On the Underlying Mathematical and Quantum Structure of Quantum Cryptography

Quantum cryptography is a novel approach to provide secure communication, based on the laws of physics. It offers perfect security for the communication between two authorized parties, while assuming very high computational capacity for the eavesdropper, who may be attempting to intrude into this communication. It provides a very high rate of intrusion detection as against the classical systems. Classical cryptography is built on a fundamental assumption that it is difficult to invert some of mathematical functions, in a limited time, with the use of efficient computing resources. While, quantum cryptography is based on formidable laws of nature, making it less prone to attack. With the advent of quantum computing, boundaries between various subjects like quantum physics, computer science and mathematics are getting reduced. In the early seventies, Steven Wiesner made pioneering efforts in the field Quantum Cryptography. In its present form, Quantum Cryptography depends on two essential principles of Quantum Mechanics. One is that no information is available without causing disturbance in the system and other is Principle of No-Cloning. In this paper we present some of fundamental aspects of Quantum Cryptography and the underlying structures that makes it a credible option for providing perfect security of information.