Representing the field elements with respect to the polynomial (or standard) basis, we
consider bit parallel architectures for multiplication over the finite field GF (2m). In this effect …

This paper details the design of a new high-speed pipelined application-specific instruction
set processor (ASIP) for elliptic curve cryptography (ECC) using field-programmable gate …

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 …

Based on a new representation of GF (2/sup n/), we present two multipliers for all irreducible
trinomials. Space complexities of the multipliers match the best results. The time complexity …

Multiplication and squaring are main finite field operations in cryptographic computations
and designing efficient multipliers and squarers affect the performance of cryptosystems. In …

This paper presents a method for producing hardware designs for elliptic curve cryptography
(ECC) systems over the finite field GF (2/sup m/), using the optimal normal basis for the …

In this article, a new architecture of bit-serial polynomial basis (PB) multipliers over the
binary extension field GF (2 m) generated by irreducible trinomials is presented. Bit-serial …

A new nonpipelined bit-parallel-shifted polynomial basis multiplier for GF (2 n) is presented.
For some irreducible trinomials, the space complexity of the multiplier matches the best …

Finite field accumulation is the simplest of all the finite field operations, but at the same time,
it is one of the most frequently encountered operations in finite field arithmetic. In this paper …

In this paper, an efficient recursive formulation is suggested for systolic implementation of
canonical basis finite field multiplication over GF (2 m) based on irreducible AOP. We have …