Third Party CNOT Attack on MDI QKD

In this letter, we concentrate on the very recently proposed Measurement Device Independent Quantum Key Distribution (MDI QKD) protocol by Lo, Curty and Qi (PRL, 2012). We study how one can suitably present an eavesdropping strategy on MDI QKD, that is in the direction of the fundamental CNOT attack on BB84 protocol, though our approach is quite different. In this strategy, Eve will be able to know expected half of the secret bits communicated between Alice and Bob with certainty (probability 1) without introducing any error. Further, for the remaining bits, where Eve will only be able to predict the bit values as in random guess (with probability 1/2), she will certainly find out whether her interaction induced an error in the secret bits between the communicating parties. Given the asymmetric nature of the CNOT attack, we also introduce Hadamard gates to present a symmetric version. Though our analysis does not refute the security claims in MDI QKD, adapting the CNOT attack in this scenario requires nontrivial approach using entanglement swapping.