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

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

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

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

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

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

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

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

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

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

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

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

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

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

Level structure | Isogeny | Abelian surface | POLYNOMIALS | MATHEMATICS | FIELDS | level structure | REDUCTION | BOUNDS | isogeny | SIEGEL MODULAR-FORMS | GENUS 2 | abelian surface | CURVES | CRYPTOGRAPHY

Journal Article

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

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

MATHEMATICS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | ALGORITHMS | ISOGENIES | ATKIN | Mathematics - Number Theory | Mathematics | Number Theory

Journal Article

2005, Lecture Notes in Computer Science, ISBN 3540306846, Volume 3788, 20

The aim of this paper is to justify the common cryptographic practice of selecting elliptic curves using their order as the primary criterion. We can formalize...

Discrete Mathematics in Computer Science | Data Encryption | Computer Science | Management of Computing and Information Systems | Algorithm Analysis and Problem Complexity | Computer Communication Networks | Operating Systems | Expanders | Generalized Riemann hypothesis | Discrete log | Elliptic curves | Modular forms | Rapid mixing | L-functions | Isogenies | Random reducibility | Ramanujan graphs | modular forms | random reducibility | expanders | rapid mixing | COMPUTER SCIENCE, THEORY & METHODS | generalized Riemann hypothesis | elliptic curves | discrete log | isogenies

Discrete Mathematics in Computer Science | Data Encryption | Computer Science | Management of Computing and Information Systems | Algorithm Analysis and Problem Complexity | Computer Communication Networks | Operating Systems | Expanders | Generalized Riemann hypothesis | Discrete log | Elliptic curves | Modular forms | Rapid mixing | L-functions | Isogenies | Random reducibility | Ramanujan graphs | modular forms | random reducibility | expanders | rapid mixing | COMPUTER SCIENCE, THEORY & METHODS | generalized Riemann hypothesis | elliptic curves | discrete log | isogenies

Book Chapter

20.
Full Text
Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$ F p

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

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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