@article{Cipolla:1903,
	key = "Cipolla 1903",
 	author = "M. Cipolla",
 	title = "Un metodo per la risoluzione della congruenza di 
		 secondo grado",
 	journal = RNAPOLI,
 	volume = 9,
 	pages = "154-163",
 	year = 1903}

@article{Cipolla:1904a,
	key = "Cipolla 1904a",
 	author = "M. Cipolla",
 	title = "Applicazione della teoria delle funzioni numeriche
		 del second'ordine alla risoluzione della congruenza di 
		 secondo grado",
 	journal = RNAPOLI,
 	volume = 10,
 	pages = "135-150",
 	year = 1904}

@article{Cipolla:1907a,
	key = "Cipolla 1907a",
 	author = "M. Cipolla",
 	title = "Sulla risoluzione apiristica delle congruenze binomie
		 secondo un modulo primo",
 	journal = MA,
 	volume = 63,
 	pages = "54-61",
 	year = "{\noopsort{1907a}}1907"}

@article{Cunningham:1908,
	key = "Cunningham 1908",
 	author = "A. Cunningham",
 	title = "Solution to problem 16189",
 	journal = MQET,
 	volume = 13,
 	pages = "19-20",
 	year = 1908}

@article{Cipolla:1907b,
	key = "Cipolla 1907b",
 	author = "M. Cipolla",
 	title = "Sulla risoluzione apiristica delle congruenze binomie",
 	journal = ARAL,
 	volume = 16,
 	pages = "603-608",
 	year = "{\noopsort{1907b}}1907"}

@article{Tonelli:1892,
	key = "Tonelli 1892",
 	author = "A. Tonelli",
 	title = "Sulla risoluzione della congruenza 
		 {$x^2 \equiv \mod{c} {p^\lambda}$}",
 	journal = ARAL,
 	volume = 1,
 	pages = "116-120",
 	year = 1892}

@article{Tonelli:1893,
	key = "Tonelli 1893",
 	author = "A. Tonelli",
 	title = "Sulla risoluzione della congruenza 
		 {$x^2 \equiv \mod{c} {p^\lambda}$}",
 	journal = ARAL,
 	volume = 2,
 	pages = "259-265",
	comment = "Tonelli 1892 and 1893 have the SAME TITLE!",
 	year = 1893}

@inproceedings{Yun:1977,
	key = "Yun 1977",
	author = "D. Y. Y. Yun",
	title = "Fast algorithm for rational function integration",
	booktitle = "Information Processing 77",
	publisher = "North-Holland",
	pages = "493-498",
	year = 1977}

@article{Rychlik:1924,
	key = "Rychlik 1924",
 	author = "K. Rychlik",
 	title = "Zur {B}ewertungstheorie der algebraischen {K\"o}rper",
 	journal = JFRAM,
 	volume = 153,
 	pages = "94-107",
	comment = "Pohst/Zassenhaus say 1923; check date.",
 	year = 1924}

@article{Cauchy:1847,
	key = "Cauchy 1847",
 	author = "A. Cauchy",
 	title = "M{\'e}moire sur les racines des {\'e}quivalences 
		 correspondantes {\`a} des modules quelconques 
		 premiers ou non premiers,
		 et sur les avantages que pr{\'e}sente l'emploi de ces 
		 racines dans la th{\'e}orie des nombres",
 	journal = CRASP,
 	volume = 25,
 	pages = "37-54",
	note = "Reprinted in {\it Oeuvres (1)}, Vol.~10, pp.~324--333",
 	year = 1847}

@article{Demeczky:1891,
	key = "Demeczky 1891",
 	author = "M. Demeczky",
 	title = "Ein {B}eitrag zur {T}heorie der {C}ongruenzen {h\"ohern}
	{G}rades",
 	journal = "Mathematische und {N}aturwissenschaftliche {B}erichte
		   aus {U}ngarn",
 	volume = 8,
 	pages = "51-59",
 	year = 1891}

@article{Lagrange:1769,
	key = "Lagrange 1769",
 	author = "J. L. Lagrange", 
 	title = "Sur la solution des probl{\`e}mes ind{\'e}termin{\'e}s
		 du second degr{\'e}",
 	journal = "Histoire de l'Acad{\'e}mie Royale des Sciences et
		   Belles-Lettres {\rm [Berlin]}",
	pages = "165-310",
 	volume = 23,
 	year = 1769,
	comment = "title page says 1767, article read 1768, printed 1769(!)",
	note = "Reprinted in {\it Oeuvres,} Vol.~2, pp.~377--535"
	}

@article{Legendre:1785,
	key = "Legendre 1785",
 	author = "A.-M. Legendre", 
 	title = "Recherches d'analyse ind{\'e}termin{\'e}e",
 	journal = "Histoire de l'Acad{\'e}mie Royale des Sciences
		   {\rm [Paris]}",
	pages = "465-559",
 	year = 1785}

@article{Mignotte:1980a,
	key = "Mignotte 1980a",
 	author = "M. Mignotte",
 	title = "Calcul des racines $d$-i{\`e}mes dans un corps fini",
 	journal = CRASP,
 	volume = 290,
 	pages = "A205-A206",
 	year = "{\noopsort{1980a}1980}"}

@article{Vandiver:1929,
	key = "Vandiver 1929",
 	author = "H. S. Vandiver",
 	title = "Algorithms for the solution of the quadratic congruence",
 	journal = AMM,
 	volume = 36,
 	pages = "83-86",
 	year = 1929}

@inproceedings{Williams:1972,
	key = "H. Williams 1972",
	author = "H. C. Williams",
	title = "Some algorithms for solving {$x^q \equiv \mod{N} {p}$}",
	booktitle = "Proc. 3rd Southeastern Conference on Combinatorics,
		     Graph Theory, and Computing",
	publisher = UM,
	address = "Winnipeg",
	pages = "451-462",
	note = "(= {\it Congr. Numer.} {\bf VII})",
	year = 1972}

