Development at the Technion: a semi-quantum encryption protocol

In conventional quantum encryption, quantum encryption machines are needed on both sides. With the method developed at the Technion's Faculty of Computer Science, it is possible to be satisfied with one quantum side, while the other side is provided with coding capabilities of classical information only. Although the method is semi-classical, if someone eavesdrops, the eavesdropping produces a lot of noise, which is felt by the legitimate users

The researchers of the Faculty of Computer Science at the Technion have found an innovative quantum encryption method for transferring secrets that does not require sophisticated quantum equipment on both sides. The protocol they developed may have different consequences for secret communication between a "smart" and well-equipped center, and naive and simpler users (such as satellites, small military bases or local branches of the bank).

In the classic computer world, it is easy to transmit a secret in a completely safe way if Alice (the sender of the secret) and Bob (the receiver of the message) have a common "key" in advance, that is, some information ("bits" or letters) that is secret, completely random, and the length of which is the length of the secret.
The remaining problem, then, is how to transfer the same secret key from Alice to Bob. Since 1984, it has been accepted among researchers that the only way to transfer the same secret key in a completely safe way is to code the bits of the secret key in a quantum way, for example - into certain properties of photons.

In a conversation with the Hidan website, Prof. Moore explains that "the currently accepted key transfer method is the RSA method, which relies on a very long number - with hundreds of digits - and its initial components. The assumption is that multiplying prime numbers is an easy operation to perform, while trying to decompose a large number into its prime components is a difficult operation that requires a lot of computing power. Therefore, it will always be possible to find keys long enough, that the calculation power required to decipher them will be so great, to the point of making the decipherment impossible. However, there is no proof of safety for this method and methods similar to it, and it is possible that a large intelligence agency already knows the hack, but keeps this fact a secret. It is even possible (though much less likely) that a genius hacker will succeed in developing RSA in the coming years. It is especially interesting to note that theoretically, the RSA method has already been broken, but not by a normal algorithm but on quantum computers. But in practice, cracking this is still very far away - it will happen if and when quantum computers are buildable. They will be able to decipher any RSA cipher and the like, of any length. In light of the above dangers, it is important to know that there is also a completely different method, based on quantum theory."

Prof. Moore adds: "The fundamental principle in quantum theory is that studying one property of a particle (for example, its position) necessarily affects another property (for example, its speed). In 1984, researchers Charles Bennett and Gilles Bresser showed that precisely using this fundamental principle makes it possible to transmit secrets in an innovative and completely safe way with the help of quantum information encoded in the properties of photons. Because of this law of quantum theory, an adversary trying to learn the secret will inevitably introduce noises that legitimate users will notice.”

Despite the common name, quantum computers are not closely related to quantum cryptography. While quantum computers are in the experimental stage of their life, there are quantum encryption machines on the market, and they are not even that expensive (about 80 thousand dollars per unit). The problem is that to transmit and decode encrypted messages requires sophisticated quantum capabilities on both sides of the line. Our discovery, which was a central part of Dr. Dan Koenigsberg's doctoral thesis, means that it is probably possible to reach the exact same level of safety, even if one of the users does not use the principles of quantum theory and does not even know that the protocol he is using is semi-quantum."

In the conventional model of quantum key transfer, Alice creates a string of zeros and ones and encodes each "bit" using a photon polarized in one of the following two ways: a "computational" basis, also called a "classical" basis, where ones and zeros are represented through vertical vs. horizontal polarization, or a "diagonal" basis ”, where one and zero are represented by polarities plus 45 degrees and minus 45 degrees, respectively. If we imagine a photon trying to pass through sunglasses, then a horizontally polarized photon will pass through and reach the observer's eye, while a vertically polarized photon will be absorbed by the glass or reflected back. As in the case of position versus velocity, here too the polarization cannot be learned correctly if a different basis is used than the one in which the photon is coded.

When a photon from Alice reaches Bob, he chooses one of the bases - "computational" or "diagonal" and tells Alice which basis he is using. Every time he uses the wrong base, he gets a random answer, and Alice tells him to get rid of that "bit", meaning to ignore the photon. These "bits" are removed, and the secret key is produced from the remaining ones. If there is any eavesdropper, when he receives the photons he has to guess which base to use to read them. As a result, and in accordance with the laws of quantum mechanics, he actually damages the polarization every time he guesses correctly, introduces noise, and robs Bob of his ability to correctly read some of the photons he might have read correctly. The noise that Bob notices reveals to Bob that the communication channel is jammed by an eavesdropper."

We will now look at another example, which better demonstrates why a certain base should be called "classic". Let a given particle be inside a thousand box or inside a house box. Alice sends Bob the two boxes with only a single particle in them. According to quantum theory, the single particle can also be in both boxes (a feature that has no analogy in our ordinary, "classical" world). The question "In which box is the particle?" is a question that the classic user can ask. Coding the secret in the "computational" base (that is, in the "classical" base) in this case means that "zero" is coded by placing the particle in the thousand box, and "one" is coded by placing the particle in the one box. Coding the secret in the "diagonal" base, its meaning is now more complex: we will define a "phase" between the two states (a thousand box and a house box) and then the particle can be in both boxes and with a "+" phase when coded "zero", or in both boxes and with a "-" phase When "one" is coded. The question "Is the particle found with a "+" phase or with a "-" phase can only be asked by a user with quantum capabilities.

For more than two decades, all researchers in the field were absolutely convinced that a secret quantum protocol required both Alice and Bob to have quantum capabilities. Technion researchers have now discovered, in collaboration with researcher Michel Boyer from the University of Montreal in Canada, that it is probably possible to obtain exactly the same level of safety in a system that is semi-quantum, that is, only Alice needs to be quantum. Bob only uses the "classic" basis - that is, the "calculation" basis, not the "diagonal" basis. In the new protocol, Bob returns photons back to Alice, with some of them untouched at all, and Alice is the one who measures the base corresponding to the base in which she sent each photon. This system is safe, because the eavesdropper does not know in advance which photons will be returned to Alice without being measured by Bob, and thus the eavesdropper is prevented from interfering with the communication, because any interference by him will inevitably introduce a lot of noise into the information and will be felt by Alice and Bob.

Let's think about the example in which Alice sends Bob two boxes containing a single particle. The particle is in one of four states: in a thousand box or a house box or both with a "+" phase or both with a "-" phase. Bob with quantum abilities can choose a measurement that will tell him which box the particle is in. Alternatively, he can choose a measurement that will ask what the phase is ("+" or "-"). But according to the laws of quantum theory, Bob cannot ask both questions. Now it is clear what Bob can do which is classic: he can measure in which box the particle, he can leave it in the box where he found it, and send both boxes back to Alice, and he can also return both boxes without measuring at all.

In the new protocol we showed that indeed these capabilities are sufficient to define a semi-quantum protocol, yet secure against eavesdropping.