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Applied Mathematics and Computation, ISSN 0096-3003, 2012, Volume 218, Issue 9, pp. 5249 - 5258
Isogeny volcanoes are an interesting structure that have had several recent applications... 
Isogenies | Isogeny volcanoes | Cordillera | Elliptic curves | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | Volcanoes | Graphs | Construction | Mathematical models | Modular | Computation
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2015, Volume 8895, pp. 162 - 175
Conference Proceeding
Finite Fields and Their Applications, ISSN 1071-5797, 01/2018, Volume 49, pp. 108 - 125
Volcanoes of ℓ-isogenies of elliptic curves are a special case of graphs with a cycle called crater... 
Volcano | Finite field | Elliptic curve | Distortion map | Isogeny | POLYNOMIALS | MATHEMATICS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | FINITE-FIELDS | ISOGENY VOLCANOS | Volcanoes
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2015, Volume 84, Issue 294, pp. 1953 - 1975
In this paper, we compute l-isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in l, when l is an odd prime... 
MATHEMATICS, APPLIED | ISOGENY VOLCANOS | ABELIAN-VARIETIES | IDENTITY-BASED ENCRYPTION | Symbolic Computation | Computer Science
Journal Article
Publicacions Matematiques, ISSN 0214-1493, 2007, Volume 51, pp. 165 - 180
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 196, Issue 1, pp. 67 - 76
The structure of the volcano of ℓ-isogenies, ℓ-prime, of elliptic curves over finite fields has been extensively studied over recent years... 
Finite fields | Isogenies | Elliptic curves | Volcanoes | volcanoes | finite fields | MATHEMATICS, APPLIED | elliptic curves | isogenies | ALGORITHM | Algorithms
Journal Article
Journal of Research and Practice in Information Technology, ISSN 1443-458X, 2008, Volume 40, Issue 4, pp. 263 - 273
.... The core of such a procedure lies on the usage of successive chains of isogenies, visiting different volcanoes of isogenies which are located... 
Cryptography | Isogeny volcanoes | Elliptic curves | Isogeny Volcanoes | COMPUTER SCIENCE, SOFTWARE ENGINEERING | VOLCANOS | LOGARITHMS | Elliptic Curves | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2006, Volume 176, Issue 2, pp. 739 - 750
The goal of this paper is presenting an algorithm to determine the structure of the volcano of 2-isogenies of a given elliptic curve over a finite field... 
Finite fields | Isogenies | Volcanoes’ computation | Torsion subgroups | Elliptic curves | Volcanoes' computation | Volcanism | Algorithms | Volcanoes
Journal Article
Mathematics in computer science, ISSN 1661-8270, 2018, Volume 12, Issue 3, pp. 295 - 307
Smart cards are being attacked increasingly more, due to their numerous uses and the valuable information stored inside. For this reason, efficient and secure... 
Smart cards | Isogeny volcanoes | Side-channel attacks | Mathematics, general | Elliptic curve cryptography | 14H52 | Mathematics | Computer Science, general | Cryptography | Algorithms | Volcanoes
Journal Article
APPLIED MATHEMATICS AND COMPUTATION, ISSN 0096-3003, 05/2006, Volume 176, Issue 2, pp. 739 - 750
The goal of this paper is presenting an algorithm to determine the structure of the volcano of 2-isogenies of a given elliptic curve over a finite field... 
finite fields | MATHEMATICS, APPLIED | volcanoes' computation | elliptic curves | torsion subgroups | isogenies
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2018, Volume 32, Issue 3, pp. 1741 - 1749
A permutation rational function f is an element of F-q(x) is a rational function that induces a bijection on Fq, that is, for all y. Fq there exists exactly... 
Isogenies | Elliptic curves | Permutation rational functions | Cryptography | Exceptional covers | HYPERELLIPTIC CURVES | VOLCANOS | MATHEMATICS, APPLIED | exceptional covers | cryptography | elliptic curves | isogenies | permutation rational functions | Mathematics
Journal Article
Journal of Mathematical Cryptology, ISSN 1862-2976, 02/2014, Volume 8, Issue 1, pp. 1 - 29
Given two ordinary elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit a nonzero isogeny... 
