A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Faster polynomial multiplication over finite fields
[article]

2014
*
arXiv
*
pre-print

Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two

arXiv:1407.3361v1
fatcat:ealovq6q5vaihipxo2ohyb4ygu
*polynomials*in F_p[X] of degree less than n. ... The cost is thus M p 0 (2 n ) + O(n lg p), where M p 0 (d) denotes the cost of a*multiplication*in F p [X]/(X d ¡ 1). Arithmetic in*finite**fields*Let p be a prime and let > 1. ... Our techniques also give rise to new strategies for*polynomial*evaluationinterpolation*over*F q . This may for instance be applied to the ecient*multiplication*of*polynomial*matrices*over*F q . ...##
###
Faster Polynomial Multiplication over Finite Fields

2017
*
Journal of the ACM
*

In section 3, we recall basic complexity results for arithmetic in

doi:10.1145/3005344
fatcat:6hcvdwstsfbc5nwxsml4hv5qhy
*finite**fields*. ... In this paper we are mainly interested in the case that R is the*finite**field*F p = Z / p Z for some prime p. ...##
###
Fast Three-Input Multipliers over Small Composite Fields for Multivariate Public Key Cryptography

2015
*
International Journal of Security and Its Applications
*

Third, our multipliers adapt table look-up and

doi:10.14257/ijsia.2015.9.9.15
fatcat:mnciib3dd5gz3ez4scv3bixroq
*polynomial*basis, since they are*faster**over*specific*fields*, respectively. We demonstrate the improvement of our design mathematically. ...*Finite**field**multiplication*is playing a crucial role in the implementations of multivariate cryptography and most of them use two-input multipliers. ... Since addition is much*faster*than constant*multiplication**over**finite**fields*, we have C MA . Therefore, is proved. ...##
###
Polynomial Multiplication over Binary Fields Using Charlier Polynomial Representation with Low Space Complexity
[chapter]

2010
*
Lecture Notes in Computer Science
*

One can obtain binomial or trinomial irreducible

doi:10.1007/978-3-642-17401-8_17
fatcat:v22z3uazqvbtxjzodkercsdqxq
*polynomials*in Charlier*polynomial*representation which allows us*faster*modular reduction*over*binary*fields*when there is no desirable such low weight ... In this paper, we give a new way to represent certain*finite**fields*GF (2 n ). This representation is based on Charlier*polynomials*. ... The binary extension*field**multiplication*can be performed in two steps:*polynomial**multiplication**over*GF (2) and modular reduction*over*GF (2 n ). ...##
###
Page 418 of IEEE Transactions on Computers Vol. 52, Issue 4
[page]

2003
*
IEEE Transactions on Computers
*

We consider rings modulo trinomials and 4-term

*polynomials*. In each case, we show that our multiplier is*faster*than multipliers*over*elements in a*finite**field*defined by irreducible pentanomials. ... However, this also results in faste multipliers as the ring elements are defined using simpk*polynomials**over*the*finite**field*GF(2). ...##
###
EFFICIENT OPERATIONS IN LARGE FINITE FIELDS FOR ELLIPTIC CURVE CRYPTOGRAPHIC

2020
*
International Journal of Engineering Technologies and Management Research
*

An efficient method to compute the

doi:10.29121/ijetmr.v7.i6.2020.712
fatcat:kp3v2bcjcbekjlvdabpnchr2mq
*finite**field**multiplication*for Elliptic Curve point*multiplication*at high speed encryption of the message is presented. ... The modified Horner rule method is not only to*finite**field*operations but also to Elliptic curve scalar*multiplication*in the encryption and decryption. ... The industry uses Elliptic curve groups*over*the large*finite**fields*of GF(2m) and GF(p), Koblitz EC groups in GF(2m) (Koblitz, 1987)*faster*than GF(p). ...##
###
On square-free factorization of multivariate polynomials over a finite field

1997
*
Theoretical Computer Science
*

In this paper we present a new deterministic algorithm for computing the square-free decomposition of multivariate

doi:10.1016/s0304-3975(97)00059-5
fatcat:3zucsxzip5dchdpeayu5sijx2m
*polynomials*with coefficients from a*finite**field*. ... We will show that the modular approach presented by Yun has no significant performance advantage*over*our algorithm. ... Therefore, we can compute the square-free decompositions of bl and b2*over*a*finite**field*of characteristic 7 much*faster*than*over*other*fields*. ...##
###
Practical fast algorithm for finite field arithmetics using group rings

2004
*
Hiroshima Mathematical Journal
*

This paper studies a fast algorithm for

doi:10.32917/hmj/1150998162
fatcat:ti63l64wurgslnc3yzoal3opny
*finite**field*arithmetics, by representing a*finite**field*as a residue of a group ring of a*finite*cyclic group, where the frobenius (q-th power) operation is e‰ciently ... When the characteristic of the*field*is greater than 2, our algorithm is often much*faster*than a standard method (NTL) in computing inverse and power. ... Hellekalek for informing us of NTL and other fast algorithms for*finite**field*arithmetics. ...##
###
On the Virtues of Generic Programming for Symbolic Computation
[chapter]