@inproceedings{Berlekamp:1972,
	key = "Berlekamp 1972",
	author = "E. R. Berlekamp",
	title = "Factoring Polynomials",
	booktitle = "Proc. 3rd Southeastern Conference on Combinatorics,
		     Graph Theory, and Computing",
	publisher = UM,
	address = "Winnipeg",
	pages = "1-7",
	note = "(= {\it Congr. Numer.} {\bf VII})",
	year = 1972}

@inproceedings{Shanks:1972,
	key = "Shanks 1972",
	author = "D. Shanks",
	title = "Five number-theoretic algorithms",
	booktitle = "Proc. 2nd Southeastern Conference on Combinatorics,
		     Graph Theory, and Computing",
	publisher = UM,
	address = "Winnipeg",
	pages = "51-70",
	note = "(= {\it Congr. Numer.} {\bf VII})",
	year = 1972}

@article{Peralta:1986,
	key = "Peralta 1986",
 	author = "R. C. Peralta",
 	title = "A simple and fast probabilistic algorithm for computing
		 square roots modulo a prime number",
 	journal = IEEE-IT,
 	volume = "IT-32",
 	pages = "846-847",
 	year = 1986}

@article{Chang:1960,
	key = "Chang 1960",
 	author = "T.-H. Chang",
 	title = "{L\"o}sung der {K}ongruenz $x^2 \equiv \mod{a} {p}$
                 nach einem {P}rimzahlmodul $p = 4n+1$",
 	journal = MNACH,
 	volume = 22,
 	pages = "136-142",
 	year = 1960}

@inproceedings{Huang:1985,
	key = "Huang 1985",
	author = "M.-D. A. Huang",
	title = "Riemann hypothesis and finding roots over finite fields",
	booktitle = STOC85,
	publisher = ACM,
	pages = "121-130",
	year = 1985}

@inproceedings{Huang:1984a,
	key = "Huang 1984a",
	author = "M.-D. A. Huang",
	title = "Factorization of polynomials over finite fields and
		 factorization of primes in algebraic number fields",
	booktitle = STOC84,
	publisher = ACM,
	pages = "175-182",
 	year = "{\noopsort{1984a}}1984"}

@article{Evdokimov:1989,
	key = "Evdokimov 1989",
 	author = "S. A. Evdokimov",
 	title = "Factoring a solvable polynomial over a finite field
		 and generalized {R}iemann hypothesis",
	journal = "Zapiski Nauchnyck Seminarov Leningradskogo Otdeleniya
		   Mat. Inst. V.A. Steklova Akad. Nauk SSSR (LOMI)",
	volume = 176,
	year = 1989,
	pages = "104-117",
	note = "In Russian, with English summary"}

@article{Petr:1937,
	key = "Petr 1937",
 	author = "K. Petr",
 	title = "{\"U}ber die {R}edizibilit{\"a}t eines {P}olynoms mit
		 ganzzahligen {K}oeffizienten nach einem {P}rimzalhmodul",
 	journal = CPMF,
 	volume = 66,
 	pages = "85-94",
 	year = 1937}

@article{Ronyai:1989a,
	key = "R{\'o}nyai 1989a",
	author = "L. R{\'o}nyai",
	title = "Factoring polynomials modulo special primes",
 	journal = COMB,
 	volume = 9,
 	pages = "199-206",
 	year = 1989}

@inproceedings{Ronyai:1987,
	key = "R{\'o}nyai 1987",
	author = "L. R{\'o}nyai",
	title = "Factoring polynomials over finite fields",
	booktitle = FOCS87,
	publisher = IEEEPR,
	pages = "132-137",
 	year = 1987}

@inproceedings{Ronyai:1989b,
	key = "R{\'o}nyai 1989b",
	author = "L. R{\'o}nyai",
	title = "Galois groups and factoring polynomials over finite fields",
	booktitle = FOCS89,
	publisher = IEEEPR,
	pages = "99-104",
 	year = 1989}

@article{Mignotte&Schnorr:1988,
	key = "Mignotte and Schnorr 1988",
 	author = "M. Mignotte and C. Schnorr",
 	title = "Calcul d{\'e}terministe des racines d'un polyn{\^o}me
		 dans un corps fini",
 	journal = CRASP,
 	volume = 306,
 	pages = "467-472",
 	year = 1988}

@article{Schwarz:1956,
	key = "Schwarz 1956",
	author = "{\v S}. Schwarz",
	title = "On the reducibility of polynomials over a finite field",
 	journal = QJMOX,
 	volume = "(2) 7",
 	pages = "110-124",
 	year = 1956}

@article{Butler:1954,
	key = "Butler 1954",
	author = "M. C. R. Butler",
	title = "On the reducibility of polynomials over a finite field",
	comment = "same title as Schwarz 1956",
 	journal = QJMOX,
 	volume = "(2) 5",
 	pages = "102-107",
 	year = 1954}

@article{Schwarz:1939,
	key = "Schwarz 1939",
	author = "{\v S}. Schwarz",
	title = "Contribution {\`a} la reducibilit{\'e} des polyn{\^o}mes
		 dans la th{\'e}orie des congruences",
 	journal = VKCSN,
 	volume = 7,
 	pages = "1-7",
 	year = 1939}

@article{Camion:1983a,
	key = "Camion 1983a",
 	author = "P. F. Camion",
 	title = "Improving an algorithm for factoring polynomials over
		 a finite field and constructing large irreducible 
                 polynomials",
 	journal = IEEE-IT,
 	volume = "IT-29",
 	pages = "378-385",
 	year = "{\noopsort{1983a}}1983"}

