Cryptanalysis of the extension field cancellation cryptosystem

2021 ◽  
Author(s):  
Olive Chakraborty ◽  
Jean-Charles Faugère ◽  
Ludovic Perret
Keyword(s):  
Extension Field

Preservation of elementary equivalence under scalar extension

1982 ◽  
Vol 47 (4) ◽  
pp. 734-738
Author(s):  
Bruce I. Rose
Keyword(s):  
Identity Element ◽  
Positive Answer ◽  
General Question ◽  
Division Algebras ◽  
Extension Field ◽  
Elementary Equivalence ◽  
Applied Model ◽  
Finite Dimensional ◽  
Positive Statements ◽  
Finite Dimensional Algebras

In this note we show that taking a scalar extension of two elementarily equivalent finite-dimensional algebras over the same field preserves elementary equivalence. The general question of whether or not tensor product preserves elementary equivalence was originally raised in [4]. In [3] Feferman relates an example of Ersov which answers the question negatively. Eklof and Olin [7] also provide a counterexample to the general question in the context of two-sorted structures. Thus the result proved below is a partial positive answer to a general question whose status has been resolved negatively. From the viewpoint of applied model theory it seems desirable to find contexts in which positive statements of preservation can be obtained. Our result does have an application; a corollary to it increases our understanding of what it means for two division algebras to be elementarily equivalent.All algebras are finite-dimensional algebras over fields. All algebras contain an identity element, but are not necessarily associative.Recall that the center of a not necessarily associative algebra A is the set of elements which commute and “associate” with all elements of A. The notion of a scalar extension is an important one in algebra. If A is an algebra over F and G is an extension field of F, then the scalar extension of A by G is the algebra A ⊗F G.

scholarly journals Efficient Implementation of Karatsuba Algorithm Based Three-Operand Multiplication Over Binary Extension Field

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 38234-38242 ◽  
Author(s):  
Chiou-Yng Lee ◽  
Chia-Chen Fan ◽  
Jiafeng Xie ◽  
Shyan-Ming Yuan
Keyword(s):  
Efficient Implementation ◽  
Extension Field

Brief Motivational Interviewing Training for Outreach in School Health Programming

2021 ◽  
Vol 36 (1) ◽  
Author(s):  
Kathryn J. DeShaw ◽  
Laura D. Ellingson ◽  
Laura Liechty ◽  
Gabriella M. McLoughlin ◽  
Gregory J. Welk
Keyword(s):  
Motivational Interviewing ◽  
Training Program ◽  
School Health ◽  
Effect Sizes ◽  
Extension Field ◽  
School Wellness ◽  
Phone Calls ◽  
Quasi Experimental ◽  
Health Programming ◽  
Training Protocol

This study assessed a brief 6-week motivational interviewing (MI) training program for extension field specialists (EFS) involved in supporting a statewide school wellness initiative called SWITCH. A total of 16EFS were instructed in MI principles to support the programming and half (n = 8) volunteered to participate in the hybrid (online and in-person) MI training program. Phone calls between EFS and school staff involved in SWITCH were recorded and coded using the Motivational Interviewing Treatment Integrity (MITI) system to capture data on utilization of MI principles. Differences in MI utilization between the trained (n=8) and untrained (n=8) EFS were evaluated using Cohen’s d effect sizes. Results revealed large differences for technical global scores (d=1.5) and moderate effect sizes for relational global components (d=0.76) between the two groups. This naturalistic, quasi-experimental study indicates a brief MI training protocol is effective for teaching the spirit and relational components of MI to EFS.

scholarly journals Fields of Definition for Representations of Associative Algebras

2018 ◽  
Vol 62 (1) ◽  
pp. 291-304
Author(s):  
Dave Benson ◽  
Zinovy Reichstein
Keyword(s):  
Finite Extension ◽  
Representation Type ◽  
Essential Dimension ◽  
Extension Field ◽  
Associative Algebras ◽  
Separable Extension ◽  
Finite Representation ◽  
Field Of Definition ◽  
Finite Dimensional ◽  
A Finite Group

AbstractWe examine situations, where representations of a finite-dimensionalF-algebraAdefined over a separable extension fieldK/F, have a unique minimal field of definition. Here the base fieldFis assumed to be a field of dimension ≼1. In particular,Fcould be a finite field ork(t) ork((t)), wherekis algebraically closed. We show that a unique minimal field of definition exists if (a)K/Fis an algebraic extension or (b)Ais of finite representation type. Moreover, in these situations the minimal field of definition is a finite extension ofF. This is not the case ifAis of infinite representation type orFfails to be of dimension ≼1. As a consequence, we compute the essential dimension of the functor of representations of a finite group, generalizing a theorem of Karpenko, Pevtsova and the second author.

Decidable fragments of field theories

1990 ◽  
Vol 55 (3) ◽  
pp. 1007-1018 ◽  
Author(s):  
Shih-Ping Tung
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Field Theories ◽  
Extension Field ◽  
Radical Extension ◽  
Transcendental Extension

AbstractWe say φ is an ∀∃ sentence if and only if φ is logically equivalent to a sentence of the form ∀x∃yψ(x, y), where ψ(x, y) is a quantifier-free formula containing no variables except x and y. In this paper we show that there are algorithms to decide whether or not a given ∀∃ sentence is true in (1) an algebraic number field K, (2) a purely transcendental extension of an algebraic number field K, (3) every field with characteristic 0, (4) every algebraic number field, (5) every cyclic (abelian, radical) extension field over Q, and (6) every field.

An Area-Efficient Composite Field Inverter for Elliptic Curve Cryptosystems

2014 ◽  
pp. 218-237
Author(s):  
M. M. Wong ◽  
M. L. D. Wong
Keyword(s):  
Elliptic Curve ◽  
Complexity Analysis ◽  
Extension Field ◽  
Arithmetic Operations ◽  
Hardware Cost ◽  
Elliptic Curve Cryptosystems ◽  
Look Up Table ◽  
Composite Field ◽  
Optimal Saving ◽  
Area Efficient

This chapter presents a new area-efficient composite field inverter of the form GF(q1) with q=2n.m suitable for the hardware realization of an elliptic curve (EC) cryptosystem. Considering both the security aspect and the hardware cost required, the authors propose the utilization of the composite field GF(((22)2)41) for EC cryptosystem. For efficient implementation, they have derived a compact inversion circuit over GF(2164)=GF(((22)2)41) to achieve an optimal saving in the hardware cost required. Furthermore, the authors have also developed a composite field digit serial Sunar-Koc multiplier for the multiplication in the extension field. All of the arithmetic operations in the subfield GF(24) are performed in its isomorphic composite field, GF((22)2), leading to a full combinatorial implementation without resorting to the conventional look-up table approach. To summarize the work, the final hardware implementation and the complexity analysis of the inversion is reported towards the end of this chapter.

scholarly journals On complete integral closure and Archimedean valuation domains

1996 ◽  
Vol 61 (3) ◽  
pp. 377-380 ◽  
Author(s):  
Robert Gilmer
Keyword(s):  
Integral Domain ◽  
Integral Closure ◽  
Extension Field ◽  
Quotient Field ◽  
Valuation Domains ◽  
Complete Integral Closure

AbstractSuppose D is an integral domain with quotient field K and that L is an extension field of K. We show in Theorem 4 that if the complete integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by Gilmer and Heinzer in 1965.

Sign in / Sign up

Export Citation Format

Share Document