School of Mathematics
Course 374 - Cryptography & Information Theory 1998-99 (JS & SS Mathematics )
Lecturer: Michael Purser & Timothy Murphy
Requirements/prerequisites:

Duration: 21 weeks

Number of lectures per week: 3

Assessment: Cryptography will account for 60% of the overall mark; Information Theory for 40%. Cryptography will be marked entirely by Exam. There may be a Project element in Information Theory.

End-of-year Examination: One 3-hour examination

Description:

This course is in 2 independent parts: Cryptography, given by Dr Purser; and Information Theory, given by Dr Murphy.

Dr Pursers's part of the course will be marked by Examination; Dr Murphy's part will also be marked by Examination, with a possible contribution by Project.

Dr Purser's part of the course will start in November.

## 1  Cryptography

This course discusses cryptography with particular reference to computer networks.

Topics (not necessarily in order of appearance):

• Introduction-Confidentiality and Authenticity
• Shannon's Theory
• Block Encryptors and Stream Encryptors
• ECB, CBC, CFB modes
• Integrity checks
• MDC's and MAC's
• Identification, Authentication and Authorisation
• Access control procedures: 1-way, 2-way
• Public (Asymmetric) Key Crytpology vs Private (Symmetric) Key Cryptology
• Non-repudiation
• 3-way access control
• Digital signatures
• Diffie-Hellman Key Exchange
• Some algorithms

• Vigénère, Vernam
• Enigma
• DES
• A stream encryptor based on maximum length sequences
• RSA
• IDEA
• FIAT/SHAMIR
• Hashing algorithms

• Relevant Mathematics

• Generating Primes
• Testing Primes
• Factorising
• Random Numbers
• Discrete Logarithms

• Cryptanalysis

• Statistical Analyses
• Brute force
• Differential Cryptanalysis

• Key Management

• Key Distribution
• Certification
• Sharing Keys
• PINs
• Chipcards

## 2  Information Theory

This course will cover Algorithmic Information Theory, a subject which marries Shannon's original Statistical Information Theory to the concepts of computability and Turing machines.

According to Algorithmic Information Theory, the informational content, or entropy, of a string may be measured by the minimum length to which the string can be compressed.

Notes for the course are available on the Maths Unix System in very"/usr/local/pub/AlgorithmicInformationTheory". Read README before printing them out.

Jun 10, 1998