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Abstract: Several algorithms for factoring polