Cryptography

This page contains resources about Cryptography and Number Theory in general.

Subfields and Concepts

 * Modular Arithmetic
 * Lowest Common Multiple (LCM)
 * Greatest Common Divisor (GCD)
 * Prime Factorization
 * Euclidean Algorithm
 * Extended Euclidean Algorithm
 * Chinese Remainder Theorem
 * Diophantine Equations
 * Euler's Theorem
 * Fermat's Little Theorem
 * Wilson's Theorem
 * Fermat's Method of Infinite Descent
 * Cryptography Algorithms
 * Asymmetric (public key) Encryption
 * Symmetric (secret key) Encryption
 * Cryptographic Hash Functions
 * Cryptology
 * RSA Algorithm

Lecture Notes

 * Secrets and Promises: An Introduction to Digital Security
 * Modern Cryptology
 * Theory of numbers by Abhinav Kumar

Books

 * Zhou, X. (2017). Number Theory - Modular Arithmetic: Math for Gifted Students. CreateSpace.
 * Αντωνιάδης, Α. Γ., & Αριστείδης, Κ. (2015). Θεωρία Αριθµών και Εφαρµογές. Σύνδεσµος Ελληνικών Ακαδηµαϊκών Βιβλιοθηκών. [in Greek] (link)
 * Burton, D. M. (2010). Elementary Number Theory. 7th Ed. McGraw-Hill Education.
 * Hong-Bing, Y. (2009). Problems of Number Theory in Mathematical Competitions (Volume 2). World Scientific.
 * Andreescu, T., & Andrica, D. (2009). Number Theory: Structures, Examples, and Problems. Birkhäuser.
 * Crawford, M. (2008). Introduction to Number Theory. 2nd Ed. AoPS Incorporated.
 * Andreescu, T., Andrica, D., & Feng, Z. (2007). 104 number theory problems: From the training of the USA IMO team. Birkhäuser.
 * Stopple, J. (2003). A primer of analytic number theory: from Pythagoras to Riemann. Cambridge University Press.
 * Adler, A., & Coury, J. E. (1995). Theory of Numbers: A Text and Source Book of Problems. Jones & Bartlett Pub.
 * Niven, I., Zuckerman, H. S., & Montgomery, H. L. (1991). An Introduction to the Theory of Numbers. 5th Ed. Wiley.
 * Hardy, G. H., & Wright, E. M. (1980). An Introduction to the Theory of Numbers. Oxford University Press.
 * Sierpinski, W. (1970). 250 problems in elementary number theory. Elsevier.

Other Resources

 * Computer Security and Cryptography - Google Scholar Metrics (Top Publications)
 * Discrete Mathematics - Google Scholar Metrics (Top Publications)
 * Number Theory - AoPS
 * Number Theory Problems - AoPS
 * Number Theory - Brilliant
 * Problems in Elementary Number Theory
 * 250 Problems in Elementary Number Theory - book
 * Number Theory (AoPS) - Notes