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MTHE 418  Number Theory & 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.
NOT OFFERED 2024-2025.
(Lec: 3, Lab: 0, Tut: 0)
Requirements: Prerequisites: MTHE 217 (MATH 217) or MATH 210 or MATH 211 with permission of the instructor Corequisites: Exclusions:   
Offering Term: W  
CEAB Units:    
Mathematics 18  
Natural Sciences 0  
Complementary Studies 0  
Engineering Science 9  
Engineering Design 9  
Offering Faculty: Faculty of Arts and Science  

Course Learning Outcomes:

  1. Computations and constructions in finite fields.
  2. Reasoning on elliptic curves.
  3. Understanding of the algebraic structure of a group.
  4. Rigorously proving results in number theory.
  5. Probability analysis of primality tests.
  6. Analysis of cryptographic protocols.
  7. Designing a cryptographic system with given real-world parameters.
  8. Testing various designs to determine which performs the best.