A Generalisation, a Simpli.cation and Some Applications of Paillier's Probabilistic Public-Key System

  • Ivan Damgård
  • Mads Jurik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1992)


We propose a generalisation 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 loosing the homomorphic property.We show that the generalisation is as secure as Paillier's original system. We construct a threshold variant of the generalised 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 optimised such that for a certain range of parameter values, a ballot has size only O(log L) bits.


Random Oracle Security Parameter Random Oracle Model Electronic Vote Semantic Security 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Mads Jurik
    • 1
  1. 1.University of Aarhus, BRICSAarhus

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