Anonymous Conference Key Agreement using GHZ states: Difference between revisions

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'''Tags:''' [[:Category: Multi Party Protocols|Multi Party Protocols]], [[:Category: Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category: Specific Task|Specific Task]]


==Assumptions==
==Assumptions==
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We require the following for this protocol:
We require the following resources for this protocol:
# A source of n-party GHZ states
# A source of n-party GHZ states
# Private randomness sources
# Private randomness sources
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==Notation==
==Notation==
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*<math>n</math>: Total number of nodes in the network


*<math>m</math>: Number of receiving nodes
*<math>L</math>: Number of GHZ states used
*<math>D</math>: Security parameter; expected number of GHZ states used to establish one bit of key
*<math>k</math>-partite GHZ state: <math>\frac{1}{\sqrt{2}}(|0\rangle^{\otimes k} + |1\rangle^{\otimes k})</math>
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# V resets her bit such that <math>\sum_ib_i = 0 (</math>mod <math>2)</math>. She measures in the X or Y basis if her bit equals 0 or 1 respectively, thereby also resetting her <math>m_i = m_v</math>
# V resets her bit such that <math>\sum_ib_i = 0 (</math>mod <math>2)</math>. She measures in the X or Y basis if her bit equals 0 or 1 respectively, thereby also resetting her <math>m_i = m_v</math>
# V accepts the state if and only if <math>\sum_im_i = \frac{1}{2}\sum_ib_i (</math>mod <math>2)</math>
# V accepts the state if and only if <math>\sum_im_i = \frac{1}{2}\sum_ib_i (</math>mod <math>2)</math>
==Properties==
==Properties==
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* Protocol 1 has an asymptotic key rate of <math>\frac{L}{D}</math>
==Further Information==
* This protocol satisfies the following notions of anonymity:
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** '''Sender Anonymity''': A protocol allows a sender to remain anonymous sending a message to <math>m</math> receivers, if an adversary who corrupts <math>t \leq n-2 </math> players, cannot guess the identity of the sender with probability higher than <math> \frac{1}{n-t}</math>
** '''Receiver Anonymity''': A protocol allows a receiver to remain anonymous receiving a message, if an adversary who corrupts <math>t \leq n-2 </math> players, cannot guess the identity of the receiver with probability higher than <math> \frac{1}{n-t}</math>
* Error correction and privacy amplification must be carried out anonymously and are not considered in the analysis of this protocol.


==References==
==References==
* The protocols and their security analysis, along with an experimental implementation for <math>n = 4</math> can be found in [https://arxiv.org/abs/2007.07995 Hahn et al.(2020)]
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