drinfeld_charpoly.bib

@article{BrGuYu80,
  author ={Brent, R. P. and Gustavson, F. G. and Yun, D. Y. Y.},
  title ={Fast solution of {Toeplitz} systems of equations and computation of {Pad\'e} approximants},
  journal = {J. Algorithms},
  volume ={1},
  number ={3},
  pages ={259--295},
  year = {1980},
}

@misc{Jung00,
author = {Jung, F.},
title = {Charakteristische {P}olynome von {D}rinfeld-{M}oduln},
note = {Diplomarbeit, U. Saarbr\"ucken},
year = {2000}
}

@article{Harvey14,
 author = {David Harvey},
 journal = {Annals of Mathematics},
 number = {2},
 pages = {783--803},
 title = {Counting points on hyperelliptic curves in average polynomial time},
 volume = {179},
 year = {2014}
}


@article{Satoh00,
author = {Satoh, T},
year = {2000},
pages = {247--270},
title = {The canonical lift of an ordinary elliptic curve over a finite field and its point counting},
volume = {15},
journal = {J. Ramanujan Math. Soc.}
}

@article{Shoup94,
    AUTHOR = {Shoup, V.},
     TITLE = {Fast construction of irreducible polynomials over finite fields},
   JOURNAL = {J. Symb. Comput.},
    VOLUME = {17},
      YEAR = {1994},
    NUMBER = {5},
     PAGES = {371--391},
}
@Article{BoGaSc07,
  author = {A. Bostan and P. Gaudry and {\'E}. Schost},
  title = {Linear recurrences with polynomial coefficients and application to
integer factorization and {C}artier-{M}anin operator},
  journal = {SIAM Journal on Computing},
  volume = 36,
  number = 6,
  pages = {1777--1806},
  year = 2007
}
@article{Kaltofen00,
	Author = {Kaltofen, E.},
	Journal = {J. Symb. Comp.},
	Number = 6,
	Pages = {891--919},
	Title = {Challenges of symbolic computation: my favorite open problems.},
	Volume = 29,
	Year = 2000}

@article{HsYu00, 
title={On characteristic polynomials of geometric {F}robenius associated to {D}rinfeld modules}, 
volume={122}, 
number={3}, 
journal={Compositio Mathematica}, 
author={Hsia, L.-C. and Yu, J.}, 
year={2000}, 
pages={261-280}
}


@article{vanderHeiden04,
	author = {van der Heiden, G. J.},
	title = {Factoring polynomials over finite fields with {D}rinfeld modules},
	journal= {Mathematics of Computation},
	volume={73},
	pages={317-322},
	year={2004}
}

@misc{shoup2001ntl,
	title={{NTL}: A library for doing number theory},
	author={Shoup, V.},
year={2019},
    note = {\url{http:/www.shoup.net/ntl}}
}

@inproceedings{PaPo89,
	author = {Panchishkin, A. and Potemine, I},
	title = {An algorithm for the factorization of polynomials using elliptic modules},
	booktitle = {Constructive methods and algorithms in number theory},
	year = {1989},
	pages = {117},
}

@article{Carlitz35,
author = "Carlitz, L.",
fjournal = "Duke Mathematical Journal",
journal = "Duke Math. J.",
number = "2",
pages = "137--168",
publisher = "Duke University Press",
title = "On certain functions connected with polynomials in a Galois field",
volume = "1",
year = "1935"
}

@article {KaVi04,
    AUTHOR = {Kaltofen, E. and Villard, G.},
     TITLE = {On the complexity of computing determinants},
   JOURNAL = {Computational Complexity},
    VOLUME = {13},
      YEAR = {2004},
    NUMBER = {3-4},
     PAGES = {91--130},
}
@article{LaNeZh17,
title = {Fast, deterministic computation of the {H}ermite normal form and determinant of a polynomial matrix},
journal = {J. Complexity},
volume = {42},
pages = {44-71},
year = {2017},
author = {G. Labahn and V. Neiger and W. Zhou},
}

@inproceedings{GiJeVi03,
	author = {Giorgi, P. and Jeannerod, C.-P. and Villard, G.},
	title = {On the complexity of polynomial matrix computations},
	booktitle = {ISSAC'03},
	isbn = {1-58113-641-2},
	location = {Philadelphia, PA, USA},
	pages = {135--142},
	year={2003},
	numpages = {8},
	acmid = {860889},
	publisher = {ACM},
	keywords = {column reduced form, determinant, matrix gcd, matrix polynomial, minimal basis, polynomial matrix multiplication},
} 

@Article{Coppersmith94,
  author =       {Coppersmith, D.},
  title =        {Solving homogeneous linear equations over {GF}$(2)$ via block {W}iedemann algorithm},
  journal =      {Math. Comp.},
  year =         1994,
  volume =       62,
  number =       205,
  pages =        {333-350}}