@article{Camion:1983b,
	key = "Camion 1983b",
 	author = "P. F. Camion",
 	title = "A deterministic algorithm for factoring polynomials
		 of {$\Fq[X]$}",
 	journal = ADM,
 	volume = 17,
 	pages = "149-157",
 	year = "{\noopsort{1983b}}1983"}

@article{Mann:1974,
	key = "Mann 1974",
 	author = "H. B. Mann",
 	title = "The solution of equations by radicals",
 	journal = JALG,
 	volume = 29,
 	pages = "551-554",
 	year = 1974}

@article{Moenck:1977,
	key = "Moenck 1977",
 	author = "R. T. Moenck",
 	title = "On the efficiency of algorithms for polynomial factoring",
 	journal = MC,
 	volume = 31,
 	pages = "235-250",
 	year = 1977}

@techreport{Bach&von.zur.Gathen:1988,
	key = "Bach and von zur Gathen 1988",
	author = "E. Bach and Gathen, J. von zur",
	title = "Deterministic factorization of polynomials over special
		 finite fields",
	institution = "University of Wisconsin -- Madison, 
		       Computer Sciences Department",
	number = 799,
	month = "October",
	year = 1988}

@article{von.zur.Gathen&Kaltofen:1985,
	key = "von zur Gathen and Kaltofen 1985",
	author = "Gathen, J. von zur and E. Kaltofen",
	title = "Factorization of multivariate polynomials over finite fields",
	journal = MC,
	volume = 45,
	pages = "251-261",
	year = 1985}

@article{Mignotte:1980c,
	key = "Mignotte 1980c",
 	author = "M. Mignotte",
 	title = "Factorization of univariate polynomials: a statistical study",
 	journal = ASB,
 	volume = 14,
	number = 4,
 	pages = "41-44",
 	year = "{\noopsort{1980c}}1980"}

@article{McEliece:1969,
	key = "McEliece 1969",
 	author = "R. J. McEliece",
 	title = "Factorization of polynomials over finite fields",
 	journal = MC,
 	volume = 23,
 	pages = "861-867",
 	year = 1969}

@article{Shiva&Allard:1970,
	key = "Shiva and Allard 1970",
 	author = "S. G. S. Shiva and P. E. Allard",
 	title = "A few useful details about a known technique for factoring
		 {$1 + X^{2q-1}$}",
 	journal = IEEE-IT,
 	volume = "IT-16",
 	pages = "234-235",
 	year = 1970}

@article{van.Oorschot&Vanstone:1989,
	key = "van Oorschot and Vanstone 1989",
 	author = "Oorschot, P. C. van and S. A. Vanstone",
 	title = "A geometric approach to root finding in {$GF(q^m)$}",
 	journal = IEEE-IT,
 	volume = "35",
 	pages = "444-453",
 	year = 1989}

@article{Schwarz:1940,
	key = "Schwarz 1940",
 	author = "{\v S}. Schwarz",
 	title = "Sur le nombre des racines et des facteurs
		 irr{\'e}ductibles d'une congruence donn{\'e}e",
 	journal = CPMF,
 	volume = 69,
 	pages = "128-145",
 	year = 1940}

@inproceedings{Lazard:1982,
	key = "Lazard 1982",
	author = "D. Lazard",
	title = "On polynomial factorization",
	booktitle = "Computer Algebra, EUROCAM '82, European Computer Algebra Conference",
	publisher = SV,
	series = LNICS,
	volume = 144,
	editor = "J. Calmet",
	pages = "126-134",
 	year = 1982}

@inproceedings{Shoup:1988,
	key = "Shoup 1988",
	author = "V. Shoup",
	title = "New algorithms for finding irreducible polynomials over finite
		 fields",
	booktitle = FOCS88,
	publisher = IEEEPR,
	pages = "283-290",
	year = 1988}

@article{Shoup:1990a,
	key = "Shoup 1990a",
 	author = "V. Shoup",
 	title = "On the deterministic complexity of factoring polynomials
		 over finite fields",
 	journal = IPL,
 	volume = 33,
 	pages = "261-267",
 	year = "{\noopsort{1990a}}1990"}

@article{Gunji&Arnon:1981,
	key = "Gunji and Arnon 1981",
 	author = "H. Gunji and D. Arnon",
 	title = "On polynomial factorization over finite fields",
 	journal = MC,
 	volume = 36,
 	pages = "281-287",
	year = 1981}

@inproceedings{Stickelberger:1898,
	key = "Stickelberger 1898",
	author = "L. Stickelberger",
	title = "{\"U}ber eine neue {E}igenschaft der {D}iskriminanten
		algebraischer {Z}ahlk{\"o}rper",
	booktitle = "Verhandlungen des ersten internationalen
		     Mathematiker-Kongresses",
	publisher = "Teubner",
	address = "Leipzig",
	pages = "182-193",
 	year = 1898}

@techreport{Shoup:1989b,
	key = "Shoup 1989b",
	author = "V. Shoup",
	title = "A theorem on factoring polynomials over
		 finite fields",
	institution = "University of Wisconsin -- Madison, 
		       Computer Sciences Department",
	number = 866,
	month = "August",
 	year = "{\noopsort{1989b}1989}" }

@article{Presic:1970,
	key = "Pre{\v s}i{\'c} 1970",
 	author = "M. D. Pre{\v s}i{\'c}",
 	title = "A method for solving equations in finite fields",
 	journal = MV,
 	volume = 7,
 	pages = "507-509",
	year = 1970}

@article{Kempfert:1969,
	key = "Kempfert 1969",
 	author = "H. Kempfert",
 	title = "On the factorization of polynomials",
 	journal = JNT,
 	volume = 1,
 	pages = "116-120",
	comment = "basic ideas of the p-1 poly factoring method",
	year = 1969}

@book{Gregory:1980,
  	key = "Gregory 1980",
  	author = "R. T. Gregory",
  	title = "Error-Free Computation",
	address = "Huntington, NY",
  	publisher = "Krieger",
  	year = 1980}

