A Computational Introduction to Number Theory and Algebra by Victor Shoup

Product Description

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
Product Details
Amazon Sales Rank: #125444 in Books
Published on: 2005-06-06
Number of items: 1
Binding: Hardcover
534 pages
Editorial Reviews

Download Description
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.

Review
"This is an outstanding and well-written book whose aim is to introduce the reader to a broad range of material -- ranging from basic to relatively advanced -- without requiring any prior knowledge on the part of the reader other than calculus and mathematical maturity. That the book succeeds at this goal is quite an accomplishment! ...this book is a must-read for anyone interested in computational number theory or algebra and especially applications of the latter to cryptography. I would not hesitate, though, to recommend this book even to students 'only' interested in the algebra itself (and not the computational aspects thereof); especially for computer science majors, this book is one of the best available introductions to that subject."
SIGACT News

“As computer science students have very likely not previously mastered probability theory, linear algebra, or basic abstract algebra, Shoup packages crash courses in each. Despite taking time for so many basics, Shoup climaxes with careful treatment of the late-breaking, ingenious, polynomial-time deterministic primality test of Agrawal, Kayal, and Saxena. Apart from number theory, one could easily build a fine discrete mathematics course on this book. Highly recommended.”
Choice

Download Description
Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
Customer Reviews

Really a treasure
I'm a student digging into the cryptology for an year. The more article I read, the more confusion I encounter because of my poor mathematical background. However, when I get this, I could find answer to my puzzles, and make an more explicit way to settle down my own idea.

The background you really need, clear and sweet
This book is a marvel. It is clear and concise yet thorough. The author is obviously a bit of an obsessive compulsive, he has found the shortest paths from the clearest definitions to the most important results, each given with the cleanest, most insight-inducing proofs ... the results (and definitions) he gives are the ones any student (practitioner!) of modern computer science (especially cryptology) *needs* to know -- having this book on your shelves (and its contents in your head) should be a requirement for any degree, at any level, in computer science.
[Caveat: I know the author and have read his book in draft form. I also required my students to get it and read it, in a computer science course I taught.