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Anonymous veto network

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In cryptography, the Anonymous Veto Network (or AV-net) is a multi-party secure computation protocol to compute the boolean-OR function[1]. It presents an efficient solution to the Dining cryptographers problem.

DescriptionEdit

All participants agree on a group G with a generator g of prime order q in which the discrete logarithm problem is hard. For example, a Schnorr group can be used. For a group of n participants, the protocol executes in two rounds.

Round 1: each participant i selects a random value x_i \in_R \mathbb{Z}_q and publishes the ephemeral public key g^{x_i} together with a Zero-knowledge proof for the proof of the exponent x_i.

After this round, each participant computes:

g^{y_i} = \prod_{j<i} g^{x_j} / \prod_{j>i} g^{x_j}.

Round 2: each participant i publishes g^{c_i y_i} and a Zero-knowledge proof for the proof of the exponent c_i. Here, the participants chose c_i=x_i if they want to send a "0" bit (no veto), or a random value if they want to send a "1" bit (veto).

After round 2, each participant computes \prod g^{c_i y_i}. If no one vetoed, each will obtain \prod g^{c_i y_i}=1. On the other hand, if one or more participants vetoed, each will have \prod g^{c_i y_i} \neq 1.

The protocol designEdit

The protocol is designed by combining random public keys in such a structured way to achieve a vanishing effect. In this case, \sum {x_i \cdot y_i} = 0. For example, if there are three participants, then x_1 \cdot y_1 + x_1 \cdot y_2 + x_3 \cdot y_3 = x_1 \cdot (- x_2 - x_3) + x_2 \cdot (x_1 - x_3) + x_3 \cdot (x_1 + x_2) = 0. A similar idea - though in a non-public-key context - can be traced back to David Chaum's original solution to the Dining cryptographers problem[2].

ReferencesEdit

  1. F. Hao, P. Zieliński. A 2-round anonymous veto protocol. Proceedings of the 14th International Workshop on Security Protocols, 2006.
  2. David Chaum. The Dining Cryptographers Problem: Unconditional Sender and Recipient Untraceability Journal of Cryptology, vol. 1, No, 1, pp. 65-75, 1988

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