Computing supersingular endomorphism rings using inseparable endomorphisms

Συγγραφείς: Fuselier, Jenny, Iezzi, Annamaria, Kozek, Mark, Morrison, Travis, Namoijam, Changningphaabi

Συνεισφορές: High Point University, Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie (CASC), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA), Dipartimento di Matematica e Applicazioni 'Renato Caccioppoli', University of Naples Federico II = Università degli studi di Napoli Federico II, Laboratoire de Géométrie Algébrique et Applications à la Théorie de l'Information (GAATI), Université de la Polynésie Française (UPF), Whittier College, Virginia Tech Blacksburg, Colby College, ANR-20-CE40-0013,MELODIA,Méthodes pour les variétés abéliennes de petite dimension(2020), ANR-21-CE39-0009,BARRACUDA,Algèbre, preuves, protocoles, algorithmes, courbes, et surfaces pour les codes et leurs applications(2021)

Πηγή: Journal of Algebra. 668:145-189

Θεματικοί όροι: cryptography, Mathematics - Number Theory, Quaternion algebras, isogenies, quaternion algebras, 11Y16, Curves over finite and local fields, Isogenies, Cryptography, FOS: Mathematics, [INFO]Computer Science [cs], Quaternion and other division algebras: arithmetic, zeta functions, supersingular elliptic curves, Number Theory (math.NT), [MATH]Mathematics [math], Supersingular elliptic curves, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2306.03051
https://zbmath.org/8015272
https://doi.org/10.1016/j.jalgebra.2025.01.012
https://hdl.handle.net/11588/995159
https://hdl.handle.net/11588/995159
https://doi.org/10.1016/j.jalgebra.2025.01.012

A generalization of Lehman’s method: A generalization of Lehman's method

Συγγραφείς: Hales, Jonathon, Hiary, Ghaith

Πηγή: The Ramanujan Journal. 65:1773-1790

Θεματικοί όροι: algorithm, Mathematics - Number Theory, square-free numbers, 0102 computer and information sciences, 01 natural sciences, integer factorization, FOS: Mathematics, 11Y05, 11Y16, Number Theory (math.NT), Factorization, primality, 0101 mathematics, rational approximation, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2209.15586

Algorithms for Inversion Mod $p^k$

Συγγραφείς: Koc, C.K.

Πηγή: IEEE Transactions on Computers IEEE Trans. Comput. Computers, IEEE Transactions on. 69(6):907-913 Jun, 2020

Complexity investigations on decomposable form equations

Συγγραφείς: Pethö, Attila

Πηγή: Publicationes Mathematicae Debrecen. 39:163-169

Θεματικοί όροι: algorithm, homogeneous polynomial, factorization of polynomials, factorization into linear forms, Factorization, 0101 mathematics, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), decomposable form, Number-theoretic algorithms, complexity, Polynomials (irreducibility, etc.)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/38433

Computational search for Gaussian perfect integers

Συγγραφείς: Banerjee, Ashmi, Mukherjee, Shaunak, Datta, Somjit, Majumder, Subhashis

Πηγή: 2015 International Conference on Control Communication & Computing India (ICCC) Control Communication & Computing India (ICCC), 2015 International Conference on. :710-715 Nov, 2015

Relation: 2015 International Conference on Control Communication & Computing India (ICCC)

Partial Correctness of an Algorithm Computing Lucas Sequences: Partial correctness of an algorithm computing Lucas sequences

Συγγραφείς: Adrian Jaszczak

Πηγή: Formalized Mathematics. 28:279-288

Θεματικοί όροι: program verification, Lucas sequences, Logic in computer science, Specification and verification (program logics, model checking, etc.), nominative data, Formalization of mathematics in connection with theorem provers, 0202 electrical engineering, electronic engineering, information engineering, Fibonacci and Lucas numbers and polynomials and generalizations, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/10981/1/10.2478_forma-2020-0025.pdf
https://www.sciendo.com/article/10.2478/forma-2020-0025
https://repozytorium.uwb.edu.pl/jspui/handle/11320/10981

Approximately counting semismooth integers

Συγγραφείς: Bach, Eric, Sorenson, Jonathan P.