@book{Strang:1980,
  	key = "Strang 1980",
  	author = "G. Strang",
  	title = "Linear Algebra and its Applications",
	address = NY,
  	publisher = AP,
  	year = 1980}

@book{Serret:1885,
  	key = "Serret 1885",
  	author = "J.-A. Serret",
  	title = "Cours d'Alg{\`e}bre Sup{\'e}rieure",
	address = "Paris",
  	publisher = "Gauthier-Villars",
  	year = 1885}

@book{Gregory&Krishnamurthy:1984,
  	key = "Gregory and Krishnamurthy 1984",
  	author = "R. T. Gregory and E. V. Krishnamurthy",
  	title = "Methods and Applications of Error-Free Computation",
	address = NY,
  	publisher = SV,
  	year = 1984}

@article{Mignotte:1975,
	key = "Mignotte 1975",
 	author = "M. Mignotte",
 	title = "Un algorithme sur la d{\'e}composition des polynomes
		 dans un corps fini",
 	journal = CRASP,
 	volume = 280,
 	pages = "A137-A139",
	comment = "uses Fq[A] instead of Fq[X]/(f); contains errors",
	year = 1969}

@article{Beard:1974,
	key = "Beard 1974",
 	author = "Beard, Jr., J. T. B.",
 	title = "Computing in {$GF(q)$}",
 	journal = MC,
 	volume = 28,
 	pages = "1159-1166",
	comment = "to factor f in k[X], find 0-divisors mod f; exponential",
	year = 1974}

@book{Hensel:1908,
  	key = "Hensel 1908",
  	author = "K. Hensel",
  	title = "Theorie der Algebraischen Zahlen",
	address = "Leipzig",
  	publisher = "Teubner",
  	year = 1908}

@article{Boffgen&Reichert:1987,
	key = "B{\"o}ffgen and Reichert 1987",
 	author = "R. B{\"o}ffgen and M. A. Reichert",
 	title = "Computing the decomposition of primes $p$ and $p$-adic
		 absolute values in semi-simple algebras over {$\openQ$}",
 	journal = JSC,
 	volume = 4,
 	pages = "3-10",
	year = 1987}

@techreport{Golomb&Welch&Hales:1959,
	key = "Golomb, Welch, and Hales 1959",
	author = "S. W. Golomb and L. R. Welch and A. Hales",
	title = "On the factorization of trinomials over {$GF(2)$}",
	institution = "Jet Propulsion Laboratory",
	number = "20-189",
	month = "July",
	note = "Reprinted as Chapter 5 of Golomb [1967]\nocite{Golomb:1967}",
	year = 1959}

@article{Camion:1980,
	key = "Camion 1980",
 	author = "P. F. Camion",
 	title = "Un algorithme de construction des idempotents primitifs
		 {d'id\'eaux} d'alg{\`e}bres sur {$\Fq$}",
 	journal = CRASP,
 	volume = 291,
 	pages = "A479-A482",
 	year = 1980}

@article{Itoh:1987,
	key = "Itoh 1987",
 	author = "T. Itoh",
 	title = "Efficient probabilistic algorithm for solving quadratic
		 equations over finite fields",
 	journal = ELETT,
 	volume = 23,
 	pages = "869-870",
 	year = 1987}

@inproceedings{BenOr:1981,
	key = "Ben-Or 1981",
	author = "M. Ben-Or",
	title = "Probabilistic algorithms in finite fields",
	booktitle = FOCS81,
	publisher = IEEEPR,
	pages = "394-398",
	year = 1981}

@article{Zierler:1974,
	key = "Zierler 1974",
 	author = "N. Zierler",
 	title = "A conversion algorithm for logarithms on {$GF(2^n)$}",
 	journal = JPAA,
 	volume = 4,
 	pages = "353-356",
 	year = 1974}

@article{LenstraH:1991a,
	key = "H. W. Lenstra 1991a",
 	author = "Lenstra, Jr., H. W.",
 	title = "Finding isomorphisms between finite fields",
 	journal = MC,
	volume = 56,
	year = "{\noopsort{1991a}}1991",
	pages = "329-347"}

@inproceedings{Chistov:1991,
	key = "Chistov 1991",
	author = "A. L. Chistov",
	title = "Efficient factoring polynomials [sic] over local fields and its
applications",
	booktitle = ICM90,
	editor = "I. Satake",
	publisher = SV,
	pages = "1509-1519",
	year = 1991}

@article{Ronyai:1992,
	key = "R{\'o}nyai 1992",
	author = "L. R{\'o}nyai",
	title = "Galois groups and factoring polynomials over finite fields",
	journal = SIAMJDM,
	volume = 5,
	year = 1992,
	pages = "345-365"}

@incollection{van.Oorschot&Vanstone:1990a,
	key = "van Oorschot and Vanstone 1990a",
	author = "Oorschot, P. C. van and S. A. Vanstone",
	title = "Some geometric aspects of root finding in ${GF(q^m)}$",
	booktitle = "Finite Geometries and Combinatorial Designs",
	series = "Contemporary Mathematics",
	volume = 111,
	editor = "E. S. Kramer and S. S. Magliveras",
	year = "{\noopsort{1990a}}1990",
	pages = "303-307",
	publisher = AMS}

@book{Greene&Knuth:1990,
  	key = "Greene and Knuth 1990",
  	author = "D. H. Greene and D. E. Knuth",
  	title = "Mathematics for the Analysis of Algorithms",
	edition = "3rd",
	address = "Boston",
  	publisher = "Birkh{\"a}user",
  	year = 1990}

@article{Pellet:1878,
	key = "Pellet 1878",
 	author = "A.-E. Pellet",
 	title = "Sur la d{\'e}composition d'une fonction enti{\`e}re
		 en facteurs irr{\'e}ductibles suivant un module premier $p$",
 	journal = CRASP,
 	volume = 86,
 	pages = "1071-1072",
 	year = 1878}

