Spectral theory of isogeny graphs

Συγγραφείς: Giulio Codogni, Guido Maria Lido

Πηγή: Journal of Number Theory. 286:131-184

Θεματικοί όροι: 14K02, 14H52, 11F52, 05C48, 14G50, Isogeny graphs, Elliptic curves, Isogeny based cryptography, Expander graphs, Modular forms, Hecke operators, Number Theory, FOS: Mathematics, Number Theory (math.NT), Algebraic Geometry, Algebraic Geometry (math.AG)

Περιγραφή αρχείου: application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2308.13913
https://arxiv.org/abs/2308.13913
https://hdl.handle.net/2108/458043
https://doi.org/10.1016/j.jnt.2026.02.006

Elliptic curves over Hasse pairs

Συγγραφείς: Eleni Agathocleous, Antoine Joux, Daniele Taufer

Συνεισφορές: Moree, Pieter, Sofos, Efthymios

Πηγή: Journal of Number Theory

Θεματικοί όροι: FOS: Computer and information sciences, Isogeny graphs, General Mathematics, Elliptic curves over local fields, Complex multiplication and moduli of abelian varieties, Fermat and Mersenne primes, 0101 Pure Mathematics, NUMBER, Hasse pairs, Number Theory, elliptic curves, FOS: Mathematics, Elliptic curves, Number Theory (math.NT), ALIQUOT CYCLES, isogeny graphs, CONSECUTIVE PRIMES, Science & Technology, AMICABLE PAIRS, Cryptography and Security, Isogeny, Andrica's conjecture, 11G07, 11G15, 14K02, Physical Sciences, 4904 Pure mathematics, Cryptography and Security (cs.CR), Mathematics

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2406.03399
https://zbmath.org/8072266
https://doi.org/10.1016/j.jnt.2025.05.008
https://lirias.kuleuven.be/handle/20.500.12942/767198
https://doi.org/10.1016/j.jnt.2025.05.008
https://hdl.handle.net/21.11116/0000-000F-82B2-4
https://hdl.handle.net/21.11116/0000-000F-82B4-2
https://hdl.handle.net/21.11116/0000-0011-6BF3-3

Frobenius endomorphisms and minimal polynomials in supersingular isogeny rings

Συγγραφείς: El Baraka, Mohammed^{Aff1, IDs11565026006972_cor1}, Ezzouak, Siham^Aff1

Πηγή: ANNALI DELL'UNIVERSITA' DI FERRARA: SEZIONE VII - SCIENZE MATEMATICHE. 72(3)

Non-backtracking cycle estimates in supersingular isogeny graphs

Συγγραφείς: El Baraka, Mohammed^{Aff1, IDs1219002602868y_cor1}, Ezzouak, Siham^Aff1

Πηγή: Journal of Applied Mathematics and Computing. 72(8)

Distribution of cycles in supersingular ℓ-isogeny graphs: Distribution of cycles in supersingular \(\ell \)-isogeny graphs

Συγγραφείς: Eli Orvis

Πηγή: Journal of Number Theory. 277:236-261

Θεματικοί όροι: cryptography, Mathematics - Number Theory, Elliptic curves over global fields, Isogeny, Cryptography, elliptic curves, supersingular curves, FOS: Mathematics, Algebraic coding theory, cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Number Theory (math.NT), 11G05, 11T71, 14G50, 14K02, 94A60, isogeny graphs

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2403.14831
https://eprint.iacr.org/2024/509

Hashing by Walking Over Expanders: A Recipe for Constructing Provably Secure Hash Functions

Συγγραφείς: Aikawa, Yusuke^Aff32

Συνεισφορές: Wakayama, Masato, Editor-in-Chief^{Aff1, Aff27}, Anderssen, Robert S., Series Editor^Aff2, Baryshnikov, Yuliy, Series Editor^Aff3, Bauschke, Heinz H., Series Editor^Aff4, Broadbridge, Philip, Series Editor^Aff5, Cheng, Jin, Series Editor^Aff6, Chyba, Monique, Series Editor^Aff7, Cottet, Georges-Henri, Series Editor^Aff8, Cuminato, José Alberto, Series Editor^Aff9, Ei, Shin-ichiro, Series Editor^Aff10, Fukumoto, Yasuhide, Series Editor^Aff11, Hosking, Jonathan R. M., Series Editor^Aff12, Jofré, Alejandro, Series Editor^Aff13, Kimura, Masato, Series Editor^Aff14, Landman, Kerry, Series Editor^Aff15, McKibbin, Robert, Series Editor^Aff16, Parmeggiani, Andrea, Series Editor^Aff17, Pipher, Jill, Series Editor^Aff18, Polthier, Konrad, Series Editor^Aff19, Saeki, Osamu, Series Editor^Aff20, Schilders, Wil, Series Editor^Aff21, Shen, Zuowei, Series Editor^Aff22, Toh, Kim Chuan, Series Editor^Aff23, Verbitskiy, Evgeny, Series Editor^Aff24, Yoshida, Nakahiro, Series Editor^Aff25, Takagi, Tsuyoshi, editor^Aff26, Kunihiro, Noboru, editor^Aff28, Tanaka, Keisuke, editor^Aff29, Kimoto, Kazufumi, editor^Aff30, Kudo, Momonari, editor^Aff31