Πηγή: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation. :23-30

Διαθεσιμότητα: http://dl.acm.org/doi/10.1145/2465506.2465933

A Lower Bound on the Complexity of Polynomial Multiplication over Finite Fields: A lower bound on the complexity of polynomial multiplication over finite fields

Συγγραφείς: Michael Kaminski

Πηγή: Lecture Notes in Computer Science ISBN: 9783540249986

Θεματικοί όροι: polynomial multiplication, 4. Education, 0102 computer and information sciences, 02 engineering and technology, Symbolic computation and algebraic computation, 01 natural sciences, Polynomials over finite fields, 0202 electrical engineering, electronic engineering, information engineering, Computational aspects of field theory and polynomials, Recurrences, quadratic algorithms, finite fields, Number-theoretic algorithms, complexity, Polynomials in number theory

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2205880
https://doi.org/10.1137/s0097539704442118
https://link.springer.com/chapter/10.1007/978-3-540-31856-9_40
https://dblp.uni-trier.de/db/conf/stacs/stacs2005.html#Kaminski05
https://rd.springer.com/chapter/10.1007/978-3-540-31856-9_40
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp34.html#Kaminski05
https://locus.siam.org/doi/abs/10.1137/S0097539704442118
https://epubs.siam.org/doi/abs/10.1137/S0097539704442118
https://doi.org/10.1137/S0097539704442118

On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields: On the bounded sum-of-digits discrete logarithm problem in finite fields

Συγγραφείς: Qi Cheng

Πηγή: Lecture Notes in Computer Science ISBN: 9783540226680

Θεματικοί όροι: discrete logarithm problem, Analysis of algorithms and problem complexity, 0202 electrical engineering, electronic engineering, information engineering, 0102 computer and information sciences, 02 engineering and technology, finite fields, Symbolic computation and algebraic computation, sum-of-digits, 01 natural sciences, Number-theoretic algorithms, complexity, parameterized complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://cr.yp.to/bib/2004/cheng-digits.pdf
https://link.springer.com/content/pdf/10.1007%2F978-3-540-28628-8_12.pdf
http://cs.ou.edu/~qcheng/paper/lw.pdf
https://www.iacr.org/cryptodb/archive/2004/CRYPTO/1141/1141.pdf
https://link.springer.com/chapter/10.1007%2F978-3-540-28628-8_12
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp34.html#Cheng05
https://link.springer.com/content/pdf/10.1007%2F978-3-540-28628-8_12.pdf
https://epubs.siam.org/doi/10.1137/S0097539704446037

On the Ultimate Complexity of Factorials: On the ultimate complexity of factorials

Συγγραφείς: Qi Cheng

Πηγή: Lecture Notes in Computer Science ISBN: 9783540006237

Θεματικοί όροι: factorization, Analysis of algorithms and problem complexity, Analysis of algorithms, Computational and structural complexity, 0102 computer and information sciences, computational and structural complexity, 0101 mathematics, 01 natural sciences, Number-theoretic algorithms, complexity, elliptic curve, Theoretical Computer Science, Computer Science(all)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://www.cs.ou.edu/~qcheng/paper/factorial.pdf
http://www.cs.ou.edu/~qcheng/paper/factorial.pdf
https://www.cs.ou.edu/~qcheng/paper/factorial.pdf
https://www.sciencedirect.com/science/article/pii/S0304397504004062
http://www.sciencedirect.com/science/article/pii/S0304397504004062
https://dblp.uni-trier.de/db/journals/tcs/tcs326.html#Cheng04
https://core.ac.uk/display/82632753
https://core.ac.uk/display/22676248
https://dblp.uni-trier.de/db/conf/stacs/stacs2003.html#Cheng03
https://rd.springer.com/chapter/10.1007/3-540-36494-3_15
https://doi.org/10.1007/3-540-36494-3_15
https://link.springer.com/10.1007/3-540-36494-3_15
https://link.springer.com/chapter/10.1007%2F3-540-36494-3_15

