# Cryptography Arithmetic

## Algorithms and Hardware Architectures

• Amos R. Omondi
Book

Part of the Advances in Information Security book series (ADIS, volume 77)

1. Front Matter
Pages i-xiv
2. ### Part I

1. Front Matter
Pages 1-1
2. Amos R. Omondi
Pages 3-68
3. ### Part II

1. Front Matter
Pages 69-69
2. Amos R. Omondi
Pages 71-87
3. Amos R. Omondi
Pages 89-104
4. Amos R. Omondi
Pages 105-141
5. Amos R. Omondi
Pages 143-181
6. Amos R. Omondi
Pages 183-201
4. ### Part III

1. Front Matter
Pages 203-203
2. Amos R. Omondi
Pages 205-224
3. Amos R. Omondi
Pages 225-241
4. Amos R. Omondi
Pages 243-252
5. Amos R. Omondi
Pages 253-287
6. Amos R. Omondi
Pages 289-313
5. Back Matter
Pages 315-336

### Introduction

Modern cryptosystems, used in numerous applications that require secrecy or privacy - electronic mail, financial transactions, medical-record keeping, government affairs, social media etc. - are based on sophisticated mathematics and algorithms that in implementation involve much computer arithmetic. And for speed it is necessary that the arithmetic be realized at the hardware (chip) level. This book is an introduction to the implementation of cryptosystems at that level.

The aforementioned arithmetic is mostly the arithmetic of finite fields, and the book is essentially one on the arithmetic of prime fields and binary fields in the context of cryptography. The book has three main parts. The first part is on generic algorithms and hardware architectures for the basic arithmetic operations: addition, subtraction, multiplication, and division. The second part is on the arithmetic of prime fields. And the third part is on the arithmetic of binary fields. The mathematical fundamentals necessary for the latter two parts are included, as are descriptions of various types of cryptosystems, to provide appropriate context.

This book is intended for advanced-level students in Computer Science, Computer Engineering, and Electrical and Electronic Engineering. Practitioners too will find it useful, as will those with a general interest in "hard" applications of mathematics.

### Keywords

cryptosystems cryptography computer arithmetic modular arithmetic finite fields elliptic curves computer architecture inversion decryption hardware architecture hardware implementation algorithms security normal basis polynomial basis prime fields binary fields

#### Authors and affiliations

• Amos R. Omondi
• 1
1. 1.State University of New York – KoreaSongdoKorea (Republic of)

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-030-34142-8
• Copyright Information Springer Nature Switzerland AG 2020
• Publisher Name Springer, Cham
• eBook Packages Computer Science
• Print ISBN 978-3-030-34141-1
• Online ISBN 978-3-030-34142-8
• Series Print ISSN 1568-2633
• Series Online ISSN 2512-2193
• Buy this book on publisher's site
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