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MA30364: Number theory and cryptography

[Page last updated: 22 May 2025]

Academic Year: 2025/26
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Honours (FHEQ level 6)
Period:
Semester 1
Assessment Summary: EXCB 100%
Assessment Detail:
  • MA32064 Closed-book written examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA12004 OR take MA12011 OR take MA12013 OR take MA10210
In taking this module you cannot take MA40238
Learning Outcomes: By the end of this unit, you will be able to: 芒锟铰olve problems involving elementary number theory. 芒锟铰emonstrate understanding in a range of more advanced topics in number theory.


Synopsis: Number theory concerns the study of the whole numbers and is one of the oldest areas of mathematics. It is a subject that can trace its history back to antiquity and has in modern times found spectacular applications to coding theory and cryptography. You will cover some of the great topics in elementary number theory and explore some of its applications.

Content: Elementary number theory, congruences, Chinese Remainder Theorem, Euler phi function, Mobius inversion, prime number theory, perfect numbers, Mersenne primes, Fermat primes, Carmichael numbers, RSA cryptography, Diffie-Hellman key exchange, discrete logarithm problem, quadratic residues, The quadratic reciprocity theorem. Further topics to be taken from: continued fractions, Diophantine equations, quadratic forms, Cryptography, and error correcting codes.

Course availability:

MA30364 is Optional on the following courses:

Department of Mathematical Sciences
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
Department of Physics
  • USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 4)
  • USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 5)
  • USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
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