When one hears about Quantum Cryptography, the first thought that comes to mind is, how can there be any relation between physics and codes? It actually appears to be one of the newest ideas in the cipher world to use physics and has been declared as the ultimate goal in security. In this short introductory text we will try to explain how these two, from first sight totally unrelated things fit together, how quantum cryptography works and what makes it so secure, and therefore important.

What is Cryptography?

Classical cryptography was always about constructing and analysing protocols in order to protect information against the influence of adversaries. Modern cryptography is composed of disciplines such as mathematics, computer science and electrical engineering. All it needs to ensure is the creation of a safe, complex and indecipherable code to third parties. With secret key cryptography, a single key is used for encryption and decryption. The sender uses the key to encrypt the plain text and sends it to the receiver. The receiver applies the same key to decrypt the message and recover the plain text. Cryptography includes everyday things like computer passwords, ATM cards, electronic commerce and much more. All of the current day classical computer cryptography are based on certain class of mathematical operations that are easy to perform in one direction but are extremely difficult in the opposite direction. Example of such a problem is prime number multiplication. It is very easy to multiply two prime numbers of any length (one direction). However, if you are given a long two million digits number and told that this number is a product of two primes, even with the help of modern computers it would take hundreds of years to find its constitutes-prime factors. This is the basis for the well known RSA (Rivest-Shamir-Adleman, 1977) cryptosystem [1], the importance of which is obvious since nowadays the internet is used by and provides essential communication between hundreds of millions of people.

New Age Methods

Differently from the classical version of cryptography which uses key, based on the assumption that there are no sufficiently fast mathematical algorithms for deciphering, quantum version of cryptography is based purely on the laws of quantum physics. Currently for deciphering, mathematical algorithms are based on computing power and brute force methods. Usually this kind of deciphering is not worth anything, since user can change the key frequently enough, so as to not to give enough time for decipherers to decrypt the key. If one decides to use faster computers and more advanced methods for decryption, another can just simply increase the length of the key used for encryption. When the idea of quantum computing became omnipresent, it soon became obvious that quantum computers could provide unprecedented ability to encrypt secret information. With the use of quantum, it is possible to create devices which allow detection of whether data transmission channel is being spied. Devices which are based on quantum physics phenomena, usually use one of the following: Heisenberg's uncertainty principle or quantum entanglement. In its modern form, the Uncertainty Principle tells that the measurement process itself is a part of physical system, and not a passive process, like it is in classical version of physics. The Uncertainty Principle implies that there exist such properties of particles which are not possible to measure exactly at the same time: measurement of one property will inevitably disturb the measurement of the other. Entanglement, on the other hand is a superposition of two or more particles when their states correlate. Entangled particles cannot be described by the use of states of individual particle. This can be used to exchange information in a way that cannot be seen when experimenting with single particle. Entanglement can be observed independently of how far particles are from one another. Based on these two phenomena, several quantum cryptography protocols were created. In the first method, bits of information are coded based on the polarization of photon and on the use of the Uncertainty Principle to try to prevent the eavesdropper (known as Eve) to steal and decipher the information. The second method uses entangled states of photon, and information is revealed only when the state of a photon is measured by Alice (sender) and Bob (receiver) [2]. The correlation of quantum entanglement can not be explained simply using the concepts of classical physics.

[caption id="attachment_418" align="aligncenter" width="700"]Quantum version of cryptogra- phy is based purely on the laws of quantum physics Quantum version of cryptography is based purely on the laws
of quantum physics [4][/caption]

Examples

[caption id="attachment_419" align="aligncenter" width="494"]Every type of polarization can code one bit of information Every type of polarization can code one bit of information [5][/caption][caption id="attachment_420" align="aligncenter" width="296"]Quantum cryptography systems are safe against "Man-in-the-middle" attacks Quantum cryptography systems are safe against "Man-in-the-middle" attacks [6][/caption]

Scheme of quantum cryptography known as BB84 protocol (Bennet&Brassard, 1984)[3], uses pulses of polarised light. Two types of polarisation are used: linear and circular. Linearly polarised light can be vertically or horizontally polarised, whereas circularly polarised light can be left or right handed. Every type of polarisation can code one bit of information, for example horizontal polarisation := 1, left handed := 1, vertical := 0, right handed := 0. To generate a key, random sequence of vertically (or left handed) and horizontally (or right handed) light is sent through a channel with an equal probability in order to mislead a spy. Simple quantum cryptography protocol can be described as follows: 1. Light source creates light pulses of very low intensity. Then, Alice (sender) modulates polarization of these light pulses in a random order of one to four possible states described above. 2. Bob (receiver) measures polarization of photons received in a randomly selected bases (linear or circular). Here it should be noted that quantum systems are very fragile by their nature. Therefore Bob has only one chance to perform a measurement before a quantum state is destroyed. Investigation of non-destructive quantum state measurement techniques is currently very wide field, and in the future could have huge benefits in quantum cryptography. 3. Bob publicly announces what was the sequence of his bases used for measurements. 4. Alice publicly announces which bases were chosen successfully and are the same as sent by her when modulating light pulses. 5. Alice and Bob disregards results of incorrectly chosen bases. 6. Results are interpreted using binary system: horizontal or left handed polarization corresponds to 1, vertical or right handed polarization corresponds to 0. Entangled pairs scheme uses entangled states of photons. These photons can be generated by Alice, Bob and Eve. However, in any case photons should be distributed in such a way that Alice and Bob have one photon from each pair generated. Ideally correlated states can be created, such that when measuring polarization of correlated states Alice and Bob always get the opposite values. On the other hand, when measuring individually, result is always random: it is not possible to predict what will be the polarization of the next photon. These states have what is known as a non-locality property. Non-locality property does not have an analogue in classical physics. During communication, the results of measurements of states by Alice and Bob will correlate at some level, and if Eve tries to disrupt their connection she will disrupt the correlation, which can be easily detected. In other words quantum cryptography systems are safe against "Man-in-the-middle" attacks. Specifically, a pair of entangled photons has opposite rotational directions or spin states with the total spin of the system being zero. The important implication of this property is that the measurement of spin of one immediately gives the spin of the other. The measurement of any measurable property of a photon disturbs its state. This is the the measurement problem. However, this fact provides the advantage that the presence of an eavesdropper can be detected.

Conclusions

Quantum computing has become a reality. And even though it is still in its infancy, there is already a threat of using classical cryptographic coding schemes because quantum tools could be able to quickly crack almost any code. In order to avoid this, we need new breakthroughs, new cryptography ideas, new tools. Quantum cryptography sounds like a solution. Currently there already exist few companies selling quantum key distribution systems, examples include IDQuantique and MagiQ. This type of technique provides a possibility of extremely safe data transmission, as well as avoiding any influence of third parties because the interference can not be overlooked and "Man-in-the-middle" attacks can be prevented. Seemingly it is fair to say that quantum future will bring us new, safer and more reliable tools for protecting our secrets and all this would be impossible without physics.

References

[1] R. Rivest, A. Shamir, L. Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, Communications of the ACM 21(2), 120-126 (1978), DOI:10.1145/359340.359342.

[2] G. Brassard, C. Crépeau, R. Jozsa, L. Denis, A Quantum Bit Commitment Scheme Provably Unbreakable by both Parties, FOCS IEEE, 362-371 (1993).

[3] https://www.lanl.gov.

[4] http://siliconangle.com/files/2013/08/1.11849.jpg

[5] http://www.fotosimagenes.org/imagenes/criptografia-cuantica-1-thumb.jpg

[6] mindfingers.blogspot.com