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25945 Gregory Bard: Algorithms for solving linear and polynomial systems of
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T. Bartee/D. Schneider: Computation with finite fields.
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N. Biggs: Discrete mathematics.

25688 Arnaud Bodin: Number of irreducible polynomials in several variables over
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Stanley Burris/John Lawrence: Term rewrite rules for finite fields.
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17958 Alberto Caceres/Omar Colon-Reyes: Some criteria for permutation binomials.
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L. Carlitz: Diophantine approximation in fields of characteristic p.
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L. Carlitz: Gauss sums over finite fields of order 2^n.
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L. Carlitz: Primitive roots in a finite field.
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25776 Joergen Cherly/Luis Gallardo/Leonid Vaserstein/Ethel Wheland: Solving
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S. Cohen: Primitive roots in the quadratic extension of a finite field.
J. London Math. Soc. 27 (1983), 221-228.

S. Cohen: Generators in cyclic difference sets.
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polynomials. Can. Math. Bull 33 (1990), 230-234.

S. Cohen: Permutation polynomials and primitive permutation groups.
Arch. Math. 57 (1991), 417-423.

8679 S. Cohen/Harald Niederreiter (ed.): Finite fields and applications.
Cambridge UP 1996. 0-521-56736-X (pb.).

25777 Keith Conrad: Quadratic reciprocity in characteristic two. Internet ca. 2005, 15p.

D. Coppersmith: Fast evaluation of logarithms in fields of characteristic 2.
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David Cox: Galois theory. Wiley 2004, 560p. Eur 63.

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H. Davenport: Bases for finite fields.
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Richard Dedekind: Abriss einer Theorie der hoeheren Congruenzen in bezug
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R. Evans/J. Greene/Harald Niederreiter: Linearized polynomials and 
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Peter Fleischmann/Markus Holder/Peter Roelse: The black-box
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M. Fried: On a conjecture of Schur. Mich. Math. J. 17 (1970), 41-55.

M. Fried/R. Guralnick/J. Saxl: Schur covers and Carlitz's conjecture.
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7223 Sophie Frisch: When are weak permutation polynomials strong?
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7475 Shuohong Gao/Joachim von zur Gathen/Daniel Panario: Gauss periods,
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X. Gao/H. Lenstra: Optimal normal bases. Des. Codes, Crypt. 2 (1992), 315-323.

7473 Joachim von zur Gathen/Marek Karpinski/Igor Shparlinski: Counting curves
and their projections. Internet 1994, 40p.

Joachim von zur Gathen/V. Shoup: Computing Frobenius maps and factoring
polynomials. Computational Complexity 2 (1992), 187-224.

7474 Joachim von zur Gathen/Igor Shparlinski: Components and projections
of curves over finite fields. Internet 1995, 25p.

7477 Joachim von zur Gathen/Igor Shparlinski: Finding points on curves
over finite fields. Internet 1995, 20p.

7482 Joachim von zur Gathen/Igor Shparlinski: Orders of Gauss periods
in finite fields. Internet 1995, 6p.

7483 Juergen Gerhard: Faktorisieren von Polynomen ueber F_q. Ein Vergleich
neuerer Verfahren. Diplomarbeit, Erlangen 1994.

7222 Valerie Gillot: Bounds for exponential sums over finite fields.
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Kurt Girstmair: Linear dependence of zeros of polynomials and construction
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Kurt Girstmair: On the construciton of primitive elements in field
extensions. Monatshefte Math. 98 (1984), 193-209.

R. Goettfert: An acceleration of the Niederreiter factorization algorithm
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S. Golomb: Shift register sequences. Aegean Park Press 1982.

Dan Gordon: Discrete logarithms in GF(p) using the number field sieve.
SIAM J. Discrete Math. 6 (1993), 124-138.

8273 Dirk Hachenberger: Explicit iterative constructions of normal bases and
completely free elements in finite fields. Finite Fields 2 (1996), 1-20.

8274 Dirk Hachenberger: Normal bases and completely free elements in prime
power extensions over finite fields. Finite Fields 2 (1996), 21-34.

22730 Herwig Hauser/Christian Krattenthaler: Seminar über die Weilsche Vermutung.
Ankündigung. WS 2010/11, Univ. Wien. Internet 2010, 1p.

