Abstract. We propose a new encryption primitive, commitment consistent encryption (CCE), and instances of this primitive that enable building the first universally verifiable voting schemes with a perfectly private audit trail (PPAT) and practical complexity. That is:-the audit trail that is published for verifying elections guarantees everlasting privacy, and -the computational load required from the participants is only increased by a small constant factor compared to traditional voting schemes, and is optimal in the sense of Cramer, Gennaro and Schoenmakers [16]. These properties make it possible to introduce election verifiability in large scale elections as a pure benefit, that is, without loss of privacy compared to a non-verifiable scheme and at a similar level of efficiency. We propose different approaches for constructing voting schemes with PPAT from CCE, as well as two efficient CCE constructions: one is tailored for elections with a small number of candidates, while the second is suitable for elections with complex ballots.

Abstract. We investigate the problem of solving traditional combinatorial graph problems using secure multi-party computation techniques, focusing on the shortest path and the maximum flow problems. To the best of our knowledge, this is the first time these problems have been addressed in a general multi-party computation setting. Our study highlights several complexity gaps and suggests the exploration of various trade-offs, while also offering protocols that are efficient enough to solve real-world problems.

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