MTH3137 · Number theory and cryptography (Advanced)

Overview

Prime numbers; Euclidean algorithm; congruences; the Euler totient function; the theorems of Fermat, Euler and Wilson; RSA public key cryptosystem; Chinese remainder theorem; quadratic reciprocity; primitive roots; factorisation and primality testing algorithms; secure key exchange; elliptic curve cryptography.

Areas of study: Mathematics Pure mathematics Applied mathematics Statistics Computer Science (pending FIT approval)

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Apply the classification of numbers and analyse their relationships, such as divisibility and primality;
2. Illustrate the power of pure mathematics and appreciate its beauty;
3. Demonstrate a deep understanding of the fundamental concepts of number theory;
4. Develop proofs involving number theoretic insights and techniques;
5. Demonstrate advanced problem solving and theorem proving skills;
6. Explain how thousands of years of pure mathematical developments have enabled secure electronic communication and commerce;
7. Analyse fundamental number theoretic algorithms for a range of tasks including exchanging information securely and testing whether numbers are prime.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week

Student experience, not official rules. Nothing here changes what the Handbook says.