@book{Lang:1965,
  	key = "Lang 1965",
  	author = "S. Lang",
  	title = "Algebra",
  	publisher = AW,
  	year = 1965}

@book{Artin:1942,
  	key = "Artin 1942",
  	author = "E. Artin",
  	title = "Galois Theory",
  	publisher = "University of Notre Dame Press",
  	year = 1942,
	series = "Notre Dame Mathematical Lectures",
	volume = 2}

@book{van.der.Waerden:1970,
  	key = "van der Waerden 1970",
  	author = "Waerden, B. L. van der",
  	title = "Algebra",
  	publisher = "Ungar",
	edition = "7th",
  	year = 1970,
	note = "2 volumes",
	comment = "7th edn. -- 2 volumes --
                  might want to cite first edition too"}

@book{Lidl&Niederreiter:1983,
  	key = "Lidl and Niederreiter 1983",
  	author = "R. Lidl and H. Niederreiter",
  	title = "Finite Fields",
  	publisher = CUP,
  	year = 1983}

@book{Peterson&Weldon:1972,
  	key = "W. Peterson and Weldon 1972",
  	author = "W. W. Peterson and Weldon, Jr., E. J.",
  	title = "Error-correcting Codes",
  	publisher = MIT,
  	year = 1972,
	comment = "2nd edition"}

@book{Albert:1961,
  	key = "Albert 1961",
  	author = "A. A. Albert",
  	title = "Fundamental Concepts of Higher Algebra",
  	publisher = UCP,
  	year = 1961,
	comment = "1st Phoenix edition"}

@book{Berlekamp:1968,
  	key = "Berlekamp 1968",
  	author = "E. R. Berlekamp",
  	title = "Algebraic Coding Theory",
  	publisher = MH,
  	year = 1968,
	comment = "Reprinted by Aegean Park Press"}

@book{Ireland&Rosen:1990,
  	key = "Ireland and Rosen 1990",
  	author = "K. Ireland and M. Rosen",
  	title = "A Classical Introduction to Modern Number Theory",
  	publisher = SV,
	edition = "2nd",
  	year = 1990}

@article{Herstein:1987,
	key = "Herstein 1987",
 	author = "I. N. Herstein",
 	title = "A remark on finite fields",
 	journal = AMM,
 	volume = 94,
 	pages = "290-291",
 	year = 1987}

@article{Gordon:1976,
	key = "J. Gordon 1976",
 	author = "J. A. Gordon",
 	title = "Very simple method to find the minimum polynomial
		 of an arbitrary nonzero element of a finite field",
 	journal = ELETT,
 	volume = 12,
 	pages = "663-664",
 	year = 1976}

@article{Dedekind:1857,
	key = "Dedekind 1857",
 	author = "J. W. R. Dedekind",
 	title = "{Abri\ss} einer {Theorie} der h{\"o}hern {Congruenzen} in {Bezug}
		 auf einen reellen {Primzahl-Modulus}",
 	journal = JFRAM,
 	volume = 54,
 	pages = "1-26",
 	year = 1857,
	note = "Reprinted in {\it Werke,} Vol.~1, pp.~40--66"
	}

@article{Collins:1969,
	key = "G. Collins 1969",
 	author = "G. E. Collins",
 	title = "Computing multiplicative inverses in {$GF(p)$}",
 	journal = MC,
 	volume = 23,
 	pages = "197-200",
 	year = 1969}

@article{Collins:1971,
	key = "G. Collins 1971",
 	author = "G. E. Collins",
 	title = "The calculation of multivariate polynomial resultants",
 	journal = JACM,
 	volume = 18,
 	pages = "515-532",
 	year = 1971}

@article{Artin:1924a,
	key = "Artin 1924a",
 	author = "E. Artin",
 	title = "Quadratische {K{\"o}rper} im {Gebiete} der h{\"o}heren 
                 {Kongruenzen}",
 	journal = MZ,
 	volume = 19,
 	pages = "153-246",
 	year = "{\noopsort{1924a}}1924",
	note = "Reprinted in {\it Collected Papers,} pp.~1--94"}

@article{Kuhne:1902,
	key = "K{\"u}hne 1902",
	author = "H. K{\"u}hne",
	title = "Eine {Wechselbeziehung} zwischen {Functionen} mehrerer
	         {Unbestimmten}, die zu {R}eciprocit{\"a}ts\-gesetzen
		 f{\"u}hrt",
	journal = JFRAM,
	volume = 124,
	pages = "121-133",
	year = 1902}

@article{Ore:1934,
	key = "Ore 1934",
	author = "O. Ore",
	title = "Contributions to the theory of finite fields",
	journal = TAMS,
	volume = 36,
	pages = "243-274",
	year = 1934}

@article{Carlitz:1932,
	key = "Carlitz 1932",
	author = "L. Carlitz",
	title = "The arithmetic of polynomials in a {Galois} field",
	journal = AJM,
	volume = 54,
	pages = "39-50",
	year = 1932}

@article{Carlitz:1931,
	key = "Carlitz 1931",
	author = "L. Carlitz",
	title = "The arithmetic of polynomials in a {Galois} field",
	journal = NAS,
	volume = 17,
	pages = "120-122",
	year = 1931}

