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Anonymous Conference Key Agreement using GHZ states: Difference between revisions
Anonymous Conference Key Agreement using GHZ states (edit)
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<!-- Intro: brief description of the protocol --> | <!-- Intro: brief description of the protocol --> | ||
This [https://arxiv.org/abs/2007.07995 example protocol] achieves the functionality of quantum conference key agreement | This [https://arxiv.org/abs/2007.07995 example protocol] achieves the functionality of quantum conference key agreement. This protocol allows multiple parties in a quantum network to establish a shared secret key anonymously. | ||
<!--Tags: related pages or category --> | <!--Tags: related pages or category --> | ||
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==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: | |||
# A source of n-party GHZ states | |||
# Private randomness sources | |||
# A randomness source that is not associated with any party | |||
# A classical broadcasting channel | |||
# Pairwise private communication channels | |||
==Outline== | ==Outline== | ||
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===Protocol 2: Notification=== | ===Protocol 2: Notification=== | ||
''Input: '' Sender's choice of <math>m</math> receivers | |||
''Goal: '' The <math>m</math> receivers get notified | |||
''Requirements: '' Private pairwise classical communication channels and randomness sources | |||
For agent <math>i = 1,...,n</math>: | |||
# All agents <math>j \in \{1,...,n\}</math> do the following: | |||
#* '''When agent <math>j</math> is the sender''': If <math>i</math> is not a receiver, the sender chooses <math>n</math> random bits <math>\{r_{j,k}^i\}_{k = 1}^n</math> such that <math>\bigoplus_{k=1}^n r_{j,k}^i = 0</math>. Otherwise, if <math>i</math> is a receiver, the sender chooses <math>n</math> random bits such that <math>\bigoplus_{k=1}^n r_{j,k}^i = 1</math>. The sender sends bit <math>r_{j,k}^i</math> to agent <math>k</math> | |||
#* '''When agent <math>j</math> is not the sender''': The agent chooses <math>n</math> random bits <math>\{r_{j,k}^i\}_{k = 1}^n</math> such that <math>\bigoplus_{k=1}^n r_{j,k}^i = 0</math> and sends bit <math>r_{j,k}^i</math> to agent <math>k</math> | |||
# All agents <math>k \in \{1,...,n\}</math> receive <math>\{r_{j,k}^i\}_{j = 1}^n</math>, and compute <math>z_k^i = \bigoplus_{j=1}^n r_{j,k}^i</math> and send it to agent <math>i</math> | |||
# Agent <math>i</math> takes the received <math>\{z_k^i\}_{k=1}^n</math> to compute <math>z^i = \bigoplus_{k=1}^nz_k^i</math>. If <math>z^i = 1</math>, they are thereby notified to be a designated receiver. | |||
===Protocol 3: Anonymous Multiparty Entanglement=== | ===Protocol 3: Anonymous Multiparty Entanglement=== | ||
''Input: '' <math>n</math>-partite GHZ state <math>\frac{1}{\sqrt{2}}(|0\rangle^{\otimes n} + |1\rangle^{\otimes n})</math> | |||
''Output: '' <math>(m+1)</math>-partite GHZ state <math>\frac{1}{\sqrt{2}}(|0\rangle^{\otimes (m+1)} + |1\rangle^{\otimes (m+1)})</math> shared between the sender and receivers | |||
''Requirements: '' A broadcast channel; private randomness sources | |||
# Sender and receivers draw a random bit each. Everyone else measures their qubits in the X-basis, yielding a measurement outcome bit <math>x_i</math> | |||
# All parties broadcast their bits in a random order, or if possible, simultaneously. | |||
# The sender applies a Z gate to their qubit if the parity of the non-participating parties' bits is odd. | |||
===Protocol 4: Verification=== | ===Protocol 4: Verification=== | ||
''Input: '' A verifier V; a shared state between <math>k</math> parties | |||
''Goal: '' Verification or rejection of the shared state as the GHZ<math>_k</math> state by V | |||
''Requirements: '' Private randomness sources; a classical broadcasting channel | |||
# Everyone but V draws a random bit <math>b_i</math> and measures in the X or Y basis if their bit equals 0 or 1 respectively, obtaining a measurement outcome <math>m_i</math>. V chooses both bits at random | |||
# Everyone (including V) broadcasts <math>(b_i,m_i)</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> | |||
==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... --> | ||