Anwar HasanReadAn Efficient Look-up Table-based Approach for Multiplication over GF(2 m ) Generated by Trinomials"There are three main bases, such as polynomial basis, dual basis, and normal basis, used for the representation of elements of finite field GF(2 m ), and therefore, binary field multipliers for all the three bases have been designed for various applications.

In this paper, a novel architecture is proposed which combines Triggered Instruction and parallel condition.

Low-degree Karatsuba–Toom formulae and their multiplication complexities are considered primarily for the subquadratic multipliers.Article · Nov 2014 Haining FanM.

## Security in RFID and Sensor Networks

The LUT size, therefore, becomes quite large for the fields of large degrees recommended by the National Institute of Standards and Technology (NIST).

Show abstract] [Hide abstract] ABSTRACT: Redundant basis (RB) multipliers over Galois Field ( GF(2m)) have gained huge popularity in elliptic curve cryptography (ECC) mainly because of their negligible hardware cost for squaring and modular reduction.

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### Keshab K. Parhi - Google Scholar Citations - Академия Google

Especially, a comparative study of FPGA implementations of these polynomial basis multipliers was conducted by Beuchat et al.

The proposed digit-parallel design offers nearly 28 % improvement in area-delay product over the best of the existing LUT-based designs.

Full-text · Article · Jan 2015 Jiafeng XiePramod Kumar MeherZhi-Hong MaoRead full-textA survey of some recent bit-parallel GF(2n)GF(2n) multipliers"For example, a GF(2 n ) inverter based on this multiplier was later presented by Azarderakhsh et al. lpt port serial or parallel

More multiplier can be constructed in a variable structure depending on . elliptic curve over a finite field with a size of 160 bits or more. ... [18] L. Song and K.K. Pahri, “ Low-Energy Digit-SerialParallel Finite., Song, L., Parhi, K.K.: Low energy digit-serialparallel finite field multipliers. [ px6447113106r395.pdf .,design of efficient dedicated, low energy, finite field multipliers can lead to dramatic improvement on the .. Their hardware implementations use m bit-serial parallel multipliers resulting in expensive .

More may be polynomial, normal, dual or digit [6–8]. The ... [7] L. Song, K.K. Parhi, Low-energy digit-serialparallel finite field.,multiplier for the finite field operations is digit serial and scalable to arbitrary bit- lengths. .. At the next (lower) level are the point .. 21 Song, L., and Parhi, K.K.: ' 'Low-energy digit-serialparallel finite.,low-area and low-power digit-serial finite field multipliers and squarers in most and least significant bit first . L. Song and K.K. Parhi, "Low-Energy Digit-Serial Parallel Finite Field Multi- pliers", Journal of .

More Song, L., Parhi, K.K.: Low energy digit-serialparallel finite field multipliers. [ px6447113106r395.pdf .,Low-energy digit-serialparallel finite field multipliers . Efficient semisystolic architectures for finite-field arithmetic.,multiplier can be constructed in a variable structure depending on . elliptic curve over a finite field with a size of 160 bits or more. ... [18] L. Song and K.K. Pahri, “ Low-Energy Digit-SerialParallel Finite.

### Low-Energy Digit-Serial/Parallel Finite Field Multipliers

Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, coding theory and Quantum error correction.

The Swiss mathematician Leonhard Euler pioneered the modern approach to congruence in about 1750, when he explicitly introduced the idea of congruence modulo a number N.

Sengupta, “Algorithms for multiplication in Galois Field for implementation using systolic arrays,” IEE Proceedings-E, Vol.

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