@Article{CoWi90,
	author = 	 {D. Coppersmith and S. Winograd},
	title = 	 {Matrix multiplication via arithmetic progressions},
   JOURNAL = {J. Symb. Comput.},
	year = 	 1990,
	volume =	 9,
	number =	 3,
	pages =	 {251--280}
}
@inproceedings{LeGall14,
 author = {Le Gall, F.},
 title = {Powers of tensors and fast matrix multiplication},
 booktitle = {ISSAC'14},
 year = {2014},
 pages = {296--303},
 publisher = {ACM},
} 
@PhdThesis{Montgomery92,
  author = {Montgomery, P. L.},
  title  =  {An {FFT} extension of the elliptic curve method of factorization},
  school = {University of California, Los Angeles {CA}},
  year   = 	 {1992}
}

@book{Goss96,
  title={Basic Structures of Function Field Arithmetic},
  author={Goss, D.},
  year={1996},
  publisher={Springer Berlin Heidelberg}
}
@article{PUCHINGER2017b,
title = "Fast operations on linearized polynomials and their applications in coding theory",
   JOURNAL = {J. Symb. Comput.},
year = "2017",
author = "S. Puchinger and A. Wachter-Zeh",
keywords = "Linearized polynomials, Skew polynomials, Fast multiplication, Fast multi-point evaluation, Fast minimal subspace polynomial, Fast decoding"
}

@article{Kedlaya:2011:FPF:2340436.2340448,
 author = {Kedlaya, K. S. and Umans, C.},
 title = {Fast polynomial factorization and modular composition},
 journal = {SIAM J. Comput.},
 issue_date = {November 2011},
 volume = {40},
 number = {6},
 year = {2011},
 pages = {1767--1802},
} 

@article{BrKu78,
 author = {Brent, R. P. and Kung, H. T.},
 title = {Fast Algorithms for Manipulating Formal Power Series},
 journal = {J. ACM},
 volume = {25},
 number = {4},
 year = {1978},
 issn = {0004-5411},
 pages = {581--595},
 numpages = {15},
 acmid = {322099},
 publisher = {ACM},
 address = {New York, NY, USA},
} 

@misc{GaPa18,
Author = {S. Garai and M. Papikian},
Title = {Endomorphism rings of reductions of Drinfeld modules},
Year = {2018},
Eprint = {1804.07904},
}

@misc{eschost2017arXiv171200669D,
   author = {{Doliskani}, J. and {Narayanan}, A.~K. and {Schost}, {\'E}.},
    title = "{Drinfeld modules with complex multiplication, {H}asse invariants and factoring polynomials over finite fields}",
   eprint = {1712.00669},
     year = 2017,
}


@inproceedings{CaLe17,
  author    = {X. Caruso and J. Le Borgne},
  title     = {Fast multiplication for skew polynomials},
  booktitle   = {ISSAC'17},
pages = {77--84},
publisher = {ACM},
  year      = {2017},
}

@article {KaSh98,
    AUTHOR = {Kaltofen, E. and Shoup, V.},
     TITLE = {Subquadratic-time factoring of polynomials over finite fields},
  JOURNAL = {Mathematics of Computation},
    VOLUME = {67},
      YEAR = {1998},
    NUMBER = {223},
     PAGES = {1179--1197},
}

@article{Gekeler83,
author = {Gekeler, E.-U},
year = {1983},
pages = {167--182},
title = {Zur {A}rithmetik von {D}rinfeld-{M}oduln},
volume = {262},
journal = {Math. Ann}
}

@article{frobdist,
author = {Gekeler, E.-U.},
year = {2008},
month = {04},
pages = {1695-1721},
title = {Frobenius distributions of Drinfeld modules over finite fields},
volume = {360},
journal = {Transactions of the American Mathematical Society}
}


@article{Wiedemann:1986:SSL:13738.13744,
 author = {Wiedemann, D H},
 title = {Solving Sparse Linear Equations over Finite Fields},
 journal = {IEEE Trans. Inf. Theor.},
 issue_date = {Jan. 1986},
 volume = {32},
 number = {1},
 year = {1986},
 issn = {0018-9448},
 pages = {54--62},
 numpages = {9},
 acmid = {13744},
 publisher = {IEEE Press},
 address = {Piscataway, NJ, USA},
}

@article{kaltofen1994,
author = {Kaltofen, Erich},
year = {1994},
month = {01},
pages = {297-304},
title = {Asymptotically Fast Solution of Toeplitz-like Singular Linear Systems.}
}

