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In this paper, we describe, analyze and compare various
multipliers. Particularly, we investigate the standard modular multiplication, the Montgomery multiplication, and the matrix–vector multiplication techniques.
The reduced equations for the isomorphism classes of hyperelliptic curves of genus 2 admitting a Weierstrass point over a finite field of arbitrary characteristic, are shown and the number of such classes is included. This work picks up in a unified way a series of previous results published by...
Inversion in finite fields
is a critical operation for many applications. A well-known representation basis, i.e., normal basis, provides an efficient squaring operation realized as a simple rotation of the operand coefficients. Inversion in normal basis is computed using methods...
The ancient difficulty for establishing a common cryptographic secret key between two communicating parties Alice and Bob is nicely summarized by the Catch-22 dictum of S.J. Lomonaco , to wit: “in order to communicate in secret one must first communicate in secret”. In other words, to...
The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour...
Double-exponentiation is a crucial arithmetic operation for many cryptographic protocols. Several efficient double-exponentiation algorithms based on systolic architecture have been proposed. However, systolic architectures require large circuit space, thus increasing the cost of the protocol....
The paper presents a survey of most common hardware architectures for finite field arithmetic especially suitable for cryptographic applications. We discuss architectures for three types of finite fields and their special versions popularly used in cryptography: binary fields, prime fields and...
Algorithms for performing divisions over Z
) are described, the corresponding digital circuits are synthesized and conclusions about their computation times are drawn. The results of their implementation within field-programmable devices are given in the case of the most efficient...
We survey some applications of finite fields to finite geometries in part A and to combinatorics and error-correcting codes in parts B and C.
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