@unpublished{Atkin:1992,
	key = "Atkin 1992",
	author = "A. O. L. Atkin",
	title = "Square roots and cognate matters modulo {$p=8n+5$}",
	year = 1992,
	note = "Unpublished manuscript"}

@unpublished{Bumby:1989,
	key = "Bumby 1989",
	author = "R. T. Bumby",
	title = "How not to compute square roots mod $p$ with applications",
	year = 1989,
	note = "Unpublished manuscript"}

@article{vonzurGathen:1984c,
	key = "von zur Gathen 1984c",
	author = "Gathen, J. von zur",
	title = "Hensel and {Newton} methods in valuation rings",
	journal = MC,
	volume = 42,
	pages = "637-661",
	year = "{\noopsort{1984c}}1984"}

@article{Menezes&van.Oorschot&Vanstone:1992,
	key = "Menezes, van Oorschot, and Vanstone 1992",
	author = "Menezes, A. J. and Oorschot, P. C. van and Vanstone, S. A.",
	title = "Subgroup refinement algorithms for root finding in
		 {$GF(q)$}",
	journal = SIAMJC,
	volume = 21,
	pages = "228-239",
	year = "1992"}

@article{Camion:1982,
	key = "Camion 1982",
 	author = "P. F. Camion",
 	title = "Un algorithme de construction des idempotents primitifs
		 {d'id\'eaux} d'alg{\`e}bres sur {$\Fq$}",
 	journal = ADM,
 	volume = 12,
 	pages = "55-63",
 	year = 1982}

@article{Chistov:1987,
	key = "Chistov 1987",
	author = "A. L. Chistov",
	title = "Efficient factorization of polynomials over local fields",
	journal = DAN,
	volume = 293,
	year = 1987,
	pages = "1073-1077",
	note = "In Russian.  
                English translation in 
		{\it Soviet Math. Doklady} {\bf 35} (1987), 430--433"}

@article{Grigoriev&Chistov:1984,
	key = "Grigoriev and Chistov 1984",
	author = "D. Yu. {\noopsort{Grigoriev}}Grigor\'{}ev and A. L. Chistov",
	title = "Fast decomposition of polynomials into irreducible ones
		 and the solution of systems of algebraic equations",
	journal = DAN,
	volume = 275,
	year = "1984",
	pages = "1302-1306",
	note = "In Russian.  English translation in 
		{\it Sov.\ Math.\ Doklady} {\bf 29} (1984), 380--383"}

@article{Semaev:1988,
	key = "Semaev 1988",
	author = "I. A. Semaev",
	title = "Construction of polynomials irreducible over a finite
		 field with linearly independent roots",
	journal = MS,
	volume = 135,
	year = 1988,
	pages = "520-532",
	note = "In Russian.  
                English translation in 
		{\it Math. USSR Sbornik} {\bf 63} (1989), 507--519"}

@article{Carlitz:1953a,
	key = "Carlitz 1953a",
 	author = "L. Carlitz",
 	title = "A theorem of {Stickelberger}",
 	journal = MSCAND,
 	volume = 1,
 	pages = "82-84",
 	year = "{\noopsort{1953a}}1953"}

@article{Itoh:1989,
	key = "Itoh 1989",
 	author = "T. Itoh",
 	title = "An efficient probabilistic algorithm for solving quadratic
		 equation over finite fields",
 	journal = ECJ,
 	volume = 72,
 	pages = "88-96",
 	year = 1989}

@article{Scorza:1926,
	key = "Scorza 1926",
 	author = "G. Scorza",
 	title = "La risoluzione apiristica delle congruenze binomie
		 e la formula di interolazione di {L}agrange",
 	journal = ARAL,
	series = 6,
 	volume = 3,
 	pages = "390-394",
 	year = 1926}

@article{Arwin:1920,
	key = "Arwin 1920",
 	author = "A. Arwin",
 	title = "{\" U}ber {K}ongruenzen von dem f{\" u}nften und
		 h{\" o}heren {G}raden nach einem {P}rimzahlmodulus",
 	journal = AMAF,
 	volume = 14,
 	pages = "1-46",
 	year = 1920}

@article{Schwarz:1946,
	key = "Schwarz 1946",
	author = "{\v S}. Schwarz",
	title = "P{\v r}{\' \i}sp{\v e}vek k reducibilit{\v e} 
		binomick{\' y}ch kongruenc{\' \i}",
 	journal = CPMF,
 	volume = 71,
 	pages = "21-31",
 	year = 1946,
	note = "In Czech. French summary entitled
		``Contribution {\` a} la reductibilit{\' e} des congruences
		binomiques''",
	comment = "it's really a lone k in the title!"}

@article{Schwarz:1949,
	key = "Schwarz 1949",
	author = "{\v S}. Schwarz",
	title = "On the reducibility of binomial congruences and on the
		 bound of the least integer belonging to a given exponent
		 mod $p$",
 	journal = CPMF,
 	volume = 74,
 	pages = "1-16",
 	year = 1949}

@article{Sidelnikov:1987,
	key = "{Sidel\'{}nikov} 1987",
	author = "V. M. {Sidel\'{}nikov}",
	title = "On normal bases of a finite field",
	journal = MS,
	volume = 133,
	year = 1987,
	pages = "497-507",
	note = "In Russian.  
                English translation in 
		{\it Math. USSR Sbornik} {\bf 61} (1988), 485--494"}

@book{Shparlinski:1992,
  	key = "Shparlinski 1992",
  	author = "I. E. Shparlinski",
  	title = "Computational and Algorithmic Problems in Finite Fields",
	address = "Boston",
  	publisher = KLUWER,
  	year = 1992}

@article{Thurston:1943,
	key = "Thurston 1943",
 	author = "H. S. Thurston",
 	title = "The solution of $p$-adic equations",
 	journal = AMM,
 	volume = "50",
 	pages = "142-148",
 	year = 1943}

