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A generalization of Paillier’s public-key system with applications to electronic voting

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Abstract

We propose a generalization of Paillier’s probabilistic public-key system, in which the expansion factor is reduced and which allows to adjust the block length of the scheme even after the public key has been fixed, without losing the homomorphic property. We show that the generalization is as secure as Paillier’s original system and propose several ways to optimize implementations of both the generalized and the original scheme. We construct a threshold variant of the generalized scheme as well as zero-knowledge protocols to show that a given ciphertext encrypts one of a set of given plaintexts, and protocols to verify multiplicative relations on plaintexts. We then show how these building blocks can be used for applying the scheme to efficient electronic voting. This reduces dramatically the work needed to compute the final result of an election, compared to the previously best known schemes. We show how the basic scheme for a yes/no vote can be easily adapted to casting a vote for up to t out of L candidates. The same basic building blocks can also be adapted to provide receipt-free elections, under appropriate physical assumptions. The scheme for 1 out of L elections can be optimized such that for a certain range of the other parameter values, the ballot size is logarithmic in L.

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Authors and Affiliations

  1. Department of Computer Science, Basic Research in Computer Science (BRICS), Centre of the Danish National Research Foundation, Aarhus University, Århus, Denmark

    Ivan Damgård, Mads Jurik & Jesper Buus Nielsen

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  1. Ivan Damgård
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  2. Mads Jurik
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  3. Jesper Buus Nielsen
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Correspondence to Ivan Damgård.

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Damgård, I., Jurik, M. & Nielsen, J.B. A generalization of Paillier’s public-key system with applications to electronic voting. Int. J. Inf. Secur. 9, 371–385 (2010). https://doi.org/10.1007/s10207-010-0119-9

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