Πηγή: Mathematical Foundations for Post-Quantum Cryptography : Crypto-Math CREST. 40:371-388

On random sampling of supersingular elliptic curves

Συγγραφείς: Mula, Marzio, Murru, Nadir, Pintore, Federico

Πηγή: Annali di Matematica Pura ed Applicata (1923 -). 204:1293-1335

Θεματικοί όροι: Isogeny graphs, Isogeny-based cryptography, Supersingular elliptic curves, Elliptic curves, Algebraic coding theory, cryptography (number-theoretic aspects), supersingular elliptic curves, 0102 computer and information sciences, 0101 mathematics, isogeny-based cryptography, 01 natural sciences, isogeny graphs, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/8038244
https://doi.org/10.1007/s10231-024-01528-x
https://hdl.handle.net/11572/458172
https://doi.org/10.1007/s10231-024-01528-x

Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs: Adding level structure to supersingular elliptic curve isogeny graphs

Συγγραφείς: Arpin, Sarah

Πηγή: Journal de théorie des nombres de Bordeaux. 36:405-443

Θεματικοί όροι: supersingular, Curves over finite and local fields, Mathematics - Number Theory, elliptic curves, FOS: Mathematics, Algebraic coding theory, cryptography (number-theoretic aspects), Number Theory (math.NT), 0101 mathematics, level structure, 01 natural sciences, isogeny graphs

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2203.03531
https://zbmath.org/7948972
https://doi.org/10.5802/jtnb.1283

Supersingular Isogeny Graphs: Foundations for Quantum-Resistant Cryptography

Συγγραφείς: SÉRGIO DE ANDRADE, PAULO

Θεματικοί όροι: Supersingular Isogeny Graphs, Quantum Resistance, Elliptic Curve Cryptography, Post-Quantum Cryptography, Isogeny, SIDH

Computing Endomorphism Rings of Supersingular Elliptic Curves by Finding Cycles in Concatenated Supersingular Isogeny Graphs

Συγγραφείς: KAMBE, Yuta, KATAYAMA, Akira, AIKAWA, Yusuke, ISHIHARA, Yuki, YASUDA, Masaya, YOKOYAMA, Kazuhiro

Πηγή: COMMENTARII MATHEMATICI UNIVERSITATIS SANCTI PAULI. 72(1):19-42

Θεματικοί όροι: Endomorphism rings, Quaternion algebras, Supersingular isogeny graphs, Supersingular elliptic curves

Proposal of a New Isogeny-Based Cryptographic Protocol: Formal Analysis and Comparison

Συγγραφείς: mohammed EL BARAKA, Siham Ezzouak

Πηγή: Mathematics Interdisciplinary Research, Vol 10, Iss 1, Pp 111-132 (2025)

Θεματικοί όροι: isogeny‎, ‎cryptography‎, ‎elliptic curves‎, ‎supersingular isogeny graphs‎, ‎post-quantum cryptography, Mathematics, QA1-939

Περιγραφή αρχείου: electronic resource

Relation: https://mir.kashanu.ac.ir/article_114738_1d7999d6992df7958d505128db6197c9.pdf; https://doaj.org/toc/2476-4965

Σύνδεσμος πρόσβασης: https://doaj.org/article/add221cd90b74a20bfff458629833621

Loops, multi-edges and collisions in supersingular isogeny graphs

Συγγραφείς: Wissam Ghantous

Πηγή: Advances in Mathematics of Communications. 18:935-955

Θεματικοί όροι: bi-route number, Mathematics - Number Theory, Isogeny, Algebraic coding theory, cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, 0102 computer and information sciences, collisions, supersingular isogeny graphs, 01 natural sciences, 14H52, 14K02, loops, FOS: Mathematics, Elliptic curves, Number Theory (math.NT), 0101 mathematics, multi-edges

