Quantum cryptography

Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed (no-cloning theorem). This could be used to detect eavesdropping in quantum key distribution. Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed (no-cloning theorem). This could be used to detect eavesdropping in quantum key distribution. Quantum cryptography attributes its beginning by the work of Stephen Wiesner and Gilles Brassard. Wiesner, then at Columbia University in New York, who, in the early 1970s, introduced the concept of quantum conjugate coding. His seminal paper titled 'Conjugate Coding' was rejected by the IEEE Information Theory Society, but was eventually published in 1983 in SIGACT News. In this paper he showed how to store or transmit two messages by encoding them in two 'conjugate observables', such as linear and circular polarization of photons, so that either, but not both, of which may be received and decoded. It wasn’t until Charles H. Bennett, of the IBM's Thomas J. Watson Research Center and Gilles Brassard met at the 20th IEEE Symposium held in Puerto Rico that they discovered how to incorporate the findings of Weisner. 'The main breakthrough came when we realized that photons were never meant to store information, but rather to transmit it' In 1984, building upon this work Bennett and Brassard proposed a method for secure communication, which is now called BB84. In 1991 Artur Ekert developed a different approach to quantum key distribution based on peculiar quantum correlations known as quantum entanglement. Random rotations of the polarization by both parties have been proposed in Kak's three-stage protocol. In principle, this method can be used for continuous, unbreakable encryption of data if single photons are used. The basic polarization rotation scheme has been implemented. This represents a method of purely quantum-based cryptography as against quantum key distribution where the actual encryption is classical. The BB84 method is at the basis of quantum key distribution methods. Companies that manufacture quantum cryptography systems include MagiQ Technologies, Inc. (Boston, Massachusetts, United States), ID Quantique (Geneva, Switzerland), QuintessenceLabs (Canberra, Australia) and SeQureNet (Paris, France). The most well known and developed application of quantum cryptography is quantum key distribution (QKD), which is the process of using quantum communication to establish a shared key between two parties (Alice and Bob, for example) without a third party (Eve) learning anything about that key, even if Eve can eavesdrop on all communication between Alice and Bob. If Eve tries to learn information about the key being established, discrepancies will arise causing Alice and Bob to notice. Once the key is established, it is then typically used for encrypted communication using classical techniques. For instance, the exchanged key could be used for symmetric cryptography. The security of quantum key distribution can be proven mathematically without imposing any restrictions on the abilities of an eavesdropper, something not possible with classical key distribution. This is usually described as 'unconditional security', although there are some minimal assumptions required, including that the laws of quantum mechanics apply and that Alice and Bob are able to authenticate each other, i.e. Eve should not be able to impersonate Alice or Bob as otherwise a man-in-the-middle attack would be possible. While quantum key distribution is seemingly secure, its applications face the challenge of practicality. This is due to transmission distance and key generation rate limitations. Ongoing studies and growing technology has allowed further advancements in such limitations. In 2018 Lucamarini et. al. proposed a scheme that can possibly overcome the 'rate-distance limit'. The Twin-Field Quantum Key Distribution Scheme suggests that optimal key rates are achievable on '550 kilometers of standard optical fibre', which is already commonly used in communications today. In mistrustful cryptography the participating parties do not trust each other. For example, Alice and Bob collaborate to perform some computation where both parties enter some private inputs. But Alice does not trust Bob and Bob does not trust Alice. Thus, a secure implementation of a cryptographic task requires that after completing the computation, Alice can be guaranteed that Bob has not cheated and Bob can be guaranteed that Alice has not cheated either. Examples of tasks in mistrustful cryptography are commitment schemes and secure computations, the latter including the further examples of coin flipping and oblivious transfer. Key distribution does not belong to the area of mistrustful cryptography. Mistrustful quantum cryptography studies the area of mistrustful cryptography using quantum systems. In contrast to quantum key distribution where unconditional security can be achieved based only on the laws of quantum physics, in the case of various tasks in mistrustful cryptography there are no-go theorems showing that it is impossible to achieve unconditionally secure protocols based only on the laws of quantum physics. However, some of these tasks can be implemented with unconditional security if the protocols not only exploit quantum mechanics but also special relativity. For example, unconditionally secure quantum bit commitment was shown impossible by Mayers and by Lo and Chau. Unconditionally secure ideal quantum coin flipping was shown impossible by Lo and Chau. Moreover, Lo showed that there cannot be unconditionally secure quantum protocols for one-out-of-two oblivious transfer and other secure two-party computations. However, unconditionally secure relativistic protocols for coin flipping and bit-commitment have been shown by Kent.