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A Toolbox for Verifiable Tally-Hiding E-Voting Systems

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Computer Security – ESORICS 2022 (ESORICS 2022)

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Abstract

In most verifiable electronic voting schemes, one key step is the tally phase, where the election result is computed from the encrypted ballots. A generic technique consists in first applying (verifiable) mixnets to the ballots and then revealing all the votes in the clear. This however discloses much more information than the result of the election itself (that is, the winners, plus possibly some information required by law) and may offer the possibility to coerce voters.

In this paper, we present a collection of building blocks for designing tally-hiding schemes based on multi-party computations. From these building blocks, we design a fully tally-hiding scheme for Condorcet elections. Our implementation shows that the approach is practical, at least for medium-size elections. Similarly, we provide the first tally-hiding schemes with no leakage for three important counting functions: D’Hondt, STV, and Majority Judgment. We prove that they can be used to design a private and verifiable voting scheme. We also unveil unknown flaws or leakage in some previously proposed tally-hiding schemes.

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Author information

Authors and Affiliations

  1. Université de Lorraine, CNRS, Inria, Metz, France

    Véronique Cortier, Pierrick Gaudry & Quentin Yang

Authors
  1. Véronique Cortier
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  2. Pierrick Gaudry
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  3. Quentin Yang
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Corresponding author

Correspondence to Pierrick Gaudry .

Editor information

Editors and Affiliations

  1. Rutgers University, Newark, NJ, USA

    Vijayalakshmi Atluri

  2. Hamad Bin Khalifa University, Doha, Qatar

    Roberto Di Pietro

  3. Technical University of Denmark, Kongens Lyngby, Denmark

    Christian D. Jensen

  4. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

Appendix

Appendix

Fig. 1.
figure 1

Cost of various MPC primitives: basic functionalities for logic, integer arithmetic, and a few advanced functions. The Option column includes whether this is available in Paillier (P) or ElGamal (EG). The notations are a for the number of authorities, m for the bit-length of the operands, n for the number of operands, r for the precision (in the division). All logarithms are in base 2. The communication costs are expressed in terms of broadcast (denoted B) and full-rounds (denoted R). The unit of the transcript size is the key length. This corresponds to half the size of a ciphertext in both Paillier (typically 3072 bits) and ElGamal (typically 256 bits) settings.

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Fig. 2.
figure 2

Leading terms of the cost of tally-hiding for single choice systems. s: # seats, k: # lists, a: # authorities, n: # voters, \(m=\lceil {\log (n+1)}\rceil \), \(m_1=m+\log k\), \(m_2=m+\log (sk)\), \(m_3=m_1+\log (\textrm{lcm} (2,\cdots ,s))\), \(s'=\log (\textrm{lcm} (2,\cdots ,s))\), R: round of comm., B: broadcasts.

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Fig. 3.
figure 3

Leading terms of the cost of tally-hiding for MJ. n: # voters, \(m=\lceil {\log (n+1)}\rceil \), k: # candidates, \(d \): # grades, a: # authorities.

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Fig. 4.
figure 4

Leading terms of the cost of tally-hiding for STV. n: # voters, k: # candidates, \(m=\lceil {\log (n+1)}\rceil \), a: # authorities, r: precision in power of 2, \(m'=m+r\), \(k'=k+r\).

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Cortier, V., Gaudry, P., Yang, Q. (2022). A Toolbox for Verifiable Tally-Hiding E-Voting Systems. In: Atluri, V., Di Pietro, R., Jensen, C.D., Meng, W. (eds) Computer Security – ESORICS 2022. ESORICS 2022. Lecture Notes in Computer Science, vol 13555. Springer, Cham. https://doi.org/10.1007/978-3-031-17146-8_31

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  • DOI: https://doi.org/10.1007/978-3-031-17146-8_31

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