BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic [Illustrated] (Paperback)

~ Tom St Denis (Author)
Key Phrases: comba method, radix reduction, multiple precision algorithms, Algorithm Greatest Common Divisor, Algorithm Montgomery Reduction, Example of Montgomery Reduction (more...)

Editorial Reviews

Product Description

Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small and single precision. The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms.

Bignum math is the backbone of modern computer security algorithms. It is the ability to work with hundred-digit numbers efficiently using techniques that are both elegant and occasionally bizarre. This book introduces the reader to the concept of bignum algorithms and proceeds to build an entire library of functionality from the ground up. Through the use of theory, pseudo-code and actual fielded C source code the book explains each and every algorithm that goes into a modern bignum library. Excellent for the student as a learning tool and practitioner as a reference alike BigNum Math is for anyone with a background in computer science who has taken introductory level mathematic courses. The text is for students learning mathematics and cryptography as well as the practioner who needs a reference for any of the algorithms documented within.

* Complete coverage of Karatsuba Multiplication, the Barrett Algorithm, Toom-Cook 3-Way Multiplication, and More

* Tom St Denis is the developer of the industry standard cryptographic suite of tools called LibTom.

* This book provides step-by-step exercises to enforce concepts

About the Author

Tom St Denis is the author of the industry standard LibTom series of projects. Tom is a senior software developer and cryptographer for the Advanced Micro Devices Corporation. He has been engaged in various international development contracts and speaking engagements since 2004. He is at work on his next book, Cryptography for Developers.

Product Details

• Paperback: 320 pages
• Publisher: Syngress (September 4, 2006)
• Language: English
• ISBN-10: 1597491128
• ISBN-13: 978-1597491129
• Product Dimensions: 8.7 x 7 x 1 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #704,269 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

4.0 out of 5 stars A good overview, May 17, 2007

By	Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews (TOP 100 REVIEWER)    (REAL NAME)

As the author of this book is correct when he says that multiple-precision arithmetic is essential for cryptography, and of course this book would not have been written if this were not the case. The languages of usual choice for cryptography, namely Java and C, support only single precision arithmetic and integer values too small for effective encryption. To obtain larger values that are necessary for cryptography, one must use special data structures, and the author has developed these and put them in the public domain. The trick to using his approach, along with those developed by other researchers is to design the algorithms and data structures so as to optimize memory, as the latter can be very restricted, especially in embedded systems.

The C data structure that the author constructs and uses throughout the book is called `mp_int' and consists of a dynamically allocated array of digits representing the multiple-precision integer. This data structure also elements that denote how many digits of the array contain the digits used to represent the integer at hand. The author gives the pseudocode and the explicit algorithm for initializing and deallocating mp_int. In fact, throughout the book the author writes down the explicit C code for every algorithm he discusses. This reviewer did not attempt to run any of the code and so cannot speak to its efficacy in real applications or devices. The book was therefore read attentively but not with the intent of using any of the algorithms in the book.

The book however has much more than just C code, as the author discusses many of the details behind each algorithm, many of these taken for granted even by professional cryptographers and professional applied mathematicians, who sometimes forget about some of the difficulties in actual implementation. The standard operations of mathematics, and also modular arithmetic are discussed in detail, with the author putting particular emphasis on the features of his approach that depart from some familiar algorithms, such as the algorithm for adding two multiple-precision integers. Of particular interest, and of enormous practical interest, is the discussion on fast multiplication, such as the Comba method, and Karatsuba multiplication.

7 of 13 people found the following review helpful:

5.0 out of 5 stars Wow, who thought you would need math after school, August 8, 2006

By	David Maynor (atlanta, ga United States) - See all my reviews (REAL NAME)

I am a coder and to be honest I am somewhat afraid of crypto becasue of the heavy math needed. I have used LibTomCrypt so I thought a book by the same guy could no be bad. The book progressed at a perfect pace for following along if you are not a math genius and even provide code sample tests that allow you to apply what you have learned. I would suggest this book to anyone who wants to know more but doesn't have time for college classes.