@article{Carlitz:1953b,
	key = "Carlitz 1953b",
 	author = "L. Carlitz",
 	title = "A theorem on congruences",
 	journal = JIMS,
 	volume = 17,
 	pages = "43-45",
 	year = "{\noopsort{1953b}}1953"}

@incollection{Lewis:1969,
	key = "Lewis 1969",
	author = "D. J. Lewis",
	title = "Diophantine equations: $p$-adic methods",
	booktitle = "Studies in Number Theory",
	editor = "W. J. LeVeque",
	publisher = "Mathematical Association of America",
	year = 1969,
	pages = "25-75"}

@article{Schwarz:1988,
	key = "Schwarz 1988",
	author = "{\v S}. Schwarz",
	title = "Construction of normal bases in cyclic extensions of a field",
 	journal = CZMJ,
 	volume = "38",
 	pages = "291-312",
 	year = 1988}

@inproceedings{Chistov:1984a,
	key = "Chistov 1984a",
	author = "A. L. Chistov",
	title = "Polynomial time construction of a finite field",
 	year = "{\noopsort{1984a}}1984",
	booktitle = "Abstracts of Lectures at 7th All-Union Conference
		     in Mathematical Logic, Novosibirsk",
	pages = "196",
	note = "Not available to us.  Cited in Shoup [1993a]"}

@article{Blokh:1964,
	key = "Blokh 1964",
	author = "E. L. Blokh",
	title = "Method of decoding {B}ose-{C}haudhuri triple error correcting
		 codes",
 	journal = TK,
 	volume = "3",
 	pages = "30-37",
 	year = 1964,
	note = "In Russian.  English translation in
		{\it Engineering Cybernetics} {\bf 3} (1964), 22--32"}

@article{Cipolla:1930,
	key = "Cipolla 1930",
 	author = "M. Cipolla",
 	title = "Formule di risoluzione apiristica delle equazioni di
		 grado qualunque in un corpo finito",
 	journal = RPALERMO,
 	volume = 54,
 	pages = "199-206",
 	year = 1930}

@article{Chen&Li:1977,
	key = "J. Chen and Li 1977",
 	author = "J. M. Chen and X. M. Li",
 	title = "The structure of the polynomials over the finite field
		 defined by {$Q[f]$}-matrix",
 	journal = ACTAMS,
 	volume = 20,
 	pages = "294-297",
 	year = 1977,
 	note = "In Chinese.  Reviewed in {\it Math. Reviews}
                {\bf 80} (1980), \#12021."}

@article{Mirimanoff&Hensel:1905,
	key = "Mirimanoff and Hensel 1905",
	author = "D. Mirimanoff and K. Hensel",
	title = "Sur la relation {$\jsym D p = (-1)^{n-h}$} et la loi
	       de r{\'e}ciprocit{\'e}",
	journal = JFRAM,
	volume = 129,
	year = 1905,
	pages = "86-87"}	

@article{Polkinghorn:1966,
	key = "Polkinghorn 1966",
 	author = "Polkinghorn, Jr., F.",
	title = "Decoding of double and triple error correcting 
		 {B}ose-{C}haudhuri codes",
 	journal = IEEE-IT,
 	volume = "IT-12",
 	pages = "480-481",
 	year = 1966}

@article{Feit&Rees:1978,
	key = "Feit and Rees 1978",
 	author = "W. Feit and E. Rees",
	title = "A criterion for a polynomial to factor completely
		 over the integers",
 	journal = BLMS,
 	volume = "10",
 	pages = "191-192",
 	year = 1978}

@article{Zassenhaus:1968,
	key = "Zassenhaus 1968",
 	author = "H. Zassanhaus",
 	title = "{\"U}ber die {F}undamentalkonstruktionen der endlichen
		 {K\"o}rpertheorie",
 	journal = JDMV,
 	volume = 70,
 	pages = "177-181",
 	year = 1968}

@article{Dynkin&Agaronov:1970,
	key = "{Dyn'kin} and Agaronov 1970",
 	author = "V. N. Dyn'kin and D. A. Agaronov",
	title = "Method of expanding polynomials in a finite field",
 	journal = PPI,
 	volume = "6",
 	pages = "82-86",
 	year = 1970,
	note = "In Russian.  English translation in
		{\it Problems of Information Transmission} {\bf 6} (1973), 
		257--260"}

@article{Tu:1974,
	key = "T'u 1974",
 	author = "K. C. T'u",
 	title = "The structure of {$Q$}-matrices and the reducibility of
		 polynomials over a {G}alois field",
 	journal = ACTAMS,
 	volume = 17,
 	pages = "46-59",
 	year = 1974,
 	note = "In Chinese.  Reviewed in {\it Math. Reviews}
                {\bf 56} (1978), \#327."}

@unpublished{Bach&von.zur.Gathen&Lenstra:1994,
	key = "Bach, von zur Gathen, and Lenstra 1994",
	author = "E. Bach and Gathen, J. von zur and Lenstra, Jr., H. W.",
	title = "Deterministic factorization of polynomials over special
		 finite fields",
	note = "Unpublished manuscript, dated June",
	year = 1994}

@article{Varshamov:1984,
	key = "Varshamov 1984",
	author = "R. R. Varshamov",
	title = "A general method of synthesizing irreducible polynomials
		 over {G}alois fields",
	journal = DAN,
	volume = 275,
	year = 1984,
	pages = "1041-1044",
	note = "In Russian.  
                English translation in 
		{\it Soviet Math. Doklady} {\bf 29} (1984), 334--336"}

@unpublished{MillerV:1992a,
	key = "V. Miller 1992a",
	author = "V. S. Miller",
	title = "On the factorization method of {N}iederreiter",
	year = "{\noopsort{1992a}}1992",
	note = "Unpublished manuscript"}

