This book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.
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Text: English (translation)
Original Language: Portugese
Original Language: Portugese
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Most Helpful Customer Reviews
30 of 33 people found the following review helpful:
5.0 out of 5 stars
Excellent introduction,
By A Customer
This review is from: The Mathematics of Ciphers: Number Theory and RSA Cryptography (Hardcover)
This book is a very readable introduction to the theory of numbers. The author manages to concentrate in a relatively short book and with a very clear and pleasant style the material necessary to understand the mathematics underneath the RSA cryptosystem. No previous knowledge of advanced mathematics is assumed. Perhaps not enough for mathematicians, but more than rewarding for the rest of us. It reminds me a bit of the style of M. Gardner. Books on mathematics can be very dull without the style of exposition of Mr. Coutinho. Highly recommended !
3 of 3 people found the following review helpful:
4.0 out of 5 stars
all about understanding RSA,
By
This review is from: The Mathematics of Ciphers: Number Theory and RSA Cryptography (Hardcover)
The book revolves around RSA. The motivation for the book is that the reader wants to understand public/private key cryptography, where this is represented by the seminal RSA algorithm.
The author assumes little previous acquaintance with number theory on your part. He develops his arguments from this minimal background. So modular arithmetic is introduced, and thence such key ideas as groups, primality tests, Chinese Remainder Theorem and, finally, the RSA cryptosystem. Each chapter has a problem set of moderate difficulty. A maths undergraduate at the sophomore level or higher should be able to benefit from the book.
1 of 1 people found the following review helpful:
4.0 out of 5 stars
Good introduction to RSA,
This review is from: The Mathematics of Ciphers: Number Theory and RSA Cryptography (Hardcover)
I've used this book for teaching the basic theory of RSA cryptography. However, some knowledge of number theory is required in order to get full benefit of the text and exercises. I found "Number Theory and Its History," by Oystein Ore, to be an excellent complement to this text.
(Note that there are a few typographical errors in the exercises, but these are easily spotted.)
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Inside This Book
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First Sentence:
There are two fundamental algorithms: the division algorithm and the Euclidean algorithm. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
smallest strong pseudoprime, primitive root theorem, trial division algorithm, pth number, senior tellers, invertibility theorem, exponential formulae, strong pseudoprimes, prime smaller, smallest prime factor, finite induction, remainder algorithm, positive primes, smallest factor, unique factorization theorem, primality test, quadratic sieve, many prime numbers, complete factorization, key lemma, factorization algorithm, modular arithmetic, quotient set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclid's Elements, Oxford English Dictionary, Ancient Greece, Fermat's Last Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
There are two fundamental algorithms: the division algorithm and the Euclidean algorithm. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
smallest strong pseudoprime, primitive root theorem, trial division algorithm, pth number, senior tellers, invertibility theorem, exponential formulae, strong pseudoprimes, prime smaller, smallest prime factor, finite induction, remainder algorithm, positive primes, smallest factor, unique factorization theorem, primality test, quadratic sieve, many prime numbers, complete factorization, key lemma, factorization algorithm, modular arithmetic, quotient set Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclid's Elements, Oxford English Dictionary, Ancient Greece, Fermat's Last Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 7
books:
See all 7 books this book cites
1
book
cites this book:
- An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy in Back Matter
- Prior Analytics by Aristotle on page 43
- Mathematics Today: Twelve Informal Essays by Lynn Arthur Steen in Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil in Back Matter
- The Principles of Human Knowledge by George Berkeley in Back Matter
See all 7 books this book cites
- Wireless Security: Models, Threats, and Solutions by Randall K. Nichols in Back Matter
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