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MATH 418 Number Theory and Cryptography Units: 3.00
Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Simple cryptographic systems; public key, RSA. Primality and factoring: pseudoprimes, Pollard's rho-method, index calculus. Elliptic curve cryptography.
Learning Hours: 120 (36 Lecture, 84 Private Study)
Requirements: Prerequisite MATH 210/3.0 or (MATH 211/6.0* with permission of the Department).
Offering Faculty: Faculty of Arts and Science
Course Learning Outcomes:
- Design a cryptographic system with given real-world parameters.
- Perform analysis of cryptographic protocols.
- Perform computations and constructions in finite fields.
- Perform probability analysis of primality tests.
- Perform reasoning on elliptic curves.
- Rigorously prove results in number theory.
- Test various designs to determine which performs the best.
- Understand the algebraic structure of a group.