**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