MATH3401: CRYPTOGRAPHY AND CODES III

• Elementary Number Theory II (MATH2617)

• None.

• Codes and Cryptography (COMPNEW3X41).

• 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.

• 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

Subject-specific Knowledge:

• 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.

Subject-specific Skills:

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

Key Skills:

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

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

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