scholarly journals Analysis of the possibility of using modern packages of computer algebra in the synthesis of crypto-primitives

2021 ◽  
pp. 128-132
Author(s):  
Volodymyr Ponomar ◽  
Viktor Onoprienko
Keyword(s):  
Mathematical Model ◽  
Computer Algebra ◽  
Electronic Signature ◽  
Draft Standard ◽  
Symbolic Calculations ◽  
Asymmetric Encryption ◽  
Computer Algebra Software

The paper deals with systems of computer algebra - software for symbolic calculations, which allows to conduct the entire cycle of development of a mathematical model. The paper presents the results of the analysis of systems of computer algebra with specialized purpose Magma, evaluation of the possibility of its use for modulation of processes in symmetric and asymmetric cryptographic systems, as well as recommendations for their further improvement. Magma functionality is also analyzed for evaluation of possibility to model and study promising candidates for the post-quantum standard of electronic signature algorithms, asymmetric encryption and key encapsulation, including algorithms based on cryptographic transformations in the lattice-based, the use of hash trees, mathematical codes that are undergoing research during the NIST PQC competition, as well as the draft standard "Vershina 1".

DERIVATION OF ISOCHRONICITY CONDITIONS FOR QUASI-CUBIC HOMOGENEOUS ANALYTIC SYSTEMS

2013 ◽  
Vol 23 (09) ◽  
pp. 1350149
Author(s):  
YUSEN WU ◽  
FENG LI ◽  
PEILUAN LI
Keyword(s):  
Computer Algebra ◽  
Polynomial System ◽  
Isochronous Center ◽  
Interesting Phenomenon ◽  
Cubic Polynomial ◽  
Center Conditions ◽  
Isochronous Centers ◽  
Computer Algebra Software ◽  
Special Case

In this article, we deal with the problems of characterizing isochronous centers for real planar quasi-cubic homogeneous analytic system. The technique is based on reducing the quasi-cubic analytic system into an analytic system. With the help of common computer algebra software-MATHEMATICA, we compute the period constants of the origin and obtain the necessary isochronous center conditions for the transformed system. Finally, we give a proof of the sufficiency by various methods. Similar results are less so far. Our work is new in terms of research about quasi-cubic analytic system and consists of the existing results related to cubic polynomial system as a special case. What is worth pointing out is that we offer a kind of interesting phenomenon that the exponent parameter λ controls the nonanalyticity of the studied system (5).

scholarly journals Obtaining approximate region of asymptotic stability by computer algebra: A case study

2002 ◽  
Vol 20 (1) ◽  
pp. 56 ◽  
Author(s):  
S Prakash ◽  
J Vanualailai ◽  
T Soma
Keyword(s):  
Asymptotic Stability ◽  
Computer Algebra ◽  
System Analysis ◽  
Direct Method ◽  
Quantifier Elimination ◽  
Optimization Method ◽  
Analysis And Design ◽  
The Stability ◽  
Computer Algebra Software

One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.

scholarly journals homalg – A META-PACKAGE FOR HOMOLOGICAL ALGEBRA

2008 ◽  
Vol 07 (03) ◽  
pp. 299-317 ◽  
Author(s):  
MOHAMED BARAKAT ◽  
DANIEL ROBERTZ
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Linear Equations ◽  
Homological Algebra ◽  
Mathematical Object ◽  
Specific Knowledge ◽  
Central Notion ◽  
Computer Algebra Software ◽  
Finitely Presented

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom R, ⊗R, [Formula: see text], [Formula: see text], as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.

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