Write
33
edits
Anonymous Conference Key Agreement using GHZ states: Difference between revisions
Anonymous Conference Key Agreement using GHZ states (edit)
Revision as of 20:33, 11 January 2022
, 11 January 2022Created page for Anonymous QCKA
No edit summary |
(Created page for Anonymous QCKA) |
||
| Line 5: | Line 5: | ||
<!--Tags: related pages or category --> | <!--Tags: related pages or category --> | ||
'''Tags:''' [[:Category: Multi Party Protocols|Multi Party Protocols]], [[:Category: Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]], [[:Category: Specific Task|Specific Task]] | |||
==Assumptions== | ==Assumptions== | ||
<!-- It describes the setting in which the protocol will be successful. --> | <!-- It describes the setting in which the protocol will be successful. --> | ||
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 | ||
| Line 25: | Line 26: | ||
==Notation== | ==Notation== | ||
<!-- Connects the non-mathematical outline with further sections. --> | <!-- Connects the non-mathematical outline with further sections. --> | ||
*<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> | |||
<!-- ==Knowledge Graph== --> | <!-- ==Knowledge Graph== --> | ||
<!-- Add this part if the protocol is already in the graph --> | <!-- Add this part if the protocol is already in the graph --> | ||
| Line 85: | Line 94: | ||
# 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== | ||
<!-- important information on the protocol: parameters (threshold values), security claim, success probability... --> | <!-- important information on the protocol: parameters (threshold values), security claim, success probability... --> | ||
* Protocol 1 has an asymptotic key rate of <math>\frac{L}{D}</math> | |||
* This protocol satisfies the following notions of anonymity: | |||
< | ** '''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)] | |||