@article{Carlitz:1942,
	key = "Carlitz 1942",
	author = "L. Carlitz",
	title = "Some topics in the arithmetic of polynomials",
	journal = BAMS,
	volume = 48,
	pages = "679-691",
	year = 1942}

@article{Claasen:1977,
	key = "Claasen 1977",
	author = "H. L. Claasen",
	title = "The group of units in {$GF(q)[x]/(a(x))$}",
	journal = PKNAW,
	volume = 80,
	pages = "245-255",
	year = 1977,
	note = "(= {\it Indag. Math.} {\bf 39})"}

@book{McDonald:1974,
  	key = "McDonald 1974",
  	author = "B. McDonald",
  	title = "Finite Rings with Identity",
  	publisher = MD,
  	year = 1974}

@book{Serre:1979,
  	key = "Serre 1979",
  	author = "J.-P. Serre",
  	title = "Local Fields",
  	publisher = SV,
  	year = 1979}

@article{Berlekamp&Mc.Eliece&van.Tilborg:1978,
	key = "Berlekamp, McEliece, and van Tilborg 1978",
	author = "E. R. Berlekamp and R. J. McEliece and H. C. A. van Tilborg",
	title = "On the inherent intractability of certain coding problems",
	journal = IEEE-IT,
	volume = "IT-24",
	pages = "384-386",
	year = 1978}

@article{Berlekamp&Rumsey&Solomon:1967,
	key = "Berlekamp, Rumsey, and Solomon 1967",
	author = "E. R. Berlekamp and H. Rumsey and G. Solomon",
	title = "On the solution of algebraic equations over finite fields",
	journal = ICTRL,
	volume = "10",
	pages = "553-564",
	year = 1967}

@article{Allouche:1987,
	key = "Allouche 1987",
	author = "J.-P. Allouche",
	title = "Automates finis en th{\'e}orie des nombres",
	journal = EXM,
	volume = "5",
	pages = "239-226",
	year = 1987}

@article{Ranum:1911,
	key = "Ranum 1911",
	author = "A. Ranum",
	title = "The general term of a recurring series",
	journal = BAMS,
	volume = 17,
	pages = "457-461",
	year = 1911}

@article{Sylvester:1840,
	key = "Sylvester 1840",
	author = "J. J. Sylvester",
	title = "A method of determining by mere inspection the derivatives
                 from two equations of any degree",
	journal = PMAG,
	volume = 16,
	pages = "132-135",
	year = 1840,
	comment = "Quote occurs in his collected works at end of paper",
	note = "Reprinted in {\it Collected Mathematical Papers,} Vol.~1,
	        pp.~54--57"
	}

@article{Biermann:1891,
	key = "O. Biermann 1891",
	author = "O. Biermann",
	title = "{\"U}ber die {R}esultante ganzer {F}unctionen",
	journal = MMP,
	volume = 2,
	pages = "143-146",
	year = 1891}

@article{Pellet:1870,
	key = "Pellet 1870",
	author = "A.-E. Pellet",
	title = "Sur les fonctions irr{\'e}ductibles suivant un module
		 premier et une fonction modulaire",
	journal = CRASP,
	volume = 70,
	pages = "328-330",
	year = 1870}

@article{MacLagan-Wedderburn:1905,
	key = "MacLagan-Wedderburn 1905",
	author = "J. H. MacLagan-Wedderburn",
	title = "A theorem on finite algebras",
	journal = TAMS,
	volume = 6,
	pages = "349-352",
	year = 1905,
	comment = "MacLagan or Maclagan?"}

@article{Frobenius&Stickelberger:1879,
	key = "Frobenius and Stickelberger 1879",
	author = "F. G. Frobenius and L. Stickelberger",
	title = "{\"U}ber {G}ruppen von vertauschbaren {E}lementen",
	journal = JFRAM,
	volume = 86,
	pages = "217-262",
	year = 1879,
	note = "Reprinted in {\it Gesammelte Abhandlungen,} 
		Vol.~I, pp.~545--590"
	}

@article{Galois:1830,
	key = "Galois 1830",
	author = "E. Galois",
  	title = "Sur la th{\'e}orie des nombres",
	journal = "Bulletin des sciences math{\'e}matiques physiques 
		   et chimiques",
	volume = 13,
	number = 218,
  	year = 1830,
	pages = "428-435",
	note = "Reprinted in {\it {\'E}crits et M{\'e}moires Math{\'e}matiques 
                      d'{\'E}variste Galois,} pp.~112--128",
		}

@article{Reiner:1961,
	key = "Reiner 1961",
	author = "I. Reiner",
	title = "On the number of matrices with given characteristic
		 polynomial",
	journal = IJM,		
	volume = 5,
	pages = "324-329",
	year = 1961},

@inproceedings{Moore:1896,
	key = "E. Moore 1896",
	author = "E. H. Moore",
	title = "A doubly-infinite system of linear groups",
	booktitle = "Mathematical Papers Read at the International 
		     Mathematical Congress Held in Connection with
		     the World's Columbian Exposition Chicago 1893",
	pages = "208-242",
	publisher = "Macmillan",
	year = 1896}

