Computing and Information Systems - Theses
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ItemEfficient mixnets with application to electronic voting( 2013)Cryptographic mixnets are a fundamental tool in the construction of secure electronic elections. Traditional mixnets rely upon third party mixers to perform vote anonymisation at election time. This approach places inherent limitations on the robustness and efficiency of mixing. In this thesis we show that third party mixers are not required to be active at election time - in fact it is highly feasible for the shuffle to be constructed before the election. A basic primitive used is the public key obfuscator for a re-encryption shuffle. We show that the seminal obfuscator of Paillier shuffles by Adida and Wikstro ̈m [AW07a] can be extended to generalised Paillier shuffles [DJ01]. The resulting obfuscations are composable, allowing obfuscation of re-encryption permutation networks. This, in turn, implies an obfuscator for a Paillier shuffle with improved efficiency (N log^3.5 N vs. N^2). This leads to a very robust and efficient mixnet: when distributed over O(N) nodes the mixnet achieves mixing in polylogarithmic time, independent of the level of privacy or verifiability required. In fact, our mixnet is the first to achieve mixing in time sublinear in the number of inputs, assuming the number of nodes available is bounded by the number of inputs. Although the mixnet may have a biased distribution, we show that using particular networks leads to an acceptable bias-efficiency tradeoff. We additionally show that the mixnet is secure in the sense of indistinguishability of chosen permutations [NSNK04].