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Anonymous veto network

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 Title: Anonymous veto network Author: World Heritage Encyclopedia Language: English Subject: Password Authenticated Key Exchange by Juggling Collection: Publisher: World Heritage Encyclopedia Publication Date:

Anonymous veto network

In cryptography, the anonymous veto network (or AV-net) is a multi-party secure computation protocol to compute the boolean-OR function. It presents an efficient solution to the Dining cryptographers problem.

Description

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 $x_i \,\in_R\, \mathbb\left\{Z\right\}_q$ and publishes the ephemeral public key $g^\left\{x_i\right\}$ together with a zero-knowledge proof for the proof of the exponent $x_i$.

After this round, each participant computes:

$g^\left\{y_i\right\} = \prod_\left\{j$i} g^{x_j}

Round 2: each participant $i$ publishes $g^\left\{c_i y_i\right\}$ 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 $\prod g^\left\{c_i y_i\right\}$. If no one vetoed, each will obtain $\prod g^\left\{c_i y_i\right\} \;=\; 1$. On the other hand, if one or more participants vetoed, each will have $\prod g^\left\{c_i y_i\right\} \;\neq\; 1$.

The protocol design

The protocol is designed by combining random public keys in such a structured way to achieve a vanishing effect. In this case, $\sum \left\{x_i \cdot y_i\right\} \;=\; 0$. For example, if there are three participants, then $x_1 \cdot y_1 \,+\, x_1 \cdot y_2 \,+\, x_3 \cdot y_3 \;=\; x_1 \cdot \left(-x_2 \,-\, x_3\right) \,+\, x_2 \cdot \left(x_1 \,-\, x_3\right) \,+\, x_3 \cdot \left(x_1 \,+\, x_2\right) \;=\; 0$. 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.