![]() ![]() The key point is that many of the signals contain more than one photons and as such Eve is allowed to make copies (details are available at For short-distance applications, the relevance of such an attack remains an important subject for future investigations. Therefore, rather surprisingly, in an actual experimental implementation of polarization-coding BB84 over a significant distance (say 40 km), Eve may, in principle, break the system by a generalized beam-splitting attack. The attenuation of an optical fiber is also large (say 0.35 dB/km), and detector efficiencies are far from perfect. Unfortunately, producing almost perfect single-photon pulses is beyond current technology, and dim coherent light pulses with a Poisson distribution in the number of photons are often used instead. This conclusion is valid even if the original EPR pairs prepared by Bob do contain hidden dimensions.įor instance, in the study of standard P/M schemes such as BB84 (2), one often assumes that the signal carriers are perfect single photons. ![]() Therefore, there is no hidden Hilbert space to worry about in the reconstructed quantum system. Teleportation provides an exact counting of the effective dimensions of the Hilbert space because each qubit requires two classical bits to teleport. Now, assuming that there is no security risk in receiving classical messages, Bob can safely receive those classical messages and use them to reconstruct the original quantum state. In other words, Bob conveys the untrusted quantum state into his laboratory by means of trusted EPR pairs and untrusted classical messages. Robert teleports the nominal state of the untrusted system (that is, the state in its nonclandestine variables) into Bob's laboratory. More concretely, Bob prepares trusted EPR pairs in his laboratory and sends one member of each pair to his untrusted representative Robert, who is working in an insecure area just outside his laboratory, when the untrusted quantum data (potentially a Trojan horse) is waiting. Instead of receiving any untrusted quantum system directly from an open quantum channel, a user (say Bob) demands that the state of the system must be converted into classical messages through teleportation (30) right at his doorstep. If Alice and Bob could not afford to receive any untrusted classical message, the whole enterprise of cryptography would be hopeless. Before we present our proof, notice that the assumption that there is no security risk in receiving classical messages is most reasonable because Eve can always send classical messages to Alice and Bob in a “man-in-the-middle” attack during a classical authentication process. As long as there is no security risk for Alice and Bob to receive untrusted classical messages, quantum Trojan horse attack can be foiled. This would certainly make a rigorous proof of security of QKD based on imperfect sources impossible. One might wonder if Eve could perform a quantum Trojan horse attack by hiding robots in (the hidden Hilbert space dimensions of) the quantum systems received by Alice and Bob. Real quantum systems often contain other degrees of freedom that are ignored in quantum computation. This worry is not unfounded because it is notoriously difficult to prepare almost perfect EPR pairs. The real problem is that the Trojan horse pretends to be real EPR pairs when Alice and Bob do their testing but behaves differently when they generate key, thus causing them to leak the information themselves. One might think that this problem could be eliminated by simply shielding the laboratory very well or that such shielding is, in fact, assumed anyway in cryptographic protocols. It is not just that the Trojan horse might leak information once it is in Bob or Alice's laboratory. Smolin has often remarked (41), it is even conceivable that a robot is hidden in the received material and that it pops out to find and disclose secrets to adversaries. Any untrusted material received from an open channel poses serious security risks. A big worry in cryptography is the Trojan horse attack. ![]()
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