Seventeen Lines and One-Hundred-and-One Points: Seventeen lines and one-hundred-and-one points

Συγγραφείς: Gerhard J. Woeginger

Πηγή: Lecture Notes in Computer Science ISBN: 9783540200642

Θεματικοί όροι: algorithmic number theory, Polynomial time algorithm, geometry, Analysis of algorithms and problem complexity, Geometry, 0102 computer and information sciences, 02 engineering and technology, algorithms, IR-76359, 01 natural sciences, Algorithmic number theory, Theoretical Computer Science, METIS-219741, METIS-213364, Other combinatorial number theory, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, complexity, Number-theoretic algorithms, Computer Science(all)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2115303
https://doi.org/10.1016/j.tcs.2004.04.006
https://research.tue.nl/en/publications/00db8af7-1b24-4f89-8cea-21a91d6266c6
https://doi.org/10.1016/j.tcs.2004.04.006
https://research.utwente.nl/en/publications/db68768c-0b75-4579-a0a2-95d0f22bd157
https://doi.org/10.1016/j.tcs.2004.04.006
https://core.ac.uk/display/159247708
https://research.utwente.nl/en/publications/seventeen-lines-and-one-hundred-and-one-points-2
https://rd.springer.com/chapter/10.1007/978-3-540-39658-1_48
https://link.springer.com/chapter/10.1007/978-3-540-39658-1_48
https://dblp.uni-trier.de/db/conf/esa/esa2003.html#Woeginger03
https://research.utwente.nl/en/publications/seventeen-lines-and-one-hundred-and-one-points
https://core.ac.uk/display/92149745
https://doi.org/10.1016/j.tcs.2004.04.006
https://dblp.uni-trier.de/db/journals/tcs/tcs321.html#Woginger04
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2Fca657865-adf4-4a49-b5fb-2d7bf7246e71
https://www.sciencedirect.com/science/article/pii/S0304397504002683

The generalized Weil pairing and the discrete logarithm problem on elliptic curves

Συγγραφείς: Theodoulos Garefalakis

Πηγή: Lecture Notes in Computer Science ISBN: 9783540434009

Θεματικοί όροι: Discrete Logarithm Problem, cryptography, Weil pairing, discrete logarithm problem, Cryptography, elliptic curves, 0202 electrical engineering, electronic engineering, information engineering, Elliptic curves, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Number-theoretic algorithms, complexity, Theoretical Computer Science, Computer Science(all)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://dblp.uni-trier.de/db/journals/tcs/tcs321.html#Garefalakis04
https://www.sciencedirect.com/science/article/abs/pii/S0304397504001215
http://www.sciencedirect.com/science/article/pii/S0304397504001215
https://core.ac.uk/display/82239981
https://www.sciencedirect.com/science/article/pii/S0304397504001215
https://link.springer.com/10.1007/3-540-45995-2_15
https://dblp.uni-trier.de/db/conf/latin/latin2002.html#Garefalakis02
https://link.springer.com/chapter/10.1007%2F3-540-45995-2_15

Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree: Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree

