Voting System Properties

1. Voting System Properties • Most voting systems assume no collusion between more than one party for keys • Most voting systems require a consistency check by each voter for a small piece of the protocol • If 5-20% of voters check, the correctness of the entire protocol is determined by this weakest link

2. Choosing a Mixnet • If we can trade a mixnet that requires only one honest* mix for a mixnet that is faster but requires more than one honest mix: good trade for voting • If we can trade cryptographic soundness (1-ε) for statistical soundness (99%) and speed: good trade for voting * keep permutation private from other mixes

3. 2 Such Mixnets Assuming re-encryption: Randomized Partial Checking [JJR02] Almost Entirely Correct Mixing [BG02] Open problem 1: others? Open problem 2: throw combinatorics at BG02

4. Mix

5. Mix Σ Σ

6. Necessary but not sufficient Mix Σ Σ

7. Mix Σ ≠ Σ

8. Properties Testing product of subsets is probabilistic: boost soundness by repeating Testing product of subsets reduces anonymity: repeating makes worst Adding additional honest mixes increases anonymity Optimize number of tests per mix and number of honest mixes to balance anonymity and soundness

9. Open Problem 2 Analysis in paper is tricky Complexity seems to result from using random coins Idea: throw a combinatorial design at the problem Choose random instance from a family of { ? } so that guarantees can be made by anonymity sets within mixes and with adjacent honest mixes