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2101.08761
https://zbmath.org/7893275
https://doi.org/10.3934/amc.2022038

On the zeta functions of supersingular isogeny graphs and modular curves

Συγγραφείς: Antonio Lei, Katharina Müller

Πηγή: Archiv der Mathematik. 122:285-294

Θεματικοί όροι: Mathematics - Number Theory, Ihara zeta functions, modular curves, Enumeration in graph theory, supersingular isogeny graphs, Modular and Shimura varieties, 11M41, 05C30, 11G18, 14G35, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Other Dirichlet series and zeta functions, Arithmetic aspects of modular and Shimura varieties, Hasse-Weil zeta functions

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2307.01001
https://zbmath.org/7806706
https://doi.org/10.1007/s00013-023-01937-z

Computing a Basis of the Set of Isogenies Between Two Supersingular Elliptic Curves

Συγγραφείς: Katayama, Akira^Aff11, Yasuda, Masaya^Aff11

Συνεισφορές: Goos, Gerhard, Series Editor^Aff1, Hartmanis, Juris, Founding Editor^Aff2, Bertino, Elisa, Editorial Board Member^Aff3, Gao, Wen, Editorial Board Member^Aff4, Steffen, Bernhard, Editorial Board Member^Aff5, Yung, Moti, Editorial Board Member^Aff6, Boulier, François, editor^Aff7, Mou, Chenqi, editor^Aff8, Sadykov, Timur M., editor^Aff9, Vorozhtsov, Evgenii V., editor^Aff10

Πηγή: Computer Algebra in Scientific Computing : 26th International Workshop, CASC 2024, Rennes, France, September 2–6, 2024, Proceedings. 14938:178-192

On ordinary isogeny graphs with level structures

Συγγραφείς: Lei, Antonio ^{a, ⁎}, Müller, Katharina ^b

Πηγή: In Expositiones Mathematicae September 2024 42(5)

Isogeny graphs on superspecial abelian varieties: eigenvalues and connection to Bruhat–Tits buildings: Isogeny graphs on superspecial abelian varieties: eigenvalues and connection to Bruhat-Tits buildings

Συγγραφείς: Yusuke Aikawa, Ryokichi Tanaka, Takuya Yamauchi

Πηγή: Canadian Journal of Mathematics. 76:1891-1916

Θεματικοί όροι: Mathematics - Number Theory, Bruhat-Tits buildings, Applications to coding theory and cryptography of arithmetic geometry, Other groups and their modular and automorphic forms (several variables), 0102 computer and information sciences, 01 natural sciences, Abelian varieties of dimension \(> 1\), Mathematics - Algebraic Geometry, Buildings and the geometry of diagrams, superspecial abelian varieties, cryptographic hash functions, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Algebraic Geometry (math.AG), isogeny graphs

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2201.04293

On towers of isogeny graphs with full level structures

Συγγραφείς: Lei, Antonio^{Aff1, IDs40687024004783_cor1}, Müller, Katharina^Aff2

Πηγή: Research in the Mathematical Sciences. 12(1)

Visible Non-Overcompensation in BSD Valuation Flows Along Rational Prime Isogenies

Συγγραφείς: Rui, Tao

Θεματικοί όροι: Cremona database, valuation flow, computational number theory, regulator, elliptic curves, Birch-Swinnerton-Dyer conjecture, Tamagawa numbers, isogeny graphs, Tate-Shafarevich group

Degree-Local BSD Flows on Rational Isogeny Graphs: Valuation Potentials and Edge-Level Compensation in Cremona Isogeny Classes

Συγγραφείς: Rui, Tao

Θεματικοί όροι: elliptic curves, Birch-Swinnerton-Dyer conjecture, isogeny graphs, Cremona database, Tate-Shafarevich group, Tamagawa numbers, valuation potentials, computational number theory

Infinite families of isogeny-torsion graphs

Συγγραφείς: Garen Chiloyan

Πηγή: Journal of Number Theory. 244:369-417

Θεματικοί όροι: isogeny-torsion graphs, Mathematics - Number Theory, Galois representations, 11G05, 14H52, 01 natural sciences, rational points, Elliptic curves over global fields, elliptic curves, FOS: Mathematics, Elliptic curves, Rational points, Number Theory (math.NT), 0101 mathematics, isogeny graphs

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2104.01128
https://zbmath.org/7641110
https://doi.org/10.1016/j.jnt.2022.09.009