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GHZ-based Quantum Anonymous Transmission: Difference between revisions
→Properties
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==Properties== | ==Properties== | ||
See [[Quantum Anonymous Transmission]] for the precise security definition. [[GHZ State based Quantum Anonymous Transmission#Pseudocode|Pseudocode]] given below 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 | See [[Quantum Anonymous Transmission]] for the precise security definition. [[GHZ State based Quantum Anonymous Transmission#Pseudocode|Pseudocode]] given below 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 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></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></br> | ||