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Quantum Cryptography and Quantum Computation

Quantum Cryptography uses the principles of Quantum Mechanics to implement a cryptographic system. The key problem which is solved by using quantum techniques is that of eavesdropping detection. Conventional secret-key cryptography techniques require the communication of a secret key prior to message exchange.

Quantum principles can be used to detect eavesdropping probabilistically when it occurs. The bits are represented as qubits, physically modelled by photons, and communicated over a quantum channel. The polarization states of photons represent 0’s and 1’s.

We give a brief overview of the mathematical techniques employed to model the behavior of quantum particles, and also those behind the working of quantum algorithms on quantum computers.

We examine a few Quantum Cryptography protocols ([BB84], [?], [Ekert94]) to learn about how Quantum Cryptography can be used to implement a secure system for communication. We also explore two quantum algorithms for searching in O(pn) time [Lovk96] and prime-factoring in O(log3 n) time [Shor97] which give a running time drastically lower than conventional algorithms. To analyze these, a model of a quantum computer is required. We use the one given by Vazirani et al. [BV93] which de nes a Quantum Turing Machine and suggests how to implement simple computations on it.

We also examine the latest technologies and research, and the issues regarding feasibility of quantum algorithms and cryptography.
Source: Indian Institute of Technology
Authors: Hidayath Ansari, Aditya Parameswaran, Lakulish Antani, Bhaskara Aditya, Ankur Taly and Luv Kumar

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