Monomial Evaluation of Polynomial Functions Protected by Threshold Implementations

2020 ◽  
pp. 66-84
Author(s):  
Simon Landry ◽  
Yanis Linge ◽  
Emmanuel Prouff
Keyword(s):  
Polynomial Functions

scholarly journals On the group of unit-valued polynomial functions

2021 ◽  
Author(s):  
Amr Ali Al-Maktry
Keyword(s):  
Commutative Ring ◽  
Semidirect Product ◽  
Polynomial Functions ◽  
Dual Numbers ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Canonical Representations ◽  
Finite Commutative Ring

AbstractLet R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units $${{\mathcal{F}}}(R)^\times $$ F ( R ) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on $$R[x]/(x^2)=R[\alpha ]$$ R [ x ] / ( x 2 ) = R [ α ] , the ring of dual numbers over R, and show that the group $${\mathcal{P}}_{R}(R[\alpha ])$$ P R ( R [ α ] ) , consisting of those polynomial permutations of $$R[\alpha ]$$ R [ α ] represented by polynomials in R[x], is embedded in a semidirect product of $${{\mathcal{F}}}(R)^\times $$ F ( R ) × by the group $${\mathcal{P}}(R)$$ P ( R ) of polynomial permutations on R. In particular, when $$R={\mathbb{F}}_q$$ R = F q , we prove that $${\mathcal{P}}_{{\mathbb{F}}_q}({\mathbb{F}}_q[\alpha ])\cong {\mathcal{P}}({\mathbb{F}}_q) \ltimes _\theta {{\mathcal{F}}}({\mathbb{F}}_q)^\times $$ P F q ( F q [ α ] ) ≅ P ( F q ) ⋉ θ F ( F q ) × . Furthermore, we count unit-valued polynomial functions on the ring of integers modulo $${p^n}$$ p n and obtain canonical representations for these functions.

Level curves of open polynomial functions on the real plane

1994 ◽  
Vol 22 (14) ◽  
pp. 5973-5981
Author(s):  
J. Ferrera ◽  
M.J. de la Puente
Keyword(s):  
Real Plane ◽  
Polynomial Functions ◽  
The Real ◽  
Level Curves

A proof of a theorem by Fried and MacRae and applications to the composition of polynomial functions

2011 ◽  
Vol 97 (2) ◽  
pp. 115-124 ◽  
Author(s):  
Erhard Aichinger ◽  
Stefan Steinerberger
Keyword(s):  
Polynomial Functions

Properties of reversible polynomial functions

1997 ◽  
Vol 33 (5) ◽  
pp. 647-651
Author(s):  
A. A. Mishchenko
Keyword(s):  
Polynomial Functions

Efficient Verifiable Databases With Insertion/Deletion Operations From Delegating Polynomial Functions

2018 ◽  
Vol 13 (2) ◽  
pp. 511-520 ◽  
Author(s):  
Meixia Miao ◽  
Jianfeng Ma ◽  
Xinyi Huang ◽  
Qian Wang
Keyword(s):  
Polynomial Functions

Spline Based Design of Cam Contours for Improved Dynamic Performance

1993 ◽  
Author(s):  
Holly K. Ault ◽  
James C. Wilkinson
Keyword(s):  
Dynamic Performance ◽  
Integrated Design ◽  
Polynomial Functions ◽  
Piecewise Polynomial ◽  
Cam Design ◽  
Piecewise Polynomial Functions ◽  
Cam Follower ◽  
Cam Profile ◽  
Pitch Curve ◽  
Design And Manufacture

Abstract A method for the integrated design and manufacture of radial plate cams is discussed. Currently, a cam-follower system is designed by specifying constraints on the motion of the follower. The physical cam contour or cam pitch curve are not mathematically defined. The cam is manufactured from the discretized follower motion program. A new method for cam design is proposed which will produce a smooth, mathematically defined cam pitch curve while maintaining the proper constraints on the follower motion. Piecewise polynomial functions in the form of rational and/or non-rational splines may be used. Cams will be manufactured using smoothed profiles and tested for improved dynamic performance. The results of initial investigations of cam profile design for this research are presented.

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