Module MATH30120: Cryptography and Codes

Department: Mathematical Sciences

MATH30120: Cryptography and Codes

Prerequisites

• Prior knowledge of Elementary Number Theory at undergraduate level.

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To give a basic introduction to two topics in data transfer which rely on abstract mathematics: Error correcting Codes which are used widely in data transmission over noisy channels, Cryptography which is widely used in banking, internet browsing, and to ensure privacy on mobile networks.

Content

• Introduction to codes: The Hamming distance, Error detection and correction, equivalence of codes
• Linear Codes, Dual codes and Decoding Methods
• Hamming Codes, Golay Codes,
• Linear Codes over cyclic fields, Cyclic Codes, BCH codes, Reed-Solomon Codes
• Introduction to open-key cryptography, notion of trapdoor function. The factorisation and discrete logarithm problems
• Diffie-Hellman key exchange scheme. RSA cryptosystem
• Elliptic curves over rational numbers and finite fields, Elliptic Curve Diffie-Hellman scheme
• Lenstra factoring algorithm

Learning Outcomes

• By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Cryptography and Codes.
• have an awareness of the abstract concepts of theoretical mathematics in Codes and Cryptography.
• have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas:
• Codes: Linear, Hamming, Cyclic, BCH, Reed-Solomon Codes
• Cryptography: open-key systems
• Elliptic curves, applications in cryptography.

• In addition students will have specialised mathematical skills in the following areas which can be used in minimal guidance: Abstract Reasoning.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University