2007
*
Lecture Notes in Computer Science
*

For instance, the improved implementation of square-free factorization in AXIOM is 7 times

doi:10.1007/978-3-540-72586-2_35
fatcat:ufdfa6be6vb6pm6qgjawwiyeem
*faster*than the one in Maple and very close to the one in MAGMA. ... The purpose of this study is to measure the impact of C level code*polynomial*arithmetic on the performances of AXIOM highlevel algorithms, such as*polynomial*factorization. ... To do so, we first observe that dense univariate and multivariate*polynomials**over**finite**fields*play a central role in computer algebra, thanks to modular algorithms. ...##
###
Improving the coding speed of erasure codes with polynomial ring transforms
[article]

2017
*
arXiv
*
pre-print

Most of them use the

arXiv:1709.00178v1
fatcat:nr67tniq4jc6lnqsi6c2tbwlbq
*finite**field*arithmetic. ... In this paper, we propose an implementation and a coding speed evaluation of an original method called PYRIT (*PolYnomial*RIng Transform) to perform operations between elements of a*finite**field*into a ... in a*finite**field*by the*multiplication*in a ring by using transforms between particular*finite**fields*and*polynomial*rings. ...##
###
Improving the Coding Speed of Erasure Codes with Polynomial Ring Transforms

2017
*
GLOBECOM 2017 - 2017 IEEE Global Communications Conference
*

Most of them use the

doi:10.1109/glocom.2017.8255009
dblp:conf/globecom/DetchartL17
fatcat:56e5szeabbdjbgfdpkpzw3tj3m
*finite**field*arithmetic. ... In this paper, we propose an implementation and a coding speed evaluation of an original method called PYRIT (*PolYnomial*RIng Transform) to perform operations between elements of a*finite**field*into a ... in a*finite**field*by the*multiplication*in a ring by using transforms between particular*finite**fields*and*polynomial*rings. ...##
###
Low complexity multiplication in a finite field using ring representation

2003
*
IEEE transactions on computers
*

We consider rings modulo trinomials and 4-term

doi:10.1109/tc.2003.1190583
fatcat:kuaqotfqhzaxtlyphm7dosjnbe
*polynomials*. In each case, we show that our multiplier is*faster*than multipliers*over*elements in a*finite**field*defined by irreducible pentanomials. ... Elements of a*finite**field*, GF ð2 m Þ, are represented as elements in a ring in which*multiplication*is more time efficient. ... However, this also results in*faster*multipliers as the ring elements are defined using simpler*polynomials**over*the*finite**field*GF (2) . ...##
###
An Arithmetic over GF (2^5) Tt Implement in ECC

2012
*
International Journal of Computer Applications
*

In this paper an efficient arithmetic for operations

doi:10.5120/4863-7204
fatcat:56inlvstc5gmton2hmvxrba4bm
*over*elements of GF(2 5 ) represented in normal basis is presented. The arithmetic is applicable in public-key cryptography. ... Although the discrete logarithm problem as first employed by them was defined explicitly as the problem of finding logarithms with respect to a generator in the*multiplicative*group of the integers module ... The DLP in such a group is very hard as opposed to the DLP in the*multiplicative*group*over*a*finite**field*. ...##
###
Design of Low Register all One Polynomial Multipliers Over GF (2m) on FPGA

2019
*
VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
*

This paper presents All-one-

doi:10.35940/ijitee.k1319.10812s19
fatcat:as65tguojvdj3dtxbuzmui5jpa
*polynomial*(AOP)- based systolic multipliers*over*GF (2m) need aid as a rule not acknowledged for useful execution for cryptosystems for example, elliptic bend cryptography ... Also that, systolic AOP multipliers typically suffer from those issue from the secondary register-complexity, particularly alongside*field*programmable gate array (FPGA) platforms the place the register ...*Polynomial*basis*multiplication**over*GF (2 m ) Assume there has*field*F, and the elements a n ,a n−1 ,a n−2 ... ...##
###
Finding roots of polynomials over finite fields

2002
*
IEEE Transactions on Communications
*

We propose an improved algorithm for finding roots of

doi:10.1109/tcomm.2002.805269
fatcat:chz56rqnyrc6ximx5oky37452m
*polynomials**over**finite**fields*. ... of one exponentiation*over*the*finite**field*. ... Chien search algorithm solves it by evaluation of at all with the time complexity (1) where and are the time complexities of one addition and*multiplication*in the*finite**field*, respectively. ...
« Previous

*Showing results 1 — 15 out of 53,518 results*