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Protecting information: from classical error correction to quantum cryptography
Contents
1. Cryptography: an overview
1.1 Elementaru ciphers
1.2 Enigma
1.3 A review of modular arithmetic and Zn
1.4 The hill cipher
1.5 Attscks on the hill cipher
1.6 Feistel cipher and DES
1.7 A word about AES
1.8 Diffie-hellman public key exchange
1.9 RSA
1.10 Public key exchanges with a group
1.11 Public key exchange using elliptic curve
2. Quantum mechanics
2.1 Photo polarization
2.2 General quantum variable
2.3 Composite systems
2.4 Measuring a subsystem
2.5 Other incompele measurements
3. Quantum cryptography
3.1 The Bennett-brassard protocol
3.2 The no-cloning theorem
3.3 Quantum teleportation
4. An introduction to error- correcting codes
4.1 A few binary examples
4.2 Preliminaries and more examples
4.3 Hamming distance
4.4 Linear codes
4.5 Generator matrices
4.6 Dual codes
4.7 Syndrome decoding
4.8 The hat problem
5. Quantum cryptography revisited
5.1 Error correction for quantum key distribution
5.2 Introduction to privacy amplification
6. Generalized reed-solomon codes
6.1 Definitions and examples
6.2 A finite field with eight elements
6.3 General theorems
6.4 A generator matrix for a GRS code
6.5 The dual of a GRS code
7. Quantum computing
7.1 Introduction
7.2 Quantum gates
7.3 The deutsch algorithm
7.4 A universal set of quantum gates
7.5 Number theory for shor’s algorithm
7.6 Finding the period of f (x)
7.7 Estimating the probability of success
7.8 Efficiency of factoring
7.9 Introduction to quantum error correction
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