2009, pp 105-124

Efficient Unified Arithmetic for Hardware Cryptography

* Final gross prices may vary according to local VAT.

Get Access
This is an excerpt from the content

Introduction

The basic arithmetic operations (i.e., addition, multiplication, and inversion) in finite fields, \(GF(q)\) , where \(q = p^k\) and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1], the US federal Digital Signature Standard [2], elliptic curve cryptography [3,4], and also recently identity-based cryptography [5, 6]. Most popular finite fields that are heavily used in cryptographic applications due to elliptic curve-based schemes are prime fields \(GF(p)\) and binary extension fields \(GF(2^n)\). Recently, identity-based cryptography based on pairing operations defined over elliptic curve points has stimulated a significant level of interest in the arithmetic of ternary extension fields, \(GF(3^n)\).

Even though the aforementioned three popular finite fields are dissimilar mathematical structures, their elements are represented using similar data structures inside the digital circuits and computers. F ...