Number Theory & RSA Cryptography

This ebook presents the basics of the theory of numbers, so that the reader is able to understand the RSA cryptography algorithm.


This full version of the book contains many widgets (30) including an interactive modular calculator for RSA, detailed solutions exercises (widgets Keynote) and messages cypher / decypher (RSA 128 - 2048 bits). 


This book is not aimed only at students or high school teachers, but also to anyone interested in discovering the fascination of primes and understand RSA cryptography. Bases in algebra are welcome but not required. 


Properties of the relation of divisibility
  
Fundamental theorem of arithmetic (integer factorization)
  
Theorem of Euclid
  
Fundamental theorem of primes (without proof)
  
Congruences and properties
  
Modular Arithmetic
  
Javascript / HTML Editor ( link on math4pad.net )
Euclidean algorithm
Theorem GCD
Gauss Lemma
Uniqueness of the integer factorization
Modular Algebra
Chinese Remainder Theorem
Problem of Chinese cook
Euler's totient function and properties
Graph of phi(n) for n max : 50, 100, 500, 1000, 5000 and 10'000
Euler’s Theorem
Fermat’s Little theorem
A primality test
RSA Theorem (many examples)
Authentication, integrity, confidentiality, non-repudiation of data
Indicator function of Carmichael (without proof)



A final section discusses the concept of certification authority, the RSA key generation and the history of RSA (past, present and future).