The mathematics of ciphers:
number theory and RSA cryptography

capaThis is an introduction to number theory and its applications to cryptography. The aim of the book is to explain in detail how the public key cryptosystem known as RSA works. The system was invented in 1977 by Rivest, Shamir and Adleman--hence RSA--and it is one of the most successful of the public key cryptosystem now in use in commercial applications. Althouth this is the aim of the book, we do not follow a straight path to this end. Instead we stroll about the landscape, never forgetting our aim, but stopping to explore whatever reachs are available on the way. Thus the book includes a chapter on group theory, and it is pepered with historical notes that range from biographical facts on famous mathematicians to little anecdotes.
The mathematics behind most of the books subject is, naturally enough, number theory. Most of the traditional topics of a beginners course on number theory are to be found here. Thus there are chapters on the Euclidean algorithm, factorization of integers, primes, modular arithmetic, Fermat's little theorem, the Chinese remainder theorem and Mersenne and fermat numbers. However we follow na algorithmic approach, so that the proofs the theorems are, whenever possible, of a constructive nature.  The book is published by AK Peters.

  •  Fundamental algorithms (division and Euclidean algorithms)
  •  Unique factorization
  •  Prime numbers
  •  Modular arithmetic
  •  Induction and Fermat
  •  Pseudoprimes
  •  Systems of congruences
  •  Groups
  •  Mersenne and Fermat
  •  Primality tests and primitive roots
  •  The RSA cryptosystem