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REVIEW: "Making, Breaking Codes: An Introduction to Cryptology", Paul Garrett

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  • Rob, grandpa of Ryan, Trevor, Devon & Han
    BKMABRCO.RVW 20101128 Making, Breaking Codes: An Introduction to Cryptology , Paul Garrett, 2001, 978-0-13-030369-1 %A Paul Garrett Garrett@math.umn.edu
    Message 1 of 1 , Mar 17 7:30 PM
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      BKMABRCO.RVW 20101128

      "Making, Breaking Codes: An Introduction to Cryptology", Paul Garrett,
      2001, 978-0-13-030369-1
      %A Paul Garrett Garrett@... Paul.Garrett@...
      %C One Lake St., Upper Saddle River, NJ 07458
      %D 2001
      %G 978-0-13-030369-1 0-13-030369-0
      %I Prentice Hall
      %O 800-576-3800 416-293-3621 +1-201-236-7139 fax: +1-201-236-7131
      %O http://www.amazon.com/exec/obidos/ASIN/0130303690/robsladesinterne
      http://www.amazon.co.uk/exec/obidos/ASIN/0130303690/robsladesinte-21
      %O http://www.amazon.ca/exec/obidos/ASIN/0130303690/robsladesin03-20
      %O Audience a- Tech 2 Writing 1 (see revfaq.htm for explanation)
      %P 523 p.
      %T "Making, Breaking Codes: An Introduction to Cryptology"

      The preface states that this book is intended to address modern ideas
      in cryptology, with an emphasis on the mathematics involved,
      particularly number theory. It is seen as a text for a two term
      course, possibly in cryptology, or possibly in number theory itself.
      There is a brief introduction, listing terms related to cryptology and
      some aspects of computing.

      Chapter one describes simple substitution ciphers and the one time
      pad. The relevance to the process of the sections dealing with
      mathematics is not fully explained (and neither is the affine cipher).
      Probability is introduced in chapter two, and there is some discussion
      of the statistics of the English language, and letter frequency
      attacks on simple ciphers. This simple frequency attack is extended
      to substitution ciphers with permuted (or scrambled, but still
      monoalphabetic) ciphers, in chapter three. There is also mention of
      basic character permutation ciphers and multiple anagramming attacks.
      Chapter four looks at polyalphabetic ciphers and attacks on expected
      patterns. More probability theory is added in chapter five.

      Chapter six turns to modern symmetric ciphers, providing details of
      the DES (Data Encryption Standard) as examples of the principles of
      confusion, diffusion, and avalanche. Divisibility is important not
      only to the RSA (Rivest-Shamir-Adlemen) algorithm, but, in modular
      arithmetic, to modern cryptography as a whole, and so gets extensive
      treatment in chapter seven. The Hill cipher is used, in chapter
      eight, to demonstrate that simple diffusion is not sufficient
      protection. Complexity theory is examined, in chapter nine, with a
      view to determining the work factor (and sometimes practicality) of a
      given cryptographic algorithm.

      Chapter ten turns to public-key, or asymmetric, algorithms, detailing
      aspects of the RSA and Diffie-Hellman algorithms, along with a number
      of others. Prime numbers (important to RSA) and their characteristics
      are examined in chapter eleven, and roots in twelve and thirteen.
      Multiplicativity, and its weak form, are addressed in fourteen, and
      quadratic reciprocity (for quick primality estimates) in fifteen.
      Chapter sixteen notes pseudoprimes, which can complicate the search
      for keys. Basic group theory, covered in chapter seventeen, relates
      to Diffie-Hellman and a variety of other algorithms. Diffie-Hellman,
      along with some abstract algorithms, is reviewed in chapter eighteen.
      Rings and fields (in groups) are noted in chapter nineteen, and
      cyclotomic polynomials in twenty.

      Chapter twenty-one examines a few pseudo-random number generation
      algorithms. More group theory is presented in twenty-two. Chapter
      twenty-three looks at proofs of pseudoprimality. Factorization
      attacks are addressed in basic (chapter twenty-four), and more
      sophisticated forms (twenty-five). Finite fields are addressed in
      chapter twenty-six and discrete logarithms in twenty-seven. Some
      aspects of elliptic curves are reviewed in chapter twenty-eight. More
      material on finite fields is presented in chapter twenty-nine.

      Despite the title, this is a math textbook. You will need to have, at
      the very least, a solid introduction to number theory to get the
      benefit from it. Even at that, the application, and implications, of
      the mathematical material to cryptology is difficult to follow. The
      organization probably also works best in a math course: it certainly
      seems to skip around in a disjointed manner when trying to follow the
      crypto thread, and apply the math to it. For all its faults, "Applied
      Cryptography" (cf. BKAPCRYP.RVW) is still far superior in explaining
      what the math actually does.

      copyright, Robert M. Slade 2010 BKMABRCO.RVW 20101128


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