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GHZ-based Quantum Anonymous Transmission: Difference between revisions
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==Properties== | ==Properties== | ||
See [[Quantum Anonymous Transmission]] for the precise security definition. [[GHZ State based Quantum Anonymous Transmission#Pseudocode|Pseudocode]] implements secure anonymous transmission, i.e. it hides the identities of the sender and the receiver from other nodes in the network. That is, the maximum probability that adversaries guess the identity of <math>S</math> or <math>R</math> given all the classical and quantum information they have available at the end of the protocol is no larger than the uncertainty the adversaries have about the identities of <math>S</math> and <math>R</math> before the protocol begins. More formally, the anonymous transmission protocol with the GHZ state, [[GHZ State based Quantum Anonymous Transmission#Pseudocode|Pseudocode]], is sender- and receiver-secure: | See [[Quantum Anonymous Transmission]] for the precise security definition. [[GHZ State based Quantum Anonymous Transmission#Pseudocode|Pseudocode]] implements secure anonymous transmission, i.e. it hides the identities of the sender and the receiver from other nodes in the network. That is, the maximum probability that adversaries guess the identity of <math>S</math> or <math>R</math> given all the classical and quantum information they have available at the end of the protocol is no larger than the uncertainty the adversaries have about the identities of <math>S</math> and <math>R</math> before the protocol begins. More formally, the anonymous transmission protocol with the GHZ state, [[GHZ State based Quantum Anonymous Transmission#Pseudocode|Pseudocode]], is sender- and receiver-secure:</br> | ||
<math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[N]} P[S=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | <math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[N]} P[S=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | ||
<math>P_{\text{guess}}[R|C,S\notin \mathcal{A}] \leq \max_{i\in[N]} P[R=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math> | <math>P_{\text{guess}}[R|C,S\notin \mathcal{A}] \leq \max_{i\in[N]} P[R=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | ||
where <math>\mathcal{A}</math> is the subset of <math>t</math> adversaries among <math>N</math> nodes and <math>C</math> is the register that contains all classical and quantum side information accessible to the adversaries. Note that this implies that the protocol is also traceless, since even if the adversary hijacks any <math>t\leq N-2</math> players and gains access to all of their classical and quantum information after the end of the protocol, she cannot learn the identities of <math>S</math> and <math>R</math>. For a formal argument see [[GHZ State based Quantum Anonymous Transmission#References|(6)]]. | where <math>\mathcal{A}</math> is the subset of <math>t</math> adversaries among <math>N</math> nodes and <math>C</math> is the register that contains all classical and quantum side information accessible to the adversaries. Note that this implies that the protocol is also traceless, since even if the adversary hijacks any <math>t\leq N-2</math> players and gains access to all of their classical and quantum information after the end of the protocol, she cannot learn the identities of <math>S</math> and <math>R</math>. For a formal argument see [[GHZ State based Quantum Anonymous Transmission#References|(6)]]. | ||