scholarly journals Branched covers of elliptic curves and Kähler groups with exotic finiteness properties

2019 ◽  
Vol 69 (1) ◽  
pp. 335-363 ◽  
Author(s):  
Claudio Llosa Isenrich
Keyword(s):  
Elliptic Curves ◽  
Branched Covers ◽  
Kähler Groups ◽  
Finiteness Properties

scholarly journals Finite presentations for Kähler groups with arbitrary finiteness properties

2017 ◽  
Vol 476 ◽  
pp. 344-367 ◽  
Author(s):  
Claudio Llosa Isenrich
Keyword(s):  
Kähler Groups ◽  
Finiteness Properties ◽  
Finite Presentations

scholarly journals Kodaira fibrations, Kähler groups, and finiteness properties

2019 ◽  
Vol 372 (8) ◽  
pp. 5869-5890 ◽  
Author(s):  
Martin R. Bridson ◽  
Claudio Llosa Isenrich
Keyword(s):  
Kähler Groups ◽  
Finiteness Properties

Elliptic Curves and Big Galois Representations

2008 ◽  
Author(s):  
Daniel Delbourgo
Keyword(s):  
Elliptic Curves ◽  
Galois Representations

Elliptic Curves

1997 ◽  
Author(s):  
Henry McKean ◽  
Victor Moll
Keyword(s):  
Elliptic Curves

The Joint Universality for L-Functions of Elliptic Curves

2004 ◽  
Vol 9 (4) ◽  
pp. 331-348
Author(s):  
V. Garbaliauskienė
Keyword(s):  
Elliptic Curves ◽  
Rational Numbers ◽  
Joint Universality ◽  
Universality Theorem ◽  
Joint Universality Theorem

A joint universality theorem in the Voronin sense for L-functions of elliptic curves over the field of rational numbers is proved.

New Countermeasures Against Side-Channel Attacks for Cryptography on Elliptic Curves

2006 ◽  
Vol 65 (10) ◽  
pp. 913-922
Author(s):  
Ya. N. Imamverdiev
Keyword(s):  
Elliptic Curves ◽  
Side Channel ◽  
Side Channel Attacks

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

Structured digital multisignature algorithm based on elliptic curves

2009 ◽  
Vol 29 (1) ◽  
pp. 158-160
Author(s):  
He-gang FU ◽  
Ying CHEN
Keyword(s):  
Elliptic Curves
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