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Number Theory and Cryptography

Home/ Number Theory and Cryptography
Course TypeCourse CodeNo. Of Credits
Foundation CoreSUS1MA5154

Semester and Year Offered: VI semester

Course Coordinator and Team: Dr. Ramneek Khassa

Email of course coordinator: ramneek[at]aud[dot]ac[dot]in

Pre-requisites: Mathematics of the 12th level

Aim: The main objective of this course is to prepare students who either wish to pursue Mathematics as career or need to use it from application point of view. Cryptography and Crypto analysis is a field where even non-mathematicians who are familiar with Elementary Number theory have flourished and this course will easily feed in their needs to familiarize them with rudiments of Cryptography.

BRIEF DESCRIPTION OF MODULES/ MAIN MODULES:

  1. Euclidean Algorithm and Applications
  2. Linear Congruences
  3. Factorization methods
  4. Arithmetic Functions
  5. Primitive Roots
  6. Quadratic Reciprocity and Elementary Cryptosystems
  7. Lab work using MATHEMATICA

ASSESSMENT DETAILS WITH WEIGHTS:

ComponentsWeightageSchedule
Class Test10%First week of February
Lab Work assessments25%Throughout semester
Mid semester15%as per AUD academic calendar
End semester35%as per AUD academic calendar
Group Presentations15%early April

Reading List:

MAIN REFERENCES:

  • George E Andrews, Number Theory, Hindustan Publishing House, Indian Edition.
  • David M Burton, Elementary Number Theory (6th Edition), Tata McGraw-Hill Edition, Indian reprint, 2007.
  • Neville Robins, Beginning Number Theory (2nd Edition), Narosa Publishing House Pvt. Ltd., 2007.

ADDITIONAL REFERENCES:

  • Sigmon & Stitzinger, Applications of Abstract Algebra with MAPLE (Kindle Edition), CRC Press, 1999.
  • Zuckerman & Montgomery, An introduction to the Theory of Numbers (5th Edition), Wiley, 1991.