A Course in Number Theory and Cryptography
Neal Koblitz
A Course in Number Theory and Cryptography - A book resource
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Quadratic Residues
Brilliant.org
Interactive lessons on quadratic residues
Art of Problem Solving Wiki
Detailed article on quadratic residues with examples
Number Theory
Learn about quadratic residues with this number theory course from Andrew Sutherland at MIT. Explore fundamental concepts!
mathworld.wolfram.com
MathWorld is Wolfram’s comprehensive online mathematics encyclopedia featuring concise articles that explain concepts, provide definitions, theorems, proofs, and examples. It covers topics across math, including number theory concepts like quadratic residues, with formulas and references for deeper study.
ocw.mit.edu
MIT OpenCourseWare (OCW) provides free, openly accessible course materials from MIT, including lecture notes, assignments, exams, and videos, across hundreds of disciplines. The site lets you browse courses by topic or department and download resources for self-paced study.
Number Theory and Cryptography
A prominent expert in the number theory Godfrey Hardy described it in the beginning of 20th century as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the world nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this course we will start with the basics of the number theory and get to cryptographic protocols based on it. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest! As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.