## FANDOM

566 Pages

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:

$g^{y_i} = \prod_{ji} g^{x_j}$.

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