Συγγραφείς: Markus Maurer, Edlyn Teske, Alfred Menezes

Πηγή: Lecture Notes in Computer Science ISBN: 9783540430100

Θεματικοί όροι: Cryptography, Analysis of algorithms, Applications to coding theory and cryptography of arithmetic geometry, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D4B264D082FF67354EE9968D9803102A/S1461157000000723a.pdf/div-class-title-analysis-of-the-ghs-weil-descent-attack-on-the-ecdlp-over-characteristic-two-finite-fields-of-composite-degree-div.pdf
https://zbmath.org/2116739
https://doi.org/10.1112/s1461157000000723
https://link.springer.com/content/pdf/10.1007%2F3-540-45311-3_19.pdf
https://link.springer.com/chapter/10.1007/3-540-45311-3_19
https://rd.springer.com/chapter/10.1007/3-540-45311-3_19
https://core.ac.uk/display/21688843
https://dblp.uni-trier.de/db/conf/indocrypt/indocrypt2001.html#MaurerMT01
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D4B264D082FF67354EE9968D9803102A/S1461157000000723a.pdf/div-class-title-analysis-of-the-ghs-weil-descent-attack-on-the-ecdlp-over-characteristic-two-finite-fields-of-composite-degree-div.pdf
https://www.cambridge.org/core/journals/lms-journal-of-computation-and-mathematics/article/analysis-of-the-ghs-weil-descent-attack-on-the-ecdlp-over-characteristic-two-finite-fields-of-composite-degree/D4B264D082FF67354EE9968D9803102A

Efficient Arithmetic on Koblitz Curves: Efficient arithmetic on Koblitz curves

Συγγραφείς: Jerome A. Solinas

Πηγή: Towards a Quarter-Century of Public Key Cryptography ISBN: 9781441949721

Θεματικοί όροι: Algebraic coding theory, cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, 0102 computer and information sciences, 02 engineering and technology, Koblitz curves, algorithms, public key cryptography, 01 natural sciences, Cryptography, elliptic curves, 0202 electrical engineering, electronic engineering, information engineering, windowing methods, efficient exponentiation, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1442090
https://doi.org/10.1023/a:1008306223194
https://dblp.uni-trier.de/db/journals/dcc/dcc19.html#Solinas00
https://doi.org/10.1023/A:1008306223194
https://link.springer.com/article/10.1023/A:1008306223194
https://ci.nii.ac.jp/naid/30011963360
https://dl.acm.org/doi/10.1023/A%3A1008306223194
https://rd.springer.com/chapter/10.1007/978-1-4757-6856-5_6

Discrete Logarithms: The Past and the Future: Discrete logarithms: The past and the future

Συγγραφείς: Andrew Odlyzko

Πηγή: Towards a Quarter-Century of Public Key Cryptography ISBN: 9781441949721

Θεματικοί όροι: Diffie-Hellman key exchange algorithm, Cryptography, 0202 electrical engineering, electronic engineering, information engineering, 0102 computer and information sciences, 02 engineering and technology, discrete logarithms, 01 natural sciences, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Detecting perfect powers in essentially linear time

Συγγραφείς: Daniel J. Bernstein

Πηγή: Mathematics of Computation. 67:1253-1283

Θεματικοί όροι: 0301 basic medicine, 03 medical and health sciences, Newton's method, Roundoff error, perfect powers, number theoretic algorithms, fast multiplication, linear forms in logarithms, transcendental number theory, 0101 mathematics, 01 natural sciences, Number-theoretic algorithms, complexity, Linear forms in logarithms, Baker's method

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00952-1/S0025-5718-98-00952-1.pdf
https://zbmath.org/1165754
https://doi.org/10.1090/s0025-5718-98-00952-1
https://research.tue.nl/en/publications/81a80bd1-0ffb-4a4b-9695-7eeee15cdc4f
https://doi.org/10.1090/S0025-5718-98-00952-1
https://dl.acm.org/doi/10.1090/S0025-5718-98-00952-1
http://cr.yp.to/papers/powers-ams.pdf
https://dblp.uni-trier.de/db/journals/moc/moc67.html#Bernstein98
https://ui.adsabs.harvard.edu/abs/1998MaCom..67.1253B/abstract
https://www.ams.org/mcom/1998-67-223/S0025-5718-98-00952-1/S0025-5718-98-00952-1.pdf
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2F81a80bd1-0ffb-4a4b-9695-7eeee15cdc4f

A Polynomial Time Algorithm for Diophantine Equations in One Variable: A polynomial time algorithm for diophantine equations in one variable