@inproceedings{AKLenstra:1983,
	key = "A. Lenstra 1983",
	author = "A. K. Lenstra",
	title = "Factoring multivariate polynomials over finite fields",
	booktitle = STOC83,
	publisher = ACM,
	pages = "189-192",
 	year = 1983}

@article{Grigoriev:1984,
	key = "Grigoriev 1984",
	author = "D. Yu. {\noopsort{Grigoriev}}Grigor\'{}ev",
	title = "Factorization of polynomials over a finite field and
		 the solution of systems of algebraic equations",
	journal = ZNSLOMI,
	volume = 137,
	year = 1984,
	pages = "20-79",
	note = "In Russian with English summary.  
                English translation in {\it J. Soviet Math.} {\bf 34}
		(1986), 1762-1803"}
		
@article{Chistov:1984b,
	key = "Chistov 1984b",
	author = "A. L. Chistov",
	title = "An algorithm of polynomial complexity for factoring
		 polynomials, and determination of the components of
	  	 a variety in subexponential time",
	journal = ZNSLOMI,
	volume = 137,
	year = "{\noopsort{1984b}}1984",
	pages = "124-188",
	note = "In Russian with English summary.  
                English translation in {\it J. Soviet Math.} {\bf 34}
		(1986), 1838-1882"}
		
@article{Hensel:1904,
	key = "Hensel 1904",
 	author = "K. Hensel",
 	title = "Neue {G}rundlagen der {A}rithmetik",
 	journal = JFRAM,
 	volume = 127,
 	pages = "51-84",
 	year = 1904}

@inproceedings{Menezes&van.Oorschot&Vanstone:1988,
	key = "Menezes, van Oorschot, and Vanstone 1988",
 	author = "A. J. Menezes and Oorschot, P. C. van and S. A. Vanstone",
	title = "Some computational aspects of root finding in {$GF(q^m)$}",
	booktitle = ISSAC88,
	publisher = SV,
	editor = "D. Gianni",
	pages = "259-270",
	year = 1988,
	comment = "Lecture Notes in Computer Science 358"}

@article{Tarmarkine&Friedmann:1906,
	key = "Tamarkine and Friedmann 1906",
	author = "J. Tamarkine and A. Friedmann",
	title = "Sur les congruences du second degr{\'e} et les nombres
		 de {B}ernoulli",
	journal = MA,
	pages = "409-412",
	volume = 62,
	year = 1906}

@article{Lloyd&Remmers:1967,
	key = "Lloyd and Remmers 1967",
	author = "D. B. Lloyd and H. Remmers",
	title = "Polynomial factor tables over finite fields",
	journal = MALG,
	pages = "85-99",
	volume = 2,
	year = 1967}

@article{Boos:1948,
	key = "Boos 1948",
	author = "P. Boos",
	title = "Divisibilit{\'e} des polyn{\^o}mes relativement aux
		 puissances d'un nombre entier",
	journal = BSMF,
	pages = "65-78",
	volume = 76,
	year = 1948}

@article{MorrisonD:1968,
	key = "D. Morrison 1968",
	author = "D. R. Morrison",
	title = "Arithmetic in {Galois} fields of characteristic 2",
	journal = MALG,
	pages = "176-184",
	volume = 3,
	year = 1968}

@article{Fleischmann:1993,
	key = "Fleischmann 1993",
 	author = "P. Fleischmann",
 	title = "Connections between the algorithms of {B}erlekamp
		 and {N}iederreiter for factoring polynomials over
		 {$\Fq$}",
 	journal = LAA,
 	volume = 192,
 	pages = "101-108",
 	year = 1993}

@article{Niederreiter:1993d,
	key = "Niederreiter 1993d",
 	author = "H. Niederreiter",
 	title = "Factorization of polynomials and some linear-algebra
		 problems over finite fields",
 	journal = LAA,
 	volume = 192,
 	pages = "301-328",
 	year = "{\noopsort{1993d}}1993"}

@unpublished{Knopfmacher&Warlimont:1995b,
	key = "Knopfmacher and Warlimont 1995b",
	author = "A. Knopfmacher and R. Warlimont",
	title = "Counting permutations and polynomials with a restricted
		 factorization pattern",
	year = "{\noopsort{1995b}}1995",
	note = "To appear, {\it Australasian J.\ Combinatorics}"}

@article{Knopfmacher&Warlimont:1995a,
	key = "Knopfmacher and Warlimont 1995a",
	author = "A. Knopfmacher and R. Warlimont",
	title = "Distinct degree factorizations for polynomials over a
		 finite field",
	year = "{\noopsort{1995a}}1995",
	journal = TAMS,
	volume = 347,
	pages = "2235-2243"}

@phdthesis{Shoup:1989a,
	key = "Shoup 1989a",
	author = "Shoup, V.",
	title = "Removing randomness from computational number theory",
	school = "Computer Sciences Department, University of Wisconsin",
 	year = "{\noopsort{1989a}1989}" }

@article{Artin&Schreier:1927,
	key = "Artin and Schreier 1927",
 	author = "E. Artin and O. Schreier",
 	title = "Eine {K}ennseichnung der reell abgeschlossenen {K\"orper}",
 	journal = MSHAM,
 	volume = 5,
 	pages = "225-231",
 	year = 1927,
	note = "Reprinted in {\it Collected Papers}, pp.~289--295"}
	}

@article{Lehmer&Lehmer:1984,
	key = "D. H. Lehmer and E. Lehmer 1984",
	author = "D. H. Lehmer and E. Lehmer",
	title = "The sextic period polynomial",
	journal = PJM,
	volume = 111,
	year = 1984,
	pages = "341-355"}

@article{ELehmer:1988,
	key = "E. Lehmer 1988",
	author = "E. Lehmer",
	title = "Connection between {G}aussian periods and cyclic units",
	journal = MC,
	volume = 50,
	year = 1988,
	pages = "535-541"}

