CHAPTER 15 Quantum cryptography.ppt

Quantum cryptography CHAPTER 15: Quantum cryptography An important new feature of quantum cryptography is that security of cryptographic protocols generation is based on the laws of nature and not on the unproven assumptions of computational complexity theory. Quantum cryptography is the first area in which quantum physics laws are directly exploited to bring an essential advantage in information processing. Three main outcomes so far · It has been proven that unconditionally secure quantum generation of classical secret and shared keys is possible (in the sense that any eavesdropping is detectable). · Unconditionally secure basic quantum cryptographic protocols, such as bit commitment and oblivious transfer, are impossible. · Quantum cryptography is already in advanced experimental stage. Before presenting basic schemes of quantum cryptography basic ideas of quantum information processing will be discussed shortly. Classical versus quantum computing The essense of the difference between classical computers and quantum computers is in the way information is stored and processed. In classical computers, information is represented on macroscopic level by bits, which can take one of the two values 0 or 1 In quantum computers, information is represented on microscopic level using qubits, (quantum bits) which can take on any from the following uncountable many values | 0 ń + b | 1 ń where a, b are arbitrary complex numbers such that | a | 2 + | b | 2 = 1. CLASSICAL EXPERIMENTS Figure 1: Experiment with bullets Figure 2: Experiments with waves QUANTUM EXPERIMENTS Figure 3: Two-slit experiment Figure 4: Two-slit experiment with an observation THREE BASIC PRINCIPLES P1 To each transfer from a quantum state f to a state y a complex number á y | f ń is associated. This number is called the probability amplitude of the transfer and |á y | f ń| 2 is then the probability of the transfer. QUANTUM SYSTEMS = HILBERT SPACE Hilbert