@article{Davida:1972,
	key = "Davida 1972",
	author = "G. I. Davida",
	title = "Inverse of elements of a {Galois} field",
	journal = ELETT,		
	volume = 8,
	pages = "518-520",
	year = 1972}

@article{Hilbert:1897,
	key = "Hilbert 1897",
	author = "D. Hilbert",
	title = "{Die} {Theorie} der algebraischen {Z}ahlk{\"o}rper",
	journal = "Jahresbericht der Deutschen Mathematiker-Vereinigung",
	volume = 4,
	pages = "175-546",
	year = 1897,
	note = "Reprinted in {\it Gesammelte Abhandlungen,} Vol.~I, pp.~63--363"
	}

@article{Bilharz:1937,
	key = "Bilharz 1937",
	author = "H. Bilharz",
	title = "{Primdivisoren} mit vorgegebener {P}rimitivwurzel",
	journal = MA,
	volume = 114,
	pages = "476-492",
	year = 1937}

@article{Hasse:1952,
	key = "Hasse 1952",
	author = "H. Hasse",
	title = "{\"U}ber die {A}rtinsche {V}ermutung und
		 verwandte {D}ichtefragen",
	journal = AASF,
	number = 116,
	pages = "1-17",
	year = 1952}

@article{Chor:1982,
	key = "Chor 1982",
	author = "B. Chor",
	title = "Arithmetic of finite fields", 
	journal = IPL,
	volume = 14,
	pages = "4-6",
	year = 1982}

@article{Willett:1980,
	key = "Willett 1980",
	author = "M. Willett",
	title = "Arithmetic in a finite field", 
	journal = MC,
	volume = 35,
	pages = "1353-1359",
	year = 1980}

@article{Itoh&Tsujii:1988b,
	key = "Itoh and Tsujii 1988b",
	author = "T. Itoh and S. Tsujii",
	title = "A fast algorithm for computing multiplicative inverses
		 in {$GF(2^m)$} using normal bases", 
	journal = IC,
	volume = 78,
	pages = "171-177",
	year = "{\noopsort{1988b}}1988"}

@article{Asano&Itoh&Tsujii:1989,
	key = "Asano, Itoh and Tsujii 1989",
	author = "Y. Asano and T. Itoh and S. Tsujii",
	title = "Generalised fast algorithm for computing multiplicative 
	         inverses in {$GF(2^m)$}", 
	journal = ELETT,
	volume = 25,
	pages = "664-665",
	year = "1989"}

@article{Itoh&Tsujii:1989b,
	key = "Itoh and Tsujii 1989b",
	author = "T. Itoh and S. Tsujii",
	title = "Structure of parallel multipliers for a class of fields
		 {$GF(2^m)$}", 
	journal = IC,
	volume = 83,
	pages = "21-40",
	year = "{\noopsort{1989b}}1989"}

@inproceedings{Conway:1968,
	key = "Conway 1968",
	author = "J. H. Conway",
	title = "A tabulation of some information concerning finite fields",
	booktitle = "Computers in Mathematical Research",
	editor = "R. F. Churchhouse and J.-C. Herz",
	pages = "37-50",
	publisher = NH,
	year = 1968}

@article{Hayes:1965,
	key = "Hayes 1965",
	author = "D. R. Hayes",
	title = "The distribution of irreducibles in {$GF[q,x]$}", 
	journal = TAMS,
	volume = 117,
	pages = "101-127",
	year = 1965}

@article{Leonard:1974,
	key = "Leonard 1974",
	author = "P. A. Leonard",
	title = "Factorizations of general polynomials", 
	journal = JNT,
	volume = 6,
	pages = "335-338",
	year = 1974}

@article{Ree:1971,
	key = "Ree 1971",
	author = "R. Ree",
	title = "Proof of a conjecture of {S}. {C}howla", 
	journal = JNT,
	volume = 3,
	pages = "210-212",
	year = 1971}

@article{SDCohen:1968,
	key = "S. Cohen 1968",
	author = "S. D. Cohen",
	title = "The distribution of irreducible polynomials in several
		 indeterminates over a finite field", 
	journal = PEMS,
	volume = 16,
	pages = "1-17",
	year = "1968-9"}

@article{SDCohen:1969,
	key = "S. Cohen 1969",
	author = "S. D. Cohen",
	title = "Further arithmetical functions in finite fields",
	journal = PEMS,
	volume = "16",
	pages = "349-363",
	year = "1968-9"}

@article{Cohen:1972,
	key = "S. Cohen 1972",
	author = "S. D. Cohen",
	title = "Uniform distribution of polynomials over finite fields",
	journal = JLMS,
	volume = 6,
	pages = "93-102",
	year = 1972}

@article{Cohen:1970,
	key = "S. Cohen 1970",
	author = "S. D. Cohen",
	title = "The distribution of polynomials over finite fields",
	journal = AA,
	volume = 17,
	pages = "255-271",
	year = 1970}

