BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic

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Elsevier, Aug 18, 2006 - Computers - 291 pages
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

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Chapter 1 Introduction
Chapter 2 Getting Started
Chapter 3 Basic Operations
Chapter 4 Basic Arithmetic
Chapter 5 Multiplication and Squaring
Chapter 6 Modular Reduction
Chapter 7 Exponentiation
Chapter 8 Higher Level Algorithms
Chapter 9 Number Theoretic Algorithms

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Page 289 - Montgomery. Modular multiplication without trial division. Mathematics of Computation, 44(170):519521, April 1985.
Page xvi - Tom projects, would not exist in its current form if it were not for a plethora of kind people donating their time, resources, and kind words to help support my work.
Page 15 - That is, the number 123 can be described as having a 1 in the hundreds column, 2 in the tens column, and 3 in the ones column.
Page 289 - Exponentiation Cryptosystems on the IBM PC. IBM Systems Journal 29(4): 526-538, 1990.

About the author (2006)

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.

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