Quantum

1. Name: K. Vidya Madhuri Roll no: 14311A1201 3-2, IT-A

2.  Introduction  Traditional vs Quantum Cryptography  How Quantum Cryptography works  Applications of Quantum Cryptography  Limitations

3. What is Cryptography?  Cryptography is the art of devising codes and ciphers.  Crypto analysis is the art of breaking them.  Cryptology is the combination of the two i.e Cryptography and Crypto analysis

4. What is Quantum Cryptography?  Quantum Cryptography is an effort to allow two users of a common communication channel to create a body of shared and secret information. This information, which generally takes the form of a random string of bits, can then be used as a conventional secret key for secure communication.  The Heisenberg Uncertainty principle and quantum entanglement can be exploited in as system of secure communication often referred to as “quantum Cryptography”.

6. Stephen Wiesner wrote “Conjugate Coding” in the late sixties Charles H. Bennett and Gilles Brassard revived the field in 1982 by combining quantum process with public key cryptography

7.  Traditional cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed aroundcomputational hardness assumptions, making such algorithms hard to break in practice by any adversary.  Quantum cryptographyis the science of exploiting quantummechanical properties to performcryptographictasks.

8.  The main practical problem with secret key encryption (traditional cryptographic technique) is exchanging a secret key. In principle any two users who wished to communicate could first meet to agree on a key in advance, but in practice this could be inconvenient.  Public key cryptography (PKC) systems exploit the fact that certain mathematical operations are easier to do in one direction than the other. The systems avoid the key distribution problem, but unfortunately their security depends on unproven mathematical assumptions about the intrinsic difficulty of certain operations.

9.  The most popular public key cryptosystem, RSA (Rivest- shamir-Adleman), gets its security from the difficulty of factoring large numbers. This means that if ever mathematicians or computer scientists come up with fast and clever procedures for factoring large numbers, then the whole privacy and discretion of widespread cryptosystems could vanish overnight.

10.  Quantum cryptography takes advantage of the unique and unusual behavior of microscopic objects to enable users to securely develop secret keys as well as to detect eavesdropping.  Quantum cryptography solves the problems of secret-key cryptography by providing a way for two users who are in different locations to securely establish a secret key and to detect if eavesdropping has occurred.

11.  The most important unit of information in computer science is the bit. There are two possible values that can be stored by a bit: the bit is either equal to “0” or equal to “1.”  Quantum system with at least two states can serve as a qubit. For example, the spin of an Atom or the polarization of a light particle can represent the state of a qubit.

12. Heisenberg’s Uncertainty Principle:  It is possible to encode information into quantum properties of a photon in such a way that any effort to monitor them disturbs them in some detectable way. This statement is known as the Heisenberg uncertainty principle. Quantum Entanglement:  The entangled particles cannot be described by specifying the states of individual particles and they may together share information in a form which cannot be accessed in any experiment performed on either of the particles alone.

13.  The foundation of quantum cryptography lies in the Heisenberg uncertainty principle, which states that certain pairs of physical properties are related in such a way that measuring one property prevents the observer from simultaneously knowing the value of the other.  In particular, when measuring the polarization of a photon, the choice of what direction to measure affects all subsequent measurements.

14. Polarization of Photons

15.  A pair of orthogonal (perpendicular) polarization states used to describe the polarization of photons, such as horizontal/vertical, is referred to as a basis.  A pair of bases are said to be conjugate bases if the measurement of the polarization in the first basis completely randomizes the measurement in the second basis. It is a fundamental consequence of the Heisenberg uncertainty principle that such conjugate pairs of states must exist for a quantum system.

17. Alice sends a sequence of photons to Bob. Each photon in a state with polarization corresponding to 1 or 0, but with randomly chosen basis. Bob measures the state of the photons he receives, with each state measured with respect to randomly chosen basis. Alice and Bob communicates via an open channel. For each photon, they reveal which basis was used for encoding and decoding respectively. All photons which has been encoded and decoded with the same basis are kept, while all those where the basis don't agree are discarded.   

18.  If the sender Alice, uses a filter in the 0-deg/90-deg basis to give the photon an initial polarization (either horizontal or vertical, but she doesn't reveal which), the receiver Bob can determine this by using a filter aligned to the same basis.  However if Bob uses a filter in the 45-deg/135-deg basis to measure the photon, he cannot determine any information about the initial polarization of the photon .  If an eavesdropper Eve uses a filter aligned with Alice's filter, she can recover the original polarization of the photon. But if she uses a misaligned filter she will not only receive no information, but will have influenced the original photon so that she is unable to reliably retransmit one with the original polarization. Bob will either receive no message or a garbled one, and in either case will be able to deduce Eve's presence.

19.  Switzerland has been using quantum cryptography to conduct secure online voting in federal and regional elections.  Secure communications with satellites and astronauts is an increasing concern, and a company called QuintessenceLabs is working on a project for NASA that will ensure secure communications from Earth with satellites and astronauts, using quantum cryptography.  With “Quantum encrypted” internet, our most sensitive transmissions would be passed along in an ultra-secure manner. This would achieve the ideal of a simultaneously fast and secure internet.

20.  The maximum distance covered by a message using quantum cryptography is 150km, which is very short.  When one photon was measured in one polarization, its entangled counterpart took the opposite polarization, meaning the polarization the other photon would take could be predicted.  Exchanging information using single photon needs a dedicated channel of high quality in order to achieve high speed communication. It is impossible to send keys to two or more different locations using a quantum channel as multiplexing is against quantum principles.