The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

This paper surveys bit-parallel multipliers for finite field GF (2 n) according to i) quadratic and
subquadratic arithmetic complexities of the underlying algorithms, ii) various bases used for …

With the rapid evolution of security technology, small field-size elliptic curve-based point
multiplication (PM) has gradually become obsolete, leading to the implementation of PM …

Cryptography systems have become inseparable parts of almost every communication
device. Among cryptography algorithms, public-key cryptography, and in particular elliptic …

In the context of public key cryptography, the McEliece cryptosystem represents a very smart
solution based on the hardness of the decoding problem, which is believed to be able to …

Finite field multiplication is a fundamental and frequently used operation in various
cryptographic circuits and systems. Because of its high complexity, this operation generally …

Novel binary polynomial multipliers have been designed using M-term overlap-free
Karatsuba multiplication (OFKM), where is 5–8. The proposed designs were realized in …

In this paper, we present a new method for parallel binary finite field multiplication which
results in subquadratic space complexity. The method is based on decomposing the …

Security threats affecting electronics communications in the current world make necessary
the encryption and authentication of every transaction. The increasing levels of security …

Shifted polynomial basis (SPB) and generalized polynomial basis (GPB) are two variations
of polynomial basis representation. SPB/GPB have potential for efficient bit-level and digit …