Ryuichi Harasawa

A soft-core processor for finite field arithmetic with a variable word size accelerator

This paper presents implementation and evaluation of an accelerator architecture for soft-cores to speed up reduction process for the arithmetic on GF(2m) used in Elliptic Curve Cryptography (ECC) systems. In this architecture, the word size of the accelerator can be customized when the architecture is configured on an FPGA. Focusing on the fact that the number of the reduction processing operations on GF(2m) is affected by the irreducible polynomial and the word size, we propose to employ an unconventional word size for the accelerator depending on a given irreducible polynomial and implement a MIPS-based soft-core processor coupled with a variable-word size accelerator. As a result of evaluation with several polynomials, it was shown that the performance improvement of up to 10.2 times was obtained compared to the 32-bit word size, even taking into account the maximum frequency degradation of 20.4% caused by changing the word size. The advantage of using unconventional word sizes was also shown, suggesting the promise of this approach for low-power ECC systems.

An energy-efficient FPGA-based soft-core processor with a configurable word size ECC arithmetic accelerator

This paper proposes an FPGA-based soft core processor architecture equipped with a configurable accelerator to speed up GF(2m) arithmetic for elliptic curve cryptography (ECC) systems. Focusing on the fact the number of operations required for GF(2m) arithmetic is influenced by the relationship between the irreducible polynomial and the machine word size, we propose an approach where the word size of the accelerator is tailored to a given irreducible polynomial. The evaluation results reveal that the performance and the energy efficiency of GF(2m) multiplication including reduction can be improved by up to 6.67 times and 5.24 times, respectively.

Improving the berlekamp algorithm for binomials x n -a

In this paper, we describe an improvement of the Berlekamp algorithm, a method for factoring univariate polynomials over finite fields, for binomials xn−a over finite fields

Tate and Ate pairings for y2 =x5−αx in characteristic five

\mathbb{F}_{q}

A remark on the computation of cube roots in finite fields.

. More precisely, we give a deterministic algorithm for solving the equation

Root Computation in Finite Fields

h(x)^{q} \equiv h(x) \ ({\rm mod}\ x^{n} -a)

ON THE BREAK INTERVAL SEQUENCES OF EQUITABLE ROUND-ROBIN TOURNAMENTS

directly without applying the sweeping-out method to the corresponding coefficient matrix. We show that the factorization of binomials using the proposed method is performed in

Tate pairing for y 2 =x 5 -αx in Characteristic Five.

O \, \tilde{}\, (n \log q)

A Simple Improvement for Integer Factorizations with Implicit Hints

operations in

Accelerating finite field arithmetic with a suitable word size

\mathbb{F}_{q}