted is not known to anyone
10 Properties of in practice Fairness tally confidentiality before deadline Eligibility authentication + uniqueness check Individual verifiability Event implication check Privacy LINKABILITY concept (hard), our focus here
11 Steps of (1/2) In a nutshell: Voter picks a vote and sends a signed, blinded commitment of it with its identity to Administrator Administrator checks this and returns it with own (blind) signature if approved V unblinds this and sends it to Collector anonymously Collector checks what he receives and records it on a list if correct Deadline
12 Steps of (2/2) Once the deadline is reached, Collector publishes list of commitments If V s commitment is in list, V discloses secret commitment key anonymously Collector opens V s ballot and publishes it
13 Steps of modelled
14 What is privacy in e-voting? Crucial point: privacy is NOT confidentiality of vote But unlinkability of voter and vote In Pro-Verif, done with observational equivalence between swapped votes
15 Privacy in the Inductive Method: aanalz Extract associations from honest agent s messages
16 Privacy in the Inductive Method: asynth Build up association sets from associations with common elements
17 Privacy in the Inductive Method: theorem statement If a normal voter started the protocol, the corresponding vote & identity cannot be associated
18 E-voting protocol analysis field active, yet room for improvement Inductive Method s flexiblity allows new e-voting analysis Privacy: toughest part crucial choices, ongoing
19 Complete verification toolbox with missing property formalisations Model & analyse real-world e-voting protocols Derive general design guidelines
20 Principles of the inductive method Number of agents is unbounded, session interleaving is allowed: replay attack weakness detected Cryptographic keys: type key, different subtypes for private / public / encryption / signature Events: Says (models sending), Gets (reception), Notes (knowledge) Trace: history of network events. Inductive reasoning over traces. Focus is not security of algorithms: treated as black boxes in Isabelle
21 Message set operators Fundamental operators, constantly used in security statements parts: decompose into atomic message components, even ciphertext for which decrypting key unavailable analz: like parts, but leaving undecryptable ciphertext untouched synth: build up messages from message components. Includes encryption if encrypting key available
22 Formal protocol model Every protocol step modeled as inductive rule with pre- and postconditions Protocol model is set of all admissible traces under those rules Empty trace modeled by Nil event Threat model (DY) represented by Fake event Agents knowledge derived from traces
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