D. Hayes: A geometric approach to permutation polynomials over a finite field.
Duke Math. J. 34 (1967), 293-305.

M. Hazewinkel (ed.): Handbook of algebra. North-Holland, ca. 1995.

26164 J. Hirschfeld: Projective geometries over finite fields. Oxford UP 1979.

18283 Jean-Rene' Joly: Equations et varietes algebriques sur un corps fini.
Ens. Math. 19 (1973), 1-117.

6694 Dieter Jungnickel: Finite fields. 
Bibl. Inst. 1993, 340p. 3-411-16111-6. DM 78. Beautifully written.

25689 John Kerl: Computation in finite fields. Internet 2013, 91p.

17819 Donald Knuth: Tables of finite fields. In 17655 Knuth, 277-304.

Hans Kurzweil: Endliche Körper. Springer 2007, 150p. Eur 20.
Very elementary.

8678 Ehler Lange: Cellular automata, substitions and factorization
of polynomials over finite fields. In 8679 Cohen/Niederreiter, 163-179.

7220 Philippe Langevin: Regular sections groups.
Finite Fields Appl. 1 (1995), 405-411.

24761 Hans Lausch/Wilfried Nöbauer: Algebra of polynomials. North-Holland 1973.

6690 H. Lenstra/R. Schoof: Primitive normal bases for finite fields.
Math. Comp. 48 (1987), 217-231.
The authors completely solve the question of the existence of a primitive 
normal basis for extensions of finite fields.

Rudolf Lidl/G. Mullen/G. Turnwald: Dickson polynomials.
Longman 1993, 200p. 0-582-091195.

2565 Rudolf Lidl/Harald Niederreiter: Finite fields. Cambridge UP 1987.

Rudolf Lidl/Harald Niederreiter: Introduction to finite fields and their 
applications. Cambridge UP 1994, 400p. 0-521-46094-8. Pds. 30.

Rudolf Lidl/Harald Niederreiter: Finite fields and their applications.
In Hazewinkel, ca. 1995.

2022 Rudolf Lidl/Johann Wiesenbauer: Ringtheorie und Anwendungen.
Akademische Verlagsgesellschaft 1980. ISBN 3-400-00371-9.

2291 Heinz Lueneburg: On the rational normal form of endomorphisms.
Bibl. Inst. 1987. The title is completely misleading, this book contains many 
very efficient algorithms for finite fields (for example for generators of 
their multiplicative group, pages 345-350) and polynonomials. Requires 
patient reading.

8275 Keju Ma/Joachim von zur Gathen: Tests for permutation functions.
Finite Fields 1 (1995), 31-56.

5803 Florence Jessie MacWilliams/Neil Sloane: The theory of error-correcting 
codes. North-Holland 1981.

3461 James McClellan/Charles Rader (ed.): Number theory in digital signal 
processing. Prentice-Hall 1979.

R. McEliece: Finite fields for computer scientists and engineers.
Kluwer.

Alfred Menezes (ed.): Applications of finite fields.
Kluwer 1993, 220p. 0-7923-9282-5. $72.

Carlos Moreno: Algebraic curves over finite fields.
Cambridge UP 1990, 270p. 0-521-34252-x. Pds. 30. 
Should be somewhat difficult to read.

21526 Gary Mullen/Carl Mummert: Finite fields and applications.
AMS 2007, 180p. Eur 33.

25818 Gary Mullen/Daniel Panario (ed.): Handbook of finite fields. CRC 2013, 1030p. Eur 92.

Gary Mullen/Peter Shiue (ed.): Finite fields, coding theory, and advances in 
communication and computing. Dekker 1993, 440p. 0-8247-8805-2. $145.

Gary Mullen/Peterr Shiue (ed.): Finite fields. Theory, applications, and 
algorithms. AMS (Contemporary Mathematics 168) 1994, 400p. 0-8218-5183-7. $65.

16883 Gary Mullen/Igor Shparlinski: Open problems and conjectures in finite fields.
LN London MS 233 (1996), 243-268.

26156 Amela Muratovic-Ribic/Qiang Wang: On coefficients of polynomials over
finite fields. Internet 2011, 27p.

Harald Niederreiter: Computational problems in the theory of finite fields.
Applicable Algebra 2 (1991), 81-89.

Harald Niederreiter: Factorization of polynomials and some linear-algebra
problems over finite fields. Lin. Alg. Appl. 192 (1993), 301-328.

Harald Niederreiter: New deterministic factorization algorithms for
polynomials over finite fields. Preprint, ca. 1993.

Harald Niederreiter: A new efficient factorization algorithm for polynomials
over small finite fields. Applicable Algebra 4 (1993), 81-87.

Harald Niederreiter: Factoring polynomials over finite fields using
differential equations and normal bases. Math. Comp. 62 (1994), 819-830.

7381 Harald Niederreiter: Besprechung des Buches "Computational and
algorithmic problems in finite fields" von Shparlinski.
Jber. DMV 97 (1995), B 68-69.

