Search Results - "Number-theoretic algorithms"

Computing supersingular endomorphism rings using inseparable endomorphisms

Authors: Fuselier, Jenny Iezzi, Annamaria Kozek, Mark et al.

Contributors: Fuselier, Jenny Iezzi, Annamaria Kozek, Mark et al.

Source: Journal of Algebra. 668:145-189

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Hales, Jonathon Hiary, Ghaith

Source: The Ramanujan Journal. 65:1773-1790

Subject Terms: 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

File Description: application/xml

Access URL: http://arxiv.org/abs/2209.15586

Complexity investigations on decomposable form equations

Authors: Pethö, Attila

Source: Publicationes Mathematicae Debrecen. 39:163-169

Subject Terms: 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.)

File Description: application/xml

Access URL: https://zbmath.org/38433

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

Authors: Adrian Jaszczak

Source: Formalized Mathematics. 28:279-288

Subject Terms: 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

File Description: application/xml

Access URL: 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

Algorithms for Inversion Mod $p^k$

Authors: Cetin Kaya Koc

Source: IEEE Transactions on Computers. 69:907-913

Subject Terms: 0202 electrical engineering, electronic engineering, information engineering, Computer Arithmetic, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Multiplicative Inverse, Number-Theoretic Algorithms

File Description: application/pdf

Access URL: https://acikerisim.istinye.edu.tr/xmlui/handle/20.500.12713/401
https://ieeexplore.ieee.org/document/8976264
https://dblp.uni-trier.de/db/journals/tc/tc69.html#Koc20
https://hdl.handle.net/20.500.12713/401

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

Authors: Michael Kaminski

Source: Lecture Notes in Computer Science ISBN: 9783540249986

Subject Terms: 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

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Access URL: 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

Authors: Qi Cheng

Source: Lecture Notes in Computer Science ISBN: 9783540226680

Subject Terms: 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

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Access URL: 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

Authors: Qi Cheng

Source: Lecture Notes in Computer Science ISBN: 9783540006237

Subject Terms: 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)

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Access URL: 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

Authors: Gerhard J. Woeginger

Source: Lecture Notes in Computer Science ISBN: 9783540200642

Subject Terms: 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)

File Description: application/xml

Access URL: https://zbmath.org/2115303
https://doi.org/10.1016/j.tcs.2004.04.006
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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

Authors: Theodoulos Garefalakis

Source: Lecture Notes in Computer Science ISBN: 9783540434009

Subject Terms: 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)

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Access URL: 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

Authors: Markus Maurer Edlyn Teske Alfred Menezes

Source: Lecture Notes in Computer Science ISBN: 9783540430100

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Jerome A. Solinas

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Andrew Odlyzko

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

Subject Terms: 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

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Detecting perfect powers in essentially linear time

Authors: Daniel J. Bernstein

Source: Mathematics of Computation. 67:1253-1283

Subject Terms: 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

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Access URL: 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

Authors: Cucker, Felipe Koiran, Pascal Smale, Steve et al.

Contributors: Cucker, Felipe Koiran, Pascal Smale, Steve et al.

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

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Joachim von zur Gathen Igor E. Shparlinski

Source: Lecture Notes in Computer Science ISBN: 9783540642756

Subject Terms: 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

File Description: application/xml

Access URL: 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

Authors: Dunten, Brian Jones, Julie Sorenson, Jonathan

Source: Information Processing Letters. 59:79-84

Subject Terms: 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

File Description: application/xml

Access URL: https://zbmath.org/983267
https://doi.org/10.1016/0020-0190(96)00099-3
http://www.sciencedirect.com/science/article/pii/0020019096000993
https://core.ac.uk/display/22720956
https://dblp.uni-trier.de/db/journals/ipl/ipl59.html#DuntenJS96
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

Authors: Tudor Jebelean

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

Subject Terms: 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

File Description: application/xml

Access URL: https://zbmath.org/786280
https://doi.org/10.1006/jsco.1995.1009
https://www.sciencedirect.com/science/article/pii/S0747717185710097
https://www.sciencedirect.com/science/article/abs/pii/S0747717185710097
https://core.ac.uk/display/82210021
https://dblp.uni-trier.de/db/journals/jsc/jsc19.html#Jebelean95

Efficient algorithms for computing the Jacobi symbol: Extended abstract

Authors: Meyer Eikenberry, Shawna Sorenson, Jonathan

Source: Lecture Notes in Computer Science ISBN: 9783540615811

Subject Terms: Jacobi symbol, Computational Mathematics, Algebra and Number Theory, Theory and Algorithms, Number Theory, Power residues, reciprocity, 0202 electrical engineering, electronic engineering, information engineering, 0102 computer and information sciences, 02 engineering and technology, Parallel algorithms in computer science, Symbolic computation and algebraic computation, 01 natural sciences, Number-theoretic algorithms, complexity

File Description: application/xml

Access URL: https://zbmath.org/1216482
https://doi.org/10.1006/jsco.1998.0226
https://dblp.uni-trier.de/db/conf/ants/ants1996.html#EikenberryS96
https://rd.springer.com/chapter/10.1007/3-540-61581-4_58
https://link.springer.com/chapter/10.1007/3-540-61581-4_58
https://www.sciencedirect.com/science/article/abs/pii/S0747717198902267
https://dblp.uni-trier.de/db/journals/jsc/jsc26.html#EikenberryS98
https://doi.org/10.1006/jsco.1998.0226
https://core.ac.uk/display/82664209
https://www.sciencedirect.com/science/article/pii/S0747717198902267
https://dialnet.unirioja.es/servlet/articulo?codigo=459977

The Inverse Satisfiability Problem: The inverse satisfiability problem

Authors: Dimitris J. Kavvadias Martha Sideri

Source: Lecture Notes in Computer Science ISBN: 9783540613329

Subject Terms: computational complexity, model, Analysis of algorithms and problem complexity, coNP-completeness, 0102 computer and information sciences, 02 engineering and technology, 16. Peace & justice, 01 natural sciences, polynomial-time algorithms, Boolean satisfiability, 3. Good health, Knowledge representation, 0202 electrical engineering, electronic engineering, information engineering, Parallel algorithms in computer science, Number-theoretic algorithms, complexity

File Description: application/xml

Access URL: https://link.springer.com/chapter/10.1007/3-540-61332-3_158
https://dblp.uni-trier.de/db/conf/cocoon/cocoon96.html#KavvadiasS96