Number Theory & RSA Cryptography by Pascal Cardin

Number Theory & RSA Cryptography

By Pascal Cardin

  • Release Date: 2013-02-13
  • Genre: Mathematics
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Description

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). A STUDENT VERSION is available on the iTunes Store (without details of solutions for the exercises, but with some guidance and answers). 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).

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