@article{Fredman:1972,
	key = "Fredman 1972",
	author = "M. L. Fredman",
	title = "The distribution of absolutely irreducible polynomials
		 in several indeterminates",
	journal = PAMS,
	volume = 31,
	pages = "387-390",
	year = 1972}

@book{Weil:1948a,
  	key = "Weil 1948a",
  	author = "A. Weil",
  	title = "Sur les Courbes Alg{\'e}briques et les Vari{\'e}t{\'e}s
		 qui s'en D{\'e}duisent",
  	publisher = "Hermann",
  	year = "{\noopsort{1948a}}1948"}

@article{Golovanov&Solodovnikov:1987,
	key = "Golovanov and Solodovnikov 1987",
	author = "P. N. Golovanov and V. I. Solodovnikov",
	title = "Rapid parallel calculation of degrees in a quotient
		 ring of polynomials over a finite field",
	journal = "Matematicheskie Zametki",
	volume = 42,
	pages = "886-894",
	year = 1987,
	note = "English translation in {\it Mathematical Notes},
		{\bf 42} (1987), 987--992"}

@article{Fich&Tompa:1988,
	key = "Fich and Tompa 1988",
	author = "F. E. Fich and M. Tompa",
	title = "The parallel complexity of exponentiating polynomials
		 over finite fields",
	journal = JACM,
	volume = 35,
	pages = "651-667",
	year = 1988}

@inproceedings{Fich&Tompa:1985,
	key = "Fich and Tompa 1985",
	author = "F. E. Fich and M. Tompa",
	title = "The parallel complexity of exponentiating polynomials
over finite fields",
	booktitle = STOC85,
	year = 1985,
	pages = "38-47"}

@article{Schonhage:1971,
	key = "Sch{\"o}nhage 1971",
	author = "A. Sch{\"o}nhage",
	title = "{Schnelle} {Berechnung} von {K}ettenbruchentwicklungen",
	journal = AI,
	volume = 1,
	pages = "139-144",
	year = 1971}

@article{Borodin&von.zur.Gathen&Hopcroft:1982,
	key = "Borodin, von zur Gathen, and Hopcroft 1982",
	author = "A. Borodin and Gathen, J. von zur and J. Hopcroft",
	title = "Fast parallel matrix and gcd computations",
	journal = ICTRL,
	volume = 52,
	pages = "241-256",
	year = 1982}

@article{Schonhage:1977,
	key = "Sch{\"o}nhage 1977",
	author = "A. Sch{\"o}nhage",
	title = "{Schnelle} {Multiplikation} von {Polynomen} {\"u}ber
		 {K}{\"o}rpern der {Charakteristik} 2",
	journal = AI,
	volume = 7,
	pages = "395-398",
	year = 1977}

@book{Golomb:1967,
  	key = "Golomb 1967",
  	author = "S. W. Golomb",
  	title = "Shift Register Sequences",
  	publisher = "Holden-Day",
  	year = 1967}

@incollection{Gauss:1889,
  	key = "Gauss 1889",
  	author = "C. F. Gauss",
  	title = "Die {Lehre} von den {R}esten. {II}",
  	booktitle = "Untersuchungen {\"u}ber H{\"o}here Arithmetik
		     von Carl Friedrich Gauss",
  	year = 1889,
  	pages = "602-629",
	editor = "H. Maser",
	publisher = "J. Springer",
	note = "Reprinted by Chelsea, New York, 1981"}

@techreport{Langemyr:1989,
  	key = "Langemyr 1989",
  	author = "L. Langemyr",
  	title = "Computing the gcd of two polynomials over an algebraic
		 number field",
  	institution = "Royal Institute of Technology (Stockholm)",
  	number = "TRITA-NA-8804",
  	month = "January",
  	year = 1989}

@article{Eberly:1989,
	key = "Eberly 1989",
	author = "W. Eberly",
	title = "Very fast parallel polynomial arithmetic",
	journal = SIAMJC,
	volume = 18,
	pages = "955-976",
	year = 1989}

@article{Strong:1988,
	key = "Strong 1988",
	author = "R. Strong",
	title = "Some asymptotic results on finite vector spaces",
	journal = AAM,
	volume = 9,
	pages = "167-199",
	year = 1988}

@article{Landsberg:1893,
	key = "Landsberg 1893",
	author = "G. Landsberg",
	title = "{Ueber} eine {A}nzahlbestimmung und eine damit
		 zusammenh{\"a}ngende {R}eihe",
	journal = JFRAM,
	volume = 111,
	pages = "87-88",
	year = 1893}

@book{Gordan:1885,
  	key = "Gordan 1885",
  	author = "P. Gordan",
  	title = "{V}orlesungen {\"u}ber {I}nvariantentheorie",
  	publisher = "Teubner",
  	year = 1885,
	comment = "Edited by Georg Kerschensteiner"}

@article{Schmidt:1928,
	key = "F. Schmidt 1928",
	author = "F. K. Schmidt",
	title = "Zur {Z}ahlentheorie in {K\"o}rpern von der 
		 {C}haracteristik $p$",
	journal = "Sitzungsberichte der Physikalish-medizinischen 
		   Societ{\"a}t zu Erlangen",
	volume = "58-59",
	pages = "159-172",
	comment = "don't have a copy of this yet",
	year = 1928}