Συγγραφείς: Cucker, Felipe, Koiran, Pascal, Smale, Steve

Συνεισφορές: Thomassé, Stéphan

Πηγή: Journal of Symbolic Computation. 27:21-29

Θεματικοί όροι: Algebra and Number Theory, roots of polynomials, complexity theory, 0102 computer and information sciences, [INFO] Computer Science [cs], Symbolic computation and algebraic computation, diophantine equations in one variable, Higher degree equations, Fermat's equation, 01 natural sciences, Computational Mathematics, sparse polynomials, 0101 mathematics, Computer solution of Diophantine equations, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://hal-lara.archives-ouvertes.fr/hal-02102070/file/RR1997-45.pdf
https://zbmath.org/1271790
https://doi.org/10.1006/jsco.1998.0242
https://core.ac.uk/display/24366149
https://dblp.uni-trier.de/db/journals/jsc/jsc27.html#CuckerKS99
https://www.sciencedirect.com/science/article/pii/S0747717198902425
https://www.sciencedirect.com/science/article/abs/pii/S0747717198902425
https://hal.science/hal-04649567v1
https://doi.org/10.1006/jsco.1998.0242

The CREW PRAM complexity of modular inversion

Συγγραφείς: Joachim von zur Gathen, Igor E. Shparlinski

Πηγή: Lecture Notes in Computer Science ISBN: 9783540642756

Θεματικοί όροι: Analysis of algorithms and problem complexity, 1. No poverty, Exponential sums, Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.), 0102 computer and information sciences, 0101 mathematics, modular inversion, parallel computation, CREW PRAM complexity, exponential sums, 01 natural sciences, 7. Clean energy, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1519231
https://doi.org/10.1137/s0097539797328070
https://epubs.siam.org/doi/10.1137/S0097539797328070
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp29.html#GathenS00
https://doi.org/10.1137/S0097539797328070
https://dblp.uni-trier.de/db/conf/latin/latin98.html#GathenS98
https://link.springer.com/chapter/10.1007/BFb0054331
https://cosec.bit.uni-bonn.de/fileadmin/user_upload/publications/pubs/gatshp98.pdf
https://link.springer.com/content/pdf/10.1007%2FBFb0054331.pdf
https://rd.springer.com/chapter/10.1007/BFb0054331

A space-efficient fast prime number sieve

Συγγραφείς: Dunten, Brian, Jones, Julie, Sorenson, Jonathan

Πηγή: Information Processing Letters. 59:79-84

Θεματικοί όροι: Primality, analysis of algorithms, design of algorithms, Theory and Algorithms, prime number sieve, Number Theory, number theoretic algorithms, 0101 mathematics, sieve of Eratosthenes, 01 natural sciences, Number-theoretic algorithms, complexity, Primes

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/983267
https://doi.org/10.1016/0020-0190(96)00099-3
http://www.sciencedirect.com/science/article/pii/0020019096000993
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https://doi.org/10.1016/0020-0190(96)00099-3
https://www.sciencedirect.com/science/article/abs/pii/0020019096000993

A Double-Digit Lehmer-Euclid Algorithm for Finding the GCD of Long Integers: A double-digit Lehmer-Euclid algorithm for finding the GCD of long integers

Συγγραφείς: Tudor Jebelean

Πηγή: Journal of Symbolic Computation. 19:145-157

Θεματικοί όροι: approximative GCD computation, Algebra and Number Theory, partial cosequence computation, number-theoretic algorithms, 0102 computer and information sciences, Symbolic computation and algebraic computation, 01 natural sciences, Computational Mathematics, 03 medical and health sciences, 0302 clinical medicine, Multiplicative structure, Euclidean algorithm, greatest common divisors, double digits, Number-theoretic algorithms, complexity

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/786280
https://doi.org/10.1006/jsco.1995.1009
https://www.sciencedirect.com/science/article/pii/S0747717185710097
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https://dblp.uni-trier.de/db/journals/jsc/jsc19.html#Jebelean95