@ARTICLE{2014arXiv1401.7714L,
   author = {{Le Gall}, F.},
    title = "{Powers of Tensors and Fast Matrix Multiplication}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1401.7714},
 primaryClass = "cs.DS",
 keywords = {Computer Science - Data Structures and Algorithms, Computer Science - Computational Complexity, Computer Science - Symbolic Computation},
     year = 2014,
    month = jan,
   adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1401.7714L},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{schoof85,
 ISSN = {00255718, 10886842},
 author = {R. Schoof},
 journal = {Math. Comp.},
 number = {170},
 pages = {483--494},
 publisher = {American Mathematical Society},
 title = {Elliptic curves over finite fields and the computation of square roots $\operatorname{mod} p$},
 volume = {44},
 year = {1985}
}

@article{Drinfeld74, 
title={Elliptic modules}, 
volume={94}, 
number={23}, 
journal={Matematicheskii Sbornik}, 
author={Drinfel'd, V. G.}, year={1974}, pages={561-593}
}

@Article{Scanlon01,
author="Scanlon, T.",
title="Public Key cryptosystems based on Drinfeld modules Are insecure  ",
journal="Journal of Cryptology",
year="2001",
day="01",
volume="14",
number="4",
pages="225--230",
}

@book{Gathen:2003:MCA:945759,
 author = {Gathen, J. von zur and Gerhard, J.},
 title = {Modern Computer Algebra},
 year = {2013},
 isbn = {0521826462},
 edition = {3},
 publisher = {Cambridge University Press},
 address = {New York, NY, USA},
} 

@article{HUANG1998257,
title = "Fast Rectangular Matrix Multiplication and Applications",
journal = "Journal of Complexity",
volume = "14",
number = "2",
pages = "257 - 299",
year = "1998",
issn = "0885-064X",
doi = "https://doi.org/10.1006/jcom.1998.0476",
url = "http://www.sciencedirect.com/science/article/pii/S0885064X98904769",
author = "Xiaohan Huang and Victor Y. Pan",
keywords = "rectangular matrix multiplication, asymptotic arithmetic complexity, bilinear algorithms, parallel complexity, polynomial composition, polynomial factorization over finite fields, linear programming"
}

@inproceedings{Kaltofen:1991:PEP:113379.113396,
 author = {Kaltofen, E. and Pan, V.},
 title = {Processor efficient parallel solution of linear systems over an abstract field},
 booktitle = {SPAA '91},
 year = {1991},
 isbn = {0-89791-438-4},
 location = {Hilton Head, South Carolina, USA},
 pages = {180--191},
 numpages = {12},
 acmid = {113396},
 publisher = {ACM},
} 

@inproceedings{Kaltofen-saun:1991:WMS:646027.676885,
 author = {Kaltofen, E. and Saunders, B. D.},
 title = {On Wiedemann's method of solving sparse linear systems},
 booktitle = {AAECC-9},
 year = {1991},
 isbn = {3-540-54522-0},
 pages = {29--38},
 numpages = {10},
 acmid = {676885},
 publisher = {Springer-Verlag},
} 

@Article{vonzurGathen1992,
author="Gathen, J. von zur 
and Shoup, V.",
title="Computing Frobenius maps and factoring polynomials",
journal="Computational Complexity",
year="1992",
volume="2",
number="3",
pages="187--224",
}

@inproceedings{LeUr18,
 author = {{Le Gall}, F. and Urrutia, F.},
 title = {Improved rectangular matrix multiplication using powers of the {C}oppersmith-{W}inograd tensor},
 booktitle = {SODA '18},
 year = {2018},
 pages = {1029--1046},
 publisher = {SIAM},
} 

@article{Cantor1991OnFM,
  title={On fast multiplication of polynomials over arbitrary algebras},
  author={David G. Cantor and Erich Kaltofen},
  journal={Acta Informatica},
  year={1991},
  volume={28},
  pages={693-701}
}

@Inbook{Canteaut2005,
author="Canteaut, Anne",
editor="van Tilborg, Henk C. A.",
title="Berlekamp-Massey algorithm",
bookTitle="Encyclopedia of Cryptography and Security",
year="2005",
publisher="Springer US",
address="Boston, MA    ",
pages="29--30",
isbn="978-0-387-23483-0",
doi="10.1007/0-387-23483-7_24",
url="https://doi.org/10.1007/0-387-23483-7_24"
}

@ARTICLE{massey, 
author={J. Massey}, 
journal={IEEE Transactions on Information Theory}, 
title={Shift-register synthesis and BCH decoding}, 
year={1969}, 
volume={15}, 
number={1}, 
pages={122-127}, 
keywords={BCH codes;Decoding;Shift-register sequences}, 
doi={10.1109/TIT.1969.1054260}, 
ISSN={0018-9448}, 
month={January},}