@article{Whiteman:1937,
	key = "Whiteman 1937",
	author = "A. Whiteman",
	title = "On a theorem of higher reciprocity",
	journal = BAMS,
	volume = 43,
	pages = "567-572",
	year = 1937}

@article{Vaidyanathaswamy:1927,
	key = "Vaidyanathaswamy 1927",
	author = "R. Vaidyanathaswamy",
	title = "The quadratic reciprocity of polynomials modulo $p$",
	journal = JIMS,
	comment = "JIMS = Journal of the Indian Math. Society",
	volume = 17,
	pages = "185-196",
	year = 1927}

@article{Bach:1990b,
	key = "Bach 1990b",
	author = "E. Bach",
	title = "A note on square roots in finite fields",
	volume = 36,
	journal = IEEE-IT,
	year = "{\noopsort{1990b}}1990",
	pages = "1494-1498"}

@book{Borodin&Munro:1975,
  	key = "Borodin and Munro 1975",
  	author = "A. Borodin and I. Munro",
  	title = "The Computational Complexity of Algebraic 
		 and Numeric Problems",
  	publisher = "American Elsevier",
  	year = 1975}

@article{von.zur.Gathen&Seroussi:1991,
	key = "von zur Gathen and Seroussi 1991",
	author = "Gathen, J. von zur and G. Seroussi",
	title = "Boolean circuits versus arithmetic circuits",
	journal = IC,
	volume = 91,
	year = 1991,
	pages = "142-154"}

@article{Norton:1989,
	key = "G. Norton 1989",
	author = "G. H. Norton",
	title = "Precise analyses of the right- and left-shift
		 greatest common divisor algorithms for {$GF(q)[x]$}",
	journal = SIAMJC,
	volume = 18,
	pages = "608-624",
	year = 1989
	}

@article{Lazard:1977,
	key = "Lazard 1977",
	author = "D. Lazard",
	title = "Le meilleur algorithme {d'Euclide} pour {$K[X]$} et {$\Zee$}",
	journal = CRASP,
	volume = 284,
	pages = "A1-A4",
	year = 1977
	}

@article{Wang.et.al:1985,
	key = "C. Wang et al. 1985",
	author = "C. C. Wang and T. K. Truong and H. M Shao and
		  L. J. Deutsch and J. K. Omura and I. S. Reed",
	title = "{VLSI} architectures for computing multiplications
	         and inverses in {$GF(2^m)$}",
	journal = IEEE-TC,
	volume = "C-34",
	pages = "709-717",
	year = 1985}

@inproceedings{Beth:1986,
	key = "Beth 1986",
	author = "T. Beth",
	title = "On the arithmetics of {G}aloisfields [sic] and the like",
	booktitle = AAECC3,
	publisher = "Springer-Verlag",
	pages = "2-16",
	editor = "J. Calmet",
	comment = "Lecture Notes in Computer Science 229",
	year = 1986}

@article{Cantor:1989,
	key = "Cantor 1989",
	author = "D. G. Cantor",
	title = "On arithmetical algorithms over finite fields",
	journal = JCTA,
	volume = 50,
	pages = "285-300",
	year = 1989
	}

@article{Bartee&Schneider:1963,
	key = "Bartee and Schneider 1963",
	author = "T. C. Bartee and D. I. Schneider",
	title = "Computation with finite fields",
	journal = ICTRL,
	volume = 6,
	pages = "79-98",
	year = 1963}

@article{Cayley:1848,
	key = "Cayley 1848",
	author = "A. Cayley",
	title = "Nouvelles recherches sur les fonctions de {M. Sturm}",
	journal = JMPA,
	volume = 13,
	pages = "269-274",
	year = 1848,
	note = "Reprinted in {\it Collected Papers,} Vol.~1, pp.~392--401"
	}

@incollection{Cauchy:1840,
	key = "Cauchy 1840",
	author = "A. Cauchy",
  	title = "M{\'e}moire sur l'{\'e}limination d'une variable entre deux
		 {\'e}quations alg{\'e}briques",
  	booktitle = "Exercices d'Analyse et de Physique Math\'ematique",
	volume = "I",
  	publisher = "Bachelier",
	year = 1840,
	note = "Reprinted in {\it Oeuvres (2)}, Vol.~11, pp.~466-509"}

@incollection{Netto&le.Vavasseur:1907,
	key = "Netto and le Vavasseur 1907",
	author = "E. Netto and R. le Vavasseur",
  	title = "Les fonctions rationnelles",
  	booktitle = "Encyclop{\'e}die des Sciences Math{\'e}matiques",
	volume = "I:2",
  	publisher = "Gauthier-Villars",	
	editor = "J. Molk",
  	year = 1907,
  	pages = "1-232"}

