Classical Cryptography

Working on the usual assumptions of classical cryptography, one would have thought that there is no such thing as a digital signature scheme Classical cryptographic schemes assume that a sender and a recipient have a common secret, which is unknown to outsiders from whom the sender and the recipient want to protect themselves. 

With privately used schemes, this secret may be the whole algorithm used. However, it was soon discovered that if a scheme is intended for widespread use, or to be carried out by machines, one cannot hope to keep the structure of the algorithm or the construction of the machines secret for a long time. Thus one divides the schemes intd algorithms, which may be public, and certain parameters, called keys, which have to remain secret. (See, e.g., [DiHe76] for a brief sketch after [Kahn67].) 

Nowadays, making algorithms public is not merely seen as unavoidable, but even as desirable The security will be evaluated more thoroughly if the whole (scientific) public is invited to do so. Often, even a financial incentive is offered. Furthermore, if a scheme is not to be used solely by its inventor, some supervision 

in classical cryptographic schemes, each pair or group of mutually trusting participants has a common secret key, and all the otiier information is public the schemes are therefore automatically symmetric. 

Primarily, secrecy schemes were considered, and no formal notion of security existed. Some even thought it impossible that such a notion could exist, the more so because several schemes had been broken for whose security mathematical arguments had been given. However, these arguments had only referred to some aspects of security, e.g., how many keys were possible (see, e.g., [DiHe76]). 

---

For references on classical cryptography see, e.g., D. R. Stinson, Cryptography Theory and Practice, CRC Press, Boca Raton, FL, 1995. 

In this equation, C andT refer to control and target qubits, respectively. The resulting state (output of the qugate) is said to be an entangled state of the two qubits, that is, a state that cannot be written as a product of states for each qubit [30]. The occurrence of such entangled states is another characteristic trait of QC, at the basis of secure quantum communication or cryptography. It also implies that, as opposed to what happens with a classical bit, an arbitrary quantum bit cannot be copied (the COPY classical operation is, in fact, based on the application of a succession of classical CNOT gates) [4]. 

Secret key cryptography is the classical form of cryptography. Two candidates A and B that want to share secure information use the same key for encryption and decryption, which requires prior communication between A and B over a secure channel. 

The second algorithm is the Shor algorithm, ° which demonstrates that a quantum computer could factorise very large numbers into primes much more quickly than a classical computer. This immediately becomes important because modern cryptography is dependent on the fact that classical computers are very good at multiplying many primes together to... 

In contrast to classical cryptographic methods, the security of quantum cryptography is based on the fundamental laws of physics. It is guaranteed by the Heisenberg uncertainty principle and is independent of any mathematical or technological developments. 

The quantized nature of the field and its fundamental interaction with atoms lead to many further interesting non-classical phenomena, which are treated in a field generally referred to as quantum optics [4.20- -4.28]. The field also comprises emerging practical applications such as quantum computing and quantum cryptography. 

---