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Anonymous veto network

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Title: Anonymous veto network  
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Subject: Password Authenticated Key Exchange by Juggling
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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.[1] It presents an efficient solution to the Dining cryptographers problem.


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

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

After this round, each participant computes:

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

Round 2: each participant \scriptstyle i publishes \scriptstyle g^{c_i y_i} and a zero-knowledge proof for the proof of the exponent \scriptstyle c_i. Here, the participants chose \scriptstyle 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 \scriptstyle \prod g^{c_i y_i}. If no one vetoed, each will obtain \scriptstyle \prod g^{c_i y_i} \;=\; 1. On the other hand, if one or more participants vetoed, each will have \scriptstyle \prod g^{c_i y_i} \;\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, \scriptstyle \sum {x_i \cdot y_i} \;=\; 0. For example, if there are three participants, then \scriptstyle 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]


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