@article{Gauss:1832,
  	key = "Gauss 1832",
  	author = "C. F. Gauss",
	title = "Theoria residuorum biquadraticorum (commentatio secunda)",
	journal = "Commentationes Societatis Regiae Scientarum Gottingensis
		   Recentiores",
	volume = 7,
	pages = "89-148",
	year = 1832,
	note = "Reprinted in {\it Werke,} Vol.~2, pp.~93--148.
		German translation in 
  	        {\it Untersuchungen {\"u}ber H{\"o}here Arithmetik von 
		Carl Fredrich Gauss}, ed. H. Maser, J. Springer, 1889.
		Reprinted by Chelsea, New York, 1981"}

@article{Dedekind:1882,
	key = "Dedekind 1882",
	author = "J. W. R. Dedekind",
	title = "{\"U}ber die {D}iskriminanten endlicher {K\"o}rper",
	journal = AKGWG,
	volume = 29,
	pages = "1-56",
	year = 1882,
	note = "Reprinted in {\it Werke,} Vol.~1, pp.~351--396"
	}

@article{Berlekamp:1966,
	key = "Berlekamp 1966",
	author = "E. R. Berlekamp",
	title = "Distribution of cyclic matrices in a finite field",
	journal = DMJ,
	volume = 33,
	pages = "45-48",
	year = 1966}

@book{Stevin:1585,
  	key = "Stevin 1585",
  	author = "S. Stevin",
  	title = "L'Arithm{\'e}tique",
  	publisher = "Plantin",
	city = "Leyden",
  	year = 1585,
	comment = "gcd stuff on p. 235",
	note = "Reprinted in
	        E. Crone et al., editors,
	        {\it The Principal Works of Simon Stevin,} 
	        Swets and Zeitlinger, Amsterdam, 1958"}

@article{Sanderson:1911,
	key = "Sanderson 1911",
 	author = "M. Sanderson",
 	title = "Generalizations in the theory of numbers and theory of
		 linear groups",
 	journal = AM,
 	volume = 13,
 	pages = "36-39",
 	year = 1911}

@article{Itoh&Tsujii:1989a,
	key = "Itoh and Tsujii 1989a",
 	author = "T. Itoh and S. Tsujii",
 	title = "An efficient algorithm for deciding quadratic
		 residuosity in finite fields {$GF(p^m)$}",
 	journal = IPL,
 	volume = 30,
 	pages = "111-114",
 	year = "{\noopsort{1989a}}1989"}

@article{Lempel&Weinberger:1988,
	key = "Lempel and Weinberger 1988",
 	author = "A. Lempel and M. J. Weinberger",
 	title = "Self-complementary normal bases in finite fields",
 	journal = SIAMJDM,
 	volume = 1,
 	pages = "193-198",
 	year = 1988}

@incollection{Eastman:1990,
	key = "Eastman 1990",
	author = "W. L. Eastman",
	title = "Inside {Euclid's} algorithm",
	booktitle = "Coding Theory and Design Theory, Part I",
	editor = "D. Ray-Chaudhuri",
	publisher = SV,
	year = 1990,
	series = "IMA Volumes in Mathematics and Its Applications",
	volume = 20,
	pages = "113-127"}

@article{Wang&Pei:1990,
	key = "C. Wang and Pei 1990",
	author = "C. C. Wang and D. Pei",
	title = "A {VLSI} design for computing exponentiations in 
${GF(2^m)}$ and its application to generate pseudorandom number sequences",
	journal = IEEE-TC,
	volume = 39,
	year = 1990,
	pages = "258-262"}

@article{Szele:1947,
	key = "Szele 1947",
	author = "T. Szele",
	title = "{\"Uber} die endlichen {Ordnungszahlen}, zu denen nur eine
{Gruppe} {geh\"ort}",
	journal = CMH,
	volume = 20,
	year = 1947,
	pages = "265-267"}

@article{Szep:1947,
	key = "Szep 1947",
	author = "J. Szep",
	title = "On finite groups which are necessarily commutative",
	journal = CMH,
	volume = 20,
	year = 1947,
	pages = "223-224"}

@article{Dickson:1905,
	key = "Dickson 1905",
	author = "L. E. Dickson",
	title = "Definitions of a group and a field by independent postulates",
	journal = TAMS,
	volume = 6,
	year = 1905,
	pages = "198-204"}

@article{Jungnickel:1992,
	key = "Jungnickel 1992",
	author = "D. Jungnickel",
	title = "On the uniqueness of the cyclic group of order $n$",
	journal = AMM,
	volume = 99,
	year = 1992,
	pages = "545-547"}

@incollection{Agnew&Mullin&Vanstone:1988,
	key = "Agnew, Mullin, and Vanstone 1988",
	author = "G. B. Agnew and R. C. Mullin and S. A. Vanstone",
	title = "Fast exponentiation in {$GF(2^n)$}",
	booktitle = EUROCRYPT88,
	year = 1988,
	series = LNICS,
	volume = 330,
	publisher = SV,
	editor = "C. G. {G\"unther}",
	pages = "251-255"}

@incollection{Zeugmann:1990,
	key = "Zeugmann 1990",
	author = "T. Zeugmann",
	title = "Computing large polynomial powers very fast in parallel",
	booktitle = MFCS90,
	year = 1990,
	publisher = SV,
	series = LNICS,
	volume = 452,
	editor = "B. Rovan",
	pages = "538-544"}

