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Cronus: Everlasting Privacy with Audit and Cast

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Secure IT Systems (NordSec 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11875))

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Abstract

We present a new online voting scheme with everlasting privacy and cast-as-intended verifiability. We follow the so called “audit-and-cast” paradigm where the voter audits the ballot before casting it. To mitigate the ability of this information to harm the voter’s privacy, we provide measures for avoiding coercion by allowing any party to create fake proofs for the content of any vote. We propose an efficient implementation and formally verify its security properties.

The author acknowledges support from the Luxembourg National Research Fund (FNR) and the Research Council of Norway for the joint project SURCVS. Part of this work was completed while the author was working at Polyas GmbH.

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Author information

Authors and Affiliations

  1. Norwegian University of Science and Technology, Trondheim, Norway

    Thomas Haines

Authors
  1. Thomas Haines
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Correspondence to Thomas Haines .

Editor information

Editors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Aslan Askarov

  2. Aalborg University, Aalborg, Denmark

    René Rydhof Hansen

  3. IT University of Copenhagen, Copenhagen, Denmark

    Willard Rafnsson

A Sigma protocol for consistent Abe commitments

A Sigma protocol for consistent Abe commitments

We present a sigma protocol which shows that the prover can open two of Abe et al.’s [1] commitments to the same message. Recall that Abe et al.’s commitments are defined over an elliptic curve coupled with a bilinear pairing; we denote the groups of the curve as \(\mathbb {G}_1, \mathbb {G}_2, \mathbb {G}_T\). Given two generators for \(\mathbb {G}_1\) denoted \(G_0\), \(G_1\) and a generator for \(\mathbb {G}_2\) denoted H, a commitment to a message m using randomness r, \(r'\) is a tuple \((H^{r_1}m,G_0^rG_1^{r_1})\).

  • Sigma protocol for consistent commitments. Given a \(\mathbb {G}_1, \mathbb {G}_2, G_0, G_1, H,\) \((c_1,c_2),\) \((c'_1,c'_2)\) the prover shows that they know \((r, r', r_1, r'_1)\) such that \(c_1/c'_1=H^r/H^{r'}\), \(c_2=G_0^rG_1^{r_1}\), and \(c'_2 = G_0^{r'}G_1^{r'_1}\).

    1. 1.

      Prover chooses \((s,s',s_1,s'_1)\) at random and computes \(com_1=H^s/H^{s'}\), \(com_2=G_0^sG_1^{s_1}\), and \(com_3 =G_0^{s'}G_1^{s'_1}\) and returns (\(com_1, com_2, com_3\)).

    2. 2.

      Verifier sends a challenge e chosen at random in \(\mathbb {Z}_{N}\).

    3. 3.

      Prover computes \(t_1 := s+er\), \(t_2 := s'+er'\), \(t_3 := s_1+er_1\), and \(t_4 := s'_1+er'_1\) and sends these to the verifier.

    4. 4.

      The verifier accepts if \(com_1(c_1/c'_1)^e = H^{t_1}/H^{t_2}\) and \(com_2c_2^e = G_0^{t_1}G_1^{t_3}\) and \(com_3{c'}_2^e = G_0^{t_2}G_1^{t_4}\).

The proof is straightforward and we omit it due to lack of space.

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Haines, T. (2019). Cronus: Everlasting Privacy with Audit and Cast. In: Askarov, A., Hansen, R., Rafnsson, W. (eds) Secure IT Systems. NordSec 2019. Lecture Notes in Computer Science(), vol 11875. Springer, Cham. https://doi.org/10.1007/978-3-030-35055-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-35055-0_4

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