7559 Harald Niederreiter/R. Goettfert: On a new factorization algorithm for
polynomials over finite fields. Math. Comp. 64 (1995), 347-353.

Harald Niederreiter/K. Robinson: On isomorphisms and isotopisms of Bol
loops of order 3p. Comm. in Algebra 22 (1994), 345-347.

9831 Harald Niederreiter/Chaoping Xing: Cyclotomic function fields,
Hilbert class fields, and global function fields with many rational
places. Acta Arithm. 79 (1997), 59-76.

Harald Niederreiter/Chaoping Xing: Rational points on curves over finite
fields. Cambridge UP 2001, 250p. Pds. 40.

21682 Harald Niederreiter/Chaoping Xing: Algebraic geometry in
coding theory and cryptography. Princeton UP 2009, 260p. Eur 35.

Wilfried Noebauer: Bemerkungen ueber die Darstellung von Abbildungen
durch Polynome und rationale Funktionen.
Monatshefte Math. 68 (1964), 138-142.

7039 Wilfried Noebauer: Zur Theorie der Polynomtransformationen und
Permutationspolynome. Math. Annalen 157 (1964), 332-342.

25696 Carl Offner: Finite fields and pseudo-random number generation. Internet 2007, 74p.

7219 Francesco Pappalardi/Igor Shparlinski: On Artin's conjecture over
function fields. Finite Fields Appl. 1 (1995), 399-404.

S. Pohlig/M. Hellman: An improved algorithm for computing discrete
logarithms over GF(p) and its cryptographic significane.
IEEE Trans. Inf. Theory 24 (1978), 106-110.

7272 Wolfgang Schmidt: Equations over finite fields. SLN Math. 536 (1976).

3430 R. Schoof: Elliptic curves over finite fields and the computation of 
square roots mod p. Math. Comp. 44 (1985), 483-494.

I. Semaev: Construction of polynomials over a finite field with linearly 
independent roots. Math. USSR Sbornik 63 (1989), 507-519.
The author gives an algorithm for constructing a normal basis for an 
extension of finite fields.

7565 Victor Shoup: New algorithms for finding irreducible polynomials over 
finite fields. Math. Comp. 54 (1990), 435-447.

Igor Shparlinski: On some problems in the theory of finite fields.
Russ. Math. Surveys 46 (1991), 199-240.

Igor Shparlinksi: Computational and algorithmic problems for finite fields.
Kluwer 1992, 240p. $ 118.

Igor Shparlinski: On bivariate polynomial factorization over finite fields.
Math. Comp. 60 (1993), 787-791.

Igor Shparlinski: Finite fields. Kluwer 1999, 530p. $287.
A good book, but also a terrific price.

V. Sidelnikov: On the normal bases of a finite field.
Math. USSR Sbornik 61 (1988), 485-494. 

Charles Small: Arithmetic of finite fields.
Dekker 1991, 200p. 0-8247-8526-6. $100.

6334 S. Stepanov/I. Shparlinsky: On the construction of primitive elements 
and primitive normal bases in a finite field. 3548 Pethoe, 1-14.

Lothar Stickelberger: Über eine neue Eigenschaft der Diskriminanten
algebraischer Zahlkörper. Verh. 1. Int. Math. Kongr. 1898, 182-193.

22479 Richard Swan: Factorization of polynomials over finite fields.
Pac. J. Math. 12/3 (1962), 1099-1106. Applications of a theorem of Stickelberger.

25778 Tsz Wo Sze: On solving univariate polynomial equations over finite fields
and some related problems. PhD thesis Univ. Maryland 2007, 99p.

15297 Iwaro Takahashi: Switching functions constructed by Galois
extension fields. Inf. Control 48 (1981), 95-108.

8276 Gerhard Turnwald: A new criterion for permutation polynomials.
Finite Fields 1 (1995), 64-82.

6097 Daqing Wan: Review of the books on finite fields by Shparlinski, 
Lidl/Mullen/Turnwald, Small, Mullen/Shiue, Jungnickel and Menezes.
Bull. AMS 30 (1994), 284-290.

Daqing Wan: Permutation polynomials and resolution of singularities over 
finite fields. Proc. AMS 110 (1990), 303-309.

8277 Daquing Wan: Minimal polynomials and distinctness of Kloosterman sums.
Finite Fields 1 (1995), 189-203.

18284 Zhe-xian Wan: Lectures on finite fields and Galois rings.
World Scientific 2003, 340p. Eur 44.

M. Willet: Arithmetic in a finite field. 
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