@article{vonzurGathen:1990,
	key = "von zur Gathen 1990",
	author = "Gathen, J. von zur",
	title = "Inversion in finite fields using logarithmic depth",
	journal = JSC,
	volume = 9,
	year = 1990,
	pages = "175-183"}

@article{Cerlienco&Piras:1983,
	key = "Cerlienco and Piras 1983",
	author = "L. Cerlienco and F. Piras",
	title = "Powers of a matrix",
	journal = BUMI,
	series = 6,
	volume = "2-B",
	pages = "681-690",
	year = 1983}

@incollection{Shparlinski&Tsfasman&Vladut:1992,
  	key = "Shparlinski, Tsfasman, and Vladut 1992",
  	author = "I. E. Shparlinski and M. A. Tsfasman and S. G. Vladut",
  	title = "Curves with many points and multiplication over finite fields",
  	booktitle = "Coding Theory and Algebraic Geometry",
	editor = "H. Stichtenoth and M. A. Tsfasman",
	publisher = SV,
	series = LNICS,
	volume = 1518,
	pages = "145-169",
  	year = 1992}

@incollection{Knopfmacher&Knopfmacher:1990a,
  	key = "Knopfmacher and Knopfmacher 1990a",
  	author = "A. Knopfmacher and J. Knopfmacher",
  	title = "Maximum length of the {Euclidean} algorithm and 
		 continued fractions in ${\openF(X)}$",
  	booktitle = "Applications of Fibonacci Numbers",
 	year = "{\noopsort{1990a}}1990",
  	pages = "217-222",
	volume = 3,
	address = "Boston",
	editor = "G. E. Bergum and A. N. Philippou and A. F. Horadam",
	publisher = "Kluwer"}

@article{Knopfmacher&Knopfmacher:1990b,
  	key = "Knopfmacher and Knopfmacher 1990a",
  	author = "A. Knopfmacher and J. Knopfmacher",
	title = "The distribution of values of polynomials over a finite
		 field",
	journal = LAA,
	volume = 134,
	pages = "145-151",
 	year = "{\noopsort{1990a}}1990" }

@article{Haskell:1892,
	key = "Haskell 1892",
	author = "M. W. Haskell",
	title = "Note on resultants",
	journal = BNYMS,
	volume = 1,
	pages = "223-224",
	year = 1892}

@unpublished{PMontgomery:1990,
	key = "P. Montgomery 1990",
	author = "P. L. Montgomery",
	title = "A problem of {Herb} {Doughty}",
	year = 1990,
	note = "Unpublished manuscript"}

@unpublished{Schonhage:1992,
	key = "Sch{\"o}nhage 1992",
	author = "A. Sch{\"o}nhage",
	title = "Fast parallel computation of characteristic polynomials
		 by {Leverrier's} power sum method adapted to fields
		 of finite characteristic",
	year = 1992,
	comment = "In ICALP 93?",
	note = "Unpublished manuscript"}

@article{Hellegouarch:1986,
	key = "Hellegouarch 1986",
	author = "Y. Hellegouarch",
	title = "Loi de r{\'e}ciprocit{\'e}, crit{\`e}re de primalit{\'e} 
                 dans {$\Fq[t]$}",
	journal = CRMRASC,
	volume = 8,
	pages = "291-296",
	year = 1986}

@inproceedings{Brawley&Brown:1991,
	key = "Brawley and Brown 1991",
	author = "J. V. Brawley and D. Brown",
	title = "Iterated presentations of algebraic extensions of finite
		 fields",
	booktitle = "Proc. 22nd Southeastern Conference on Combinatorics,
		     Graph Theory, and Computing",
	publisher = UM,
	address = "Winnipeg",
	pages = "3-7",
	note = "(= {\it Congr. Numer.} {\bf 85})",
	year = 1972}

@unpublished{LenstraH:1991b,
	key = "H. W. Lenstra 1991b",
 	author = "Lenstra, Jr., H. W.",
 	title = "Algorithms for finite fields",
	year = "{\noopsort{1991b}}1991",
	note = "Unpublished lecture notes"
	}

@article{Rabin:1960,
	key = "Rabin 1960",
	author = "M. O. Rabin",
	title = "Computable algebra, general theory and theory of computable
		 fields",
	journal = TAMS,
	volume = 95,
	pages = "341-360",
	year = 1960}

@article{Frohlich&Shepherdson:1955,
	key = "Fr{\"o}hlich and Shepherdson 1955",
	author = "A. Fr{\"o}hlich and J. C. Shepherdson",
	title = "Effective procedures in field theory",
	journal = PTRSA,
	volume = 248,
	pages = "407-432",
	year = 1955}

@article{Langemyr:1991c,
  	key = "Langemyr 1991c",
  	author = "L. Langemyr",
  	title = "Circuits for computing the gcd of two polynomials over 
		 an algebraic number field",
	journal = IPL,
	volume = 38,
  	year = 1991}

@book{Uspensky:1948,
  	key = "Uspensky 1948",
  	author = "J. V. Uspensky",
  	title = "Theory of Equations",
  	publisher = MH,
  	year = 1948}

