© 2020

Cryptography Arithmetic

Algorithms and Hardware Architectures


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

Table of contents

  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
  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

About this book


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.


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

  1. 1.State University of New York – KoreaSongdoKorea (Republic of)

About the authors

Amos Omondi received a Ph.D. degree in Computer Science from the University of North Carolina at Chapel Hill. Since then he has had a lengthy academic career, teaching at universities in the USA, Europe, Oceania, and Asia. He is currently a professor in the Department of Computer Science at the State University of New York in Korea, the global campus of  Stony Brook University (USA).

He is the author of several books, including three on computer arithmetic: Computer Arithmetic Systems (Prentice-Hall, 1994), Residue Number Systems (Imperial College Press, 2007), and Computer-Hardware Evaluation of Mathematical Functions (Imperial College Press, 2015).

Bibliographic information

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