Elliptic curves | 68Q12 | 14H52 | hidden shift problem | quantum algorithms | isogenies | 81P94 | 11Y40 | Isogenies | Quantum algorithms | Hidden shift problem | Quantum computing | Ellipse | Algorithms | Research | Curves, Elliptic | Methods | Cryptography
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2009, Volume 129, Issue 6, pp. 1491 - 1504
We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized... 
Expander graphs | Isogenies | Elliptic curves | L-functions | MATHEMATICS | VALUES | DISCRETE LOGARITHM PROBLEM | EXPLICIT BOUNDS | Cryptography | Universities and colleges
Journal Article
Research in Number Theory, ISSN 2363-9555, 12/2017, Volume 3, Issue 1, pp. 1 - 38
...$$ l -isogenies, resolving that, in arbitrary dimension, their structure is similar, but not identical, to the “volcanoes... 
Isogeny graphs | (\ell , \ell )$$ ( ℓ , ℓ ) -isogenies | Lattices in symplectic spaces | Orders in CM-fields | Mathematics | Principally polarised abelian varieties | Jacobians of hyperelliptic curves | Number Theory | (ℓ, ℓ) -isogenies
Journal Article
Forum of mathematics. Sigma, ISSN 2050-5094, 2016, Volume 4
Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$ , and let $G_{E}(\ell )$ be the image of the Galois representation... 
Number Theory | POLYNOMIALS | MATHEMATICS | FIELDS | MATHEMATICS, APPLIED | LOCAL-GLOBAL PRINCIPLE | MODULAR-CURVES | RATIONAL ISOGENIES | SURJECTIVITY | COMPUTATION | POINTS | PRIMES | Curves | Mathematics - Number Theory
Journal Article
Algebra and Number Theory, ISSN 1937-0652, 2011, Volume 5, Issue 4, pp. 495 - 528
For a complex abelian surface A with endomorphism ring isomorphic to the maximal order in a quartic CM field K, the Igusa invariants j(1)(A), j(2)(A), j(3)(A),... 
Level structure | Isogeny | Abelian surface | POLYNOMIALS | MATHEMATICS | FIELDS | level structure | REDUCTION | BOUNDS | isogeny | SIEGEL MODULAR-FORMS | GENUS 2 | abelian surface | CURVES | CRYPTOGRAPHY
Journal Article
by A. Bostan and F. Morain and B. Salvy and É
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2008, Volume 77, Issue 263, pp. 1755 - 1778
We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new... 
Algorithms | Differential equations | Rational functions | Polynomials | Mathematics | Coefficients | Cryptography | Power series | Number theory | Curves | Finite fields | Isogenies | Newton iteration | Schoof-Elkies-Atkin algorithm | Elliptic curves | Fast algorithms | MATHEMATICS, APPLIED | fast algorithms | FAST MULTIPLICATION | TIME | DIVISION | POLYNOMIALS | finite fields | POWER-SERIES | ATTACK | elliptic curves | POINTS | isogenies
Journal Article
LMS Journal of Computation and Mathematics, ISSN 1461-1570, 2016, Volume 19, Issue A, pp. 115 - 129
We present a specialized point-counting algorithm for a class of elliptic curves over F-p(2) that includes reductions of quadratic Q-curves modulo inert primes... 
MATHEMATICS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | ALGORITHMS | ISOGENIES | ATKIN | Mathematics - Number Theory | Mathematics | Number Theory
Journal Article
Designs, codes, and cryptography, ISSN 1573-7586, 2014, Volume 78, Issue 2, pp. 425 - 440
Let $$p>3$$ p > 3 be a prime and let $$E$$ E , $$E'$$ E ′ be supersingular elliptic curves over $${\mathbb {F}}_p$$ F p . We want to construct an isogeny... 
Information and Communication, Circuits | 14K02 | 11G15 | 14G15 | Data Encryption | Isogenies | 14H52 | Mathematics | 11G20 | Data Structures, Cryptology and Information Theory | Elliptic curves | 11Y16 | Discrete Mathematics in Computer Science | Supersingular curves | Coding and Information Theory | Combinatorics
Journal Article
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