@book{Pohst:1989:AAN:76692,
 editor = {Pohst, M. and Zassenhaus, H.},
 title = {Algorithmic Algebraic Number Theory},
 year = {1989},
 isbn = {0-521-33060-2},
 publisher = {Cambridge University Press},
} 

@book{fulton1989algebraic,
  title={Algebraic curves: an introduction to algebraic geometry},
  author={Fulton, W.},
  isbn={9780201510102},
  lccn={89000372},
  series={Advanced book classics},
  url={https://books.google.ca/books?id=SEbvAAAAMAAJ},
  year={1989},
  publisher={Addison-Wesley Pub. Co., Advanced Book Program}
}

@article{GEKELE1991187,
title = "On finite Drinfeld modules",
journal = {Journal of Algebra},
volume = "141",
number = "1",
pages = "187 - 203",
year = "1991",
issn = "0021-8693",
author = "E.-U. Gekeler"
}

@article{Narayanan18,
  author    = {A. K. Narayanan},
  title     = {Polynomial factorization over finite fields by computing {E}uler-{P}oincar{\'{e}}
               characteristics of {D}rinfeld modules},
  journal   = {Finite Fields Appl.},
  volume    = {54},
  pages     = {335--365},
  year      = {2018},
}
@manual{sagemath,
  Key          = {SageMath},
  Author       = {{The Sage Developers}},
  Title        = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion x.y.z)},
  note         = {{\tt http://www.sagemath.org}},
  Year         = {YYYY},
}

@techreport{bostan:inria-00091441,
  TITLE = {{Fast algorithms for computing isogenies between elliptic curves}},
  AUTHOR = {Bostan, Alin and Salvy, Bruno and Morain, Francois and Schost, Eric},
  URL = {https://hal.inria.fr/inria-00091441},
  TYPE = {Research Report},
  PAGES = {28},
  YEAR = {2006},
  KEYWORDS = {Fast algorithms ; elliptic curves ; finite fields ; isogenies ; Schoof-Elkies-Atkin algorithm ; Newton iteration},
  PDF = {https://hal.inria.fr/inria-00091441/file/BoMoSaSc06.pdf},
  HAL_ID = {inria-00091441},
  HAL_VERSION = {v1},
}

@article{Gathen1990ConstructingNB,
  title={Constructing Normal Bases in Finite Fields},
  author={Joachim von zur Gathen and Mark Giesbrecht},
  journal={J. Symb. Comput.},
  year={1990},
  volume={10},
  pages={547-570}
}

@article{Bach:1993:FR:158390.158392,
 author = {Bach, Eric and Driscoll, James and Shallit, Jeffrey},
 title = {Factor Refinement},
 journal = {J. Algorithms},
 issue_date = {Sept. 1993},
 volume = {15},
 number = {2},
 month = sep,
 year = {1993},
 issn = {0196-6774},
 pages = {199--222},
 numpages = {24},
 url = {http://dx.doi.org/10.1006/jagm.1993.1038},
 doi = {10.1006/jagm.1993.1038},
 acmid = {158392},
 publisher = {Academic Press, Inc.},
 address = {Duluth, MN, USA},
} 

@article{GIESBRECHT1998463,
title = "Factoring in Skew-polynomial Rings over Finite Fields",
   JOURNAL = {J. Symb. Comput.},
volume = "26",
number = "4",
pages = "463 - 486",
year = "1998",
issn = "0747-7171",
doi = "https://doi.org/10.1006/jsco.1998.0224",
url = "http://www.sciencedirect.com/science/article/pii/S0747717198902243",
author = "M. Giesbrecht"
}
@unpublished{Elkies92,
	Author = {Elkies, N. },
	Note = {Draft},
	Title = {Explicit isogenies},
	Year = 1992
}
@unpublished{Atkin92b,
	Author = {Atkin, A. O. L.},
	Note = {Available at \url{http://listserv.nodak.edu/archives/nmbrthry.html}},
	Title = {The number of points on an elliptic curve modulo a prime ({II})},
	Year = 1992
}
@article {KaKiBs88,
    AUTHOR = {Kaminski, M. and Kirkpatrick, D.G. and Bshouty, N.H.},
     TITLE = {Addition requirements for matrix and transposed matrix products},
   JOURNAL = {J. Algorithms},
    VOLUME = {9},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {354--364},
}

@misc{salvy_neiger_schost_gyu, TITLE={On the complexity of modular composition of generic polynomials}, author={Salvy, Bruno and Neiger, Vincent and Schost, Eric and Gyu Hyun, Seung and Villard, Gilles}, year={2019}, month={Feb}}

@Misc{Musleh,
author={{Musleh, Yossef}},
title={Fast Algorithms for Finding the Characteristic Polynomial of a Rank-2 Drinfeld Module},
year={2018},
publisher="UWSpace",
url={http://hdl.handle.net/10012/13889}
}