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Unit of study_

MATH2088: Number Theory and Cryptography

Cryptography is the branch of mathematics that provides the techniques for confidential exchange of information sent via possibly insecure channels. This unit introduces the tools from elementary number theory that are needed to understand the mathematics underlying the most commonly used modern public key cryptosystems. Topics include the Euclidean Algorithm, Fermat's Little Theorem, the Chinese Remainder Theorem, Mobius Inversion, the RSA Cryptosystem, the Elgamal Cryptosystem and the Diffie-Hellman Protocol. Issues of computational complexity are also discussed.

Code MATH2088
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
MATH1002 or MATH1902 or MATH1004 or MATH1904 or MATH1064 or (a mark of 65 or above in MATH1014)
MATH2068 or MATH2988

At the completion of this unit, you should be able to:

  • LO1. understand and use the basic terminology of number theory and cryptography
  • LO2. carry out simple number-theoretic computations either with a calculator or using MAGMA
  • LO3. apply standard number-theoretic algorithms
  • LO4. understand and use some classical and number-theoretic cryptosystems
  • LO5. apply standard methods to attack some classical cryptosystems
  • LO6. understand the theory underlying number-theoretic algorithms and cryptosystems, including the general properties of primes, prime factorisation, modular arithmetic, divisors and multiplicative functions, powers and discrete logarithms.