Chapter

Cryptographic Algorithms on Reconfigurable Hardware

Part of the series Signals and Communication Technology pp 139-188

Binary Finite Field Arithmetic

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Abstract

In this Chapter we review some of the most relevant arithmetic algorithm on binary extension fields GF(2m). The arithmetic over GF(2m) has many important applications in the domains of theory of code theory and in cryptography [221, 227, 380]. Finite field’s arithmetic operations include: addition, subtraction, multiplication, squaring, square root, multiplicative inverse, division and exponentiation.