@inproceedings{Adleman&HLenstra:1986,
	key = "Adleman and H. W. Lenstra 1986",
	author = "L. M. Adleman and Lenstra, Jr., H. W.",
	title = "Finding irreducible polynomials over finite fields",
	booktitle = STOC86,
	publisher = ACM,
	pages = "350-355",
	year = 1986,
	comment = "was L. Adleman in paper title"}

@article{Evans:1983,
	key = "Evans 1983",
	author = "R. J. Evans",
	title = "The octic period polynomial",
	journal = PAMS,
	volume = 87,
	year = 1983,
	pages = "389-393"}

@article{Berndt&Evans:1981,
	key = "Berndt and Evans 1981",
	author = "B. C. Berndt and R. J. Evans",
	title = "The determination of {G}auss sums",
	journal = BAMS,
	volume = 5,
	year = 1981,
	pages = "107-129"}

@misc{Cauchy:1829,
	key = "Cauchy 1829",
 	author = "A. Cauchy",
 	title = "Sur la r{\'e}solution des {\'e}quivalences dont les
		 modules se r{\'e}duisent {\'a} des nombres premiers",
	note = "{\it Exercices Math.} {\bf 4} (1829) 253--292.  Reprinted in
	{\it Oeuvres (2)}, Vol.~9, pp.~298--341"}

@book{Aitken:1949,
  	key = "Aitken 1949",
  	author = "A. C. Aitken",
  	title = "Determinants and Matrices",
	address = "Edinburgh",
  	publisher = "Oliver and Boyd",
  	year = 1949}

@article{Shepp&Lloyd:1966,
	key = "Shepp and Lloyd 1966",
 	author = "L. A. Shepp and S. P. Lloyd",
 	title = "Ordered cycle lengths in a random permutation",
 	journal = TAMS,
 	volume = 121,
 	pages = "340-357",
 	year = 1966}

@article{Knopfmacher:1994,
	key = "Knopfmacher 1994",
 	author = "A. Knopfmacher",
 	title = "Enumerating basic properties of polynomials over a finite
		 field",
 	journal = SAJS,
 	volume = 90,
 	pages = "1-2",
 	year = 1994}

@inproceedings{Bach:1987,
	key = "Bach 1987",
	author = "E. Bach",
	title = "Realistic analysis of some randomized algorithms",
	booktitle = STOC87,
	publisher = ACM,
	pages = "453-461",
	year = 1987}

@article{Calmet:1985,
	key = "Calmet 1985",
 	author = "J. Calmet",
 	title = "Algebraic algorithms in {$GF(q)$}",
 	journal = DM,
 	volume = 56,
 	pages = "101-109",
 	year = 1985}

@inproceedings{Poli&Gennero:1988,
	key = "Poli and Gennero 1988",
	author = "A. Poli and M. C. Gennero",
	title = "Fast16: a software program for factorising polynomials
		 over large {$GF(p)$}",
	booktitle = AAECC4,
	publisher = SV,
	editor = "T. Beth and M. Clausen",
	pages = "139-156",
	series = LNICS,
        volume = 307,
	year = 1988}

@inproceedings{Camion:1989,
	key = "Camion 1989",
	author = "P. F. Camion",
	title = "An iterative {E}uclidean algorithm",
	booktitle = AAECC5,
	publisher = SV,
	editor = "L. Huguet and A. Poli",
	pages = "88-128",
	series = LNICS,
        volume = 356,
	year = 1989}

@article{Lugiez:1985,
	key = "Lugiez 1985",
 	author = "D. Lugiez",
 	title = "Fast {H}ensel's lifting implementation using partial
		 fraction decomposition",
 	journal = DM,
 	volume = 56,
 	pages = "217-225",
 	year = 1985}

@article{Carlitz:1930,
	key = "Carlitz 1930",
 	author = "L. Carlitz",
 	title = "The arithmetic of polynomials in a {G}alois field",
 	journal = PNAS,
 	volume = 17,
 	pages = "120-122",
 	year = 1930}

@incollection{Gao&von.zur.Gathen:1994,
	key = "Gao and von zur Gathen 1994",
	author = "S. Gao and Gathen, J. von zur",
	title = "{Berlekamp's} and {Niederreiter's} polynomial 
factorization algorithms",
	booktitle = "Finite Fields:  Theory, Applications, and Algorithms",
	series = "Contemporary Mathematics",
	volume = 168,
	publisher = AMS,
	year = 1994,
	editor = "G. L. Mullen and P. J.-S. Shiue",
	pages = "101-116"}

@incollection{Niederreiter:1994b,
	key = "Niederreiter 1994b",
	author = "H. Niederreiter",
	title = "New deterministic factorization algorithms for polynomials
over finite fields",
	booktitle = "Finite Fields:  Theory, Applications, and Algorithms",
	series = "Contemporary Mathematics",
	volume = 168,
	publisher = AMS,
	year = "{\noopsort{1994b}}1994",
	editor = "G. L. Mullen and P. J.-S. Shiue",
	pages = "251-268"}

@article{Rothstein&Zassenhaus:1994,
	key = "Rothstein and Zassenhaus 1994",
 	author = "M. Rothstein and H. Zassenhaus",
 	title = "Deterministic analysis of aleatoric methods of
		 polynomial factorization over finite fields",
 	journal = JNT,
 	volume = 47,
 	pages = "20-42",
	year = 1994}

@article{Chistov:1989,
        key = "Chistov 1989",
        author = "A. L. Chistov",
        title = "The complexity of constructing the ring of integers of a 
                 global field",
        journal = DAN,
        volume = 306,
        year = 1989,
        pages = "1063-1067",
        note = "In Russian.
                English translation in
                {\it Soviet Math.\ Doklady} {\bf 39} (1989), 597--600"}