Man in the middle attack

[Nur Ziadah]

I have some curiosity about MIM attack in a paper that I have been found before. The diagram shows the MIM attack between Alice and Bob:

I found that the sentences state:

"We consider that the transmittance of the quantum channel is t. If Alice sends pulses with a mean photon number of N, Bob expects to receive pulses with mean photon number tN in the first stage and t³N in the third stage, and Alice expects to receive pulses with mean photon number t²N in the second stage. Therefore, for the MIM attack, Eve can extract a mean photon number of (1-t²)N to obtain the estimate
φ₁ and a mean photon number of t(1-t²)N to obtain the estimate θ_B . "

Question
How to derived (1-t²)N and t(1-t²)N?

Thank you.

 

[DrClaude]

Please give the reference where this is taken from.

 

[Spinnor]

This I think, https://arxiv.org/pdf/1503.05793.pdf

 

[DrClaude]

I assume that they consider that Eve will receive the full signal from Alice, so a mean number of photons of N, and since she needs to send t²N to Alice so she doesn't suspect the MIM attack, Eve can use at most (1-t²)N of those photons for her spying purposes. Likewise with her spying of Bob.

 

[Nur Ziadah]

This I think, https://arxiv.org/pdf/1503.05793.pdf

Thank you Spinnor.

 

[Nur Ziadah]

I assume that they consider that Eve will receive the full signal from Alice, so a mean number of photons of N, and since she needs to send t²N to Alice so she doesn't suspect the MIM attack, Eve can use at most (1-t²)N of those photons for her spying purposes. Likewise with her spying of Bob.

DrClaude, it can be assumed that Eve is trying to intercept the communication at the first stage using (1-t²)N, isn't it?

 

[DrClaude]

DrClaude, it can be assumed that Eve is trying to intercept the communication at the first stage using (1-t²)N, isn't it?

Disclaimer: I haven't read the article in detail. Eve is trying to intercept the communication by stopping all direct communication between Alice and Bob, replacing it by independent exchanges between Alice on one side and Bob on the other.