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

Online courses

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.

See also

• International Mathematical Olympiad

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