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- Rob Slade, doting grandpa of R

March 18, 2011, 1:27 am

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

2001, 978-0-13-030369-1

%A Paul Garrett Garrett@math.umn.edu Paul.Garrett@acm.org

%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 (Amazon.com product link shortened)

(Amazon.com product link shortened)

%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

======================

rslade@vcn.bc.ca slade@victoria.tc.ca rslade@computercrime.org

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