scholarly journals Elliptic curves over a chain ring of characteristic 3

2015 ◽  
Vol 9 (3) ◽  
pp. 276-287 ◽  
Author(s):  
Moulay Hachem Hassib ◽  
Abdelhakim Chillali ◽  
Mohamed Abdou Elomary
Keyword(s):  
Elliptic Curves ◽  
Chain Ring ◽  
Characteristic 3 ◽  
A Chain

scholarly journals Reduction of Elliptic Curves in Equal Characteristic 3 (and 2)

2005 ◽  
Vol 48 (3) ◽  
pp. 428-444
Author(s):  
Roland Miyamoto ◽  
Jaap Top
Keyword(s):  
Elliptic Curves ◽  
Fibre Type ◽  
Valued Fields ◽  
Characteristic 2 ◽  
Characteristic 3

AbstractWe determine conductor exponent, minimal discriminant and fibre type for elliptic curves over discrete valued fields of equal characteristic 3. Along the same lines, partial results are obtained in equal characteristic 2.

scholarly journals Application of hierarchic authentication to isogenies of elliptic curves for providing safety of data routing in the systems of analysis of digital production traffic

2018 ◽  
Vol 44 ◽  
pp. 00007
Author(s):  
Elena Alexandrova ◽  
Maria Poltavtseva ◽  
Anastasia Yarmak
Keyword(s):  
Big Data ◽  
Information Processing ◽  
Elliptic Curves ◽  
Traffic Analysis ◽  
Quantum Systems ◽  
Data Routing ◽  
Digital Production ◽  
A Chain

The article discusses the peculiarities of the process of information routing in the course of acquisition and processing big data of digital production, including systems of traffic analysis. Such a specific features variability of physical nodes-processors with the retention of functional stringency of order of information processing is distinguished. Inordertoprovidesafetyofthedescribedprocessofinformationprocessingand possibility of restoration of a chain of processing every fragment of data, the authors offer a protocol of hierarchic authentication developed thereby on isogenies of elliptic curves. The work includes algorithms of shaping parameters, generation of keys, generation and checking signature. The evaluation of signature stability again basic types of attacks has been performed. A solution offered by the authors can be used both in traditional and, in future, in quantum systems. A simulation of corresponding signature dimensions has been performed in the work.

Faster MapToPoint on Supersingular Elliptic Curves in Characteristic 3

2011 ◽  
Vol E94-A (1) ◽  
pp. 150-155 ◽  
Author(s):  
Yuto KAWAHARA ◽  
Tetsutaro KOBAYASHI ◽  
Gen TAKAHASHI ◽  
Tsuyoshi TAKAGI
Keyword(s):  
Elliptic Curves ◽  
Supersingular Elliptic Curves ◽  
Characteristic 3

scholarly journals Classification of chain rings

2021 ◽  
Vol 7 (4) ◽  
pp. 5106-5116
Author(s):  
Yousef Alkhamees ◽  
◽  
Sami Alabiad
Keyword(s):  
Artinian Ring ◽  
Chain Ring ◽  
A Chain

<abstract><p>An associative Artinian ring with an identity is a chain ring if its lattice of left (right) ideals forms a unique chain. In this article, we first prove that for every chain ring, there exists a certain finite commutative chain subring which characterizes it. Using this fact, we classify chain rings with invariants $ p, n, r, k, k', m $ up to isomorphism by finite commutative chain rings ($ k' = 1 $). Thus the classification of chain rings is reduced to that of finite commutative chain rings.</p></abstract>

Automorphisms of a chain ring

2006 ◽  
Vol 186 (2) ◽  
pp. 289-301
Author(s):  
Surjeet Singh ◽  
Yousef Alkhamees
Keyword(s):  
Chain Ring ◽  
A Chain

Non-free extensions of the simplex codes over a chain ring with four elements

2012 ◽  
Vol 66 (1-3) ◽  
pp. 27-38 ◽  
Author(s):  
Thomas Honold ◽  
Ivan Landjev
Keyword(s):  
Chain Ring ◽  
Simplex Codes ◽  
A Chain

Quantum codes from cyclic codes over F3 + vF3

2014 ◽  
Vol 12 (06) ◽  
pp. 1450042 ◽  
Author(s):  
Mohammad Ashraf ◽  
Ghulam Mohammad
Keyword(s):  
Commutative Ring ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Quantum Codes ◽  
Quantum Code ◽  
Chain Ring ◽  
Arbitrary Length ◽  
Orthogonal Codes ◽  
Finite Commutative Ring ◽  
A Chain

Let R = F3 + vF3 be a finite commutative ring, where v2 = 1. It is a finite semi-local ring, not a chain ring. In this paper, we give a construction for quantum codes from cyclic codes over R. We derive self-orthogonal codes over F3 as Gray images of linear and cyclic codes over R. In particular, we use two codes associated with a cyclic code over R of arbitrary length to determine the parameters of the corresponding quantum code.

scholarly journals Asymmetric Cryptosystem on Matrix Algebra Over a Chain Ring

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 45
Author(s):  
Muzna Yumman ◽  
Tariq Shah ◽  
Iqtadar Hussain
Keyword(s):  
Matrix Algebra ◽  
Discrete Logarithm ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Fundamental Change ◽  
Chain Ring ◽  
Asymmetric Cryptography ◽  
Novel Approach ◽  
A Chain ◽  
Asymmetric Cryptosystem

The revolutionary idea of asymmetric cryptography brings a fundamental change to our modern communication system. However, advances in quantum computers endanger the security of many asymmetric cryptosystems based on the hardness of factoring and discrete logarithm, while the complexity of the quantum algorithm makes it hard to implement in many applications. In this respect, novel asymmetric cryptosystems based on matrices over residue rings are in practice. In this article, a novel approach is introduced. [...]

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