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==Properties== | ==Properties== | ||
Security of a anonymous transmission protocol is defined in terms of the guessing probability, i.e., the maximum probability that adversaries guess the identity of the sender <math>S</math> or receiver <math>R</math> given all the classical and quantum information they have available at the end of the protocol. | Security of a anonymous transmission protocol is defined in terms of the guessing probability, i.e., the maximum probability that adversaries guess the identity of the sender <math>S</math> or receiver <math>R</math> given all the classical and quantum information they have available at the end of the protocol. | ||
'''Guessing probability''' | *'''Guessing probability''' Let <math>\mathcal{A}</math> be a subset of adversaries among <math>N</math> nodes. Let <math>C</math> be the register that contains all classical and quantum side information accessible to the adversaries. Then, the probability of adversaries guessing the sender is given by | ||
Let <math>\mathcal{A}</math> be a subset of adversaries among | <math> P_{\text{guess}}[S|C, S\notin \mathcal{A}] = \max_{\{M^i\}} \sum_{i \in [N]} P[S=i|S\notin \mathcal{A}] \text{Tr}[M^i \cdot \rho_{C|S=i} ],</math></br> | ||
<math> P_{\ | where the maximization is taken over the set of POVMs <math>{\{M^i\}}</math> for the adversaries and <math>\rho_{C|S=i}</math> is the state of the adversaries at the end of the protocol, given that node <math>i</math> is the sender | ||
where the maximization is taken over the set of POVMs <math>{\{M^i\}}</math> for the adversaries and | *'''Sender-security''' We say that an anonymous transmission protocol is ''sender-secure'' if, given that the sender is honest, the probability of the adversary guessing the sender is </br> | ||
*'''Sender-security''' We say that an anonymous transmission protocol is | <math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[N]} P[S=i|S\notin \mathcal{A}].</math></br> | ||
<math>P_{\ | *'''Receiver-security''' We say that an anonymous transmission protocol is ''receiver-secure'' if, given that the receiver is honest, the probability of the adversary guessing the receiver is:</br> | ||
*'''Receiver-security''' We say that an anonymous transmission protocol is | <math>P_{\text{guess}}[R|C,R\notin \mathcal{A}] \leq \max_{i\in[N]} P[R=i|R\notin \mathcal{A}]</math> | ||
<math>P_{\ | |||
==Further Information== | ==Further Information== | ||
The security definition presented here, are proven to be sufficient to guarantee universal composability for standard QKD in (2). For device-independent quantum key distribution, attacks presented in (1) show that security can be compromised if the same devices are used to implement another instance of the protocol. | The security definition presented here, are proven to be sufficient to guarantee universal composability for standard QKD in (2). For device-independent quantum key distribution, attacks presented in (1) show that security can be compromised if the same devices are used to implement another instance of the protocol. | ||