@book{Conway:1976,
  	key = "Conway 1976",
  	author = "J. H. Conway",
  	title = "On Numbers and Games",
  	publisher = AP,
  	year = 1976}

@book{McCoy:1948,
  	key = "McCoy 1948",
  	author = "N. H. McCoy",
  	title = "Rings and Ideals",
  	publisher = MAA,
  	year = 1948}

@article{Ash&Blake&Vanstone:1989,
	key = "Ash, Blake, and Vanstone 1989",
 	author = "D. W. Ash and I. F. Blake and S. A. Vanstone",
 	title = "Low complexity normal bases",
 	journal = DAM,
 	volume = 25,
 	pages = "191-210",
 	year = 1989}

@techreport{Gao:1992,
  	key = "Gao 1992",
  	author = "S. Gao",
  	title = "The determination of optimal normal bases of finite fields",
  	institution = "University of Waterloo, Dept. of Combinatorics and
		       Optimization",
  	number = "CORR-92-01",
  	month = "January",
  	year = 1992}

@article{Blake&Gao&Mullin:1994,
  	key = "Blake, Gao, and Mullin 1994",
  	author = "I. F. Blake and S. Gao and R. C. Mullin",
  	title = "Factorization of $cx^{q+1}+dx^q-ax-b$ and normal bases
		 over ${GF(q)}$",
	journal = SIAMJDM,
	volume = 7,
	pages = "499-512",
	year = 1994}

@article{Mullin&Onyszchuk&Vanstone&Wilson:1988,
	key = "Mullin, Onyszchuk, Vanstone, and Wilson 1988",
	author = "R. C. Mullin and I. M. Onyszchuk and S. A. Vanstone 
                  and R. M. Wilson",
 	title = "Optimal normal bases in {$GF(p^n)$}",
 	journal = DAM,
 	volume = 22,
 	pages = "149-161",
 	year = "1988/89"}

@article{Bassalygo:1978,
	key = "Bassalygo 1978",
 	author = "L. A. Bassalygo",
 	title = "A remark on fast multiplication of polynomials over
		 {G}alois fields",
 	journal = PPI,
 	volume = 14,
 	pages = "101-102",
	note = "In Russian.  English translation in 
	{\it Problems Inform. Transmission}, {\bf 14}, 1978, 71--72.",
 	year = 1978}

@article{Euler:1750,
	key = "Euler 1750",
	author = "L. Euler",
	title = "Demonstration sur le nombre des point ou deux lignes
		 des ordres quelconques peuvent se couper",
	journal = "{M\'emoires} de l'{Acad\'emie} des sciences de {B}erlin",
	volume = "4 {\rm (1748)}",
	year = "1750",
	pages = "234-248",
	note = "Reprinted in {\it Opera Omnia}, Ser.~1, Vol.~26, 
		pp.~46--59"}

@article{Gao&Vanstone:1995,
	key = "Gao and Vanstone 1995",
	author = "S. Gao and S. A. Vanstone",
	title = "On orders of optimal normal basis generators",
	year = 1994,
	journal = MC,
	volume = 64,
	pages = "1227-1233"}

@unpublished{Lindhurst:1995,
	key = "Lindhurst 1995",
	author = "S. Lindhurst",
	title = "An analysis of {Shanks'} algorithm for computing square roots
in finite fields",
	year = 1995,
	note = "Unpublished manuscript"}

@article{Hachenberger:1992,
	key = "Hachenberger 1992",
	author = "D. Hachenberger",
	title = "On primitive and free roots in a finite field",
	journal = AAECC,
	volume = 3,
	year = 1992,
	pages = "139-150"}

@article{Prabhu&Bose:1979,
	key = "Prabhu and Bose 1979",
 	author = "K. A. Prabhu and N. K. Bose",
 	title = "Number of irreducible $q$-ary polynomials in several 
		 variables with prescribed degrees",
 	journal = IEEE-TCS,
 	volume = "CAS-26",
 	pages = "973-975",
 	year = 1979}

@article{ELehmer:1978,
	key = "E. Lehmer 1978",
 	author = "E. Lehmer",
 	title = "Rational reciprocity laws",
 	journal = AMM,
 	volume = 85,
 	pages = "467-472",
 	year = 1978}

@article{Spottiswoode:1853,
	key = "Spottiswoode 1853",
 	author = "W. Spottiswoode",
 	title = "Elementary theorems relating to determinants.
		 {R}ewritten and much enlarged by the author",
 	journal = JFRAM,
 	volume = 51,
 	pages = "209-271,328-381",
 	year = 1853}

@article{Gao&Lenstra:1992,
	key = "Gao and Lenstra 1992",
	author = "S. Gao and Lenstra, Jr., H. W.",
	title = "Optimal normal bases",
	journal = DCC,
	volume = 2,
	year = 1992,
	pages = "315-323"}

@book{Gaal:1971,
  	key = "Gaal 1971",
  	author = "L. Gaal",
  	title = "Classical Galois Theory",
  	publisher = "Markham",
	city = "Chicago",
  	year = 1971,
	note = "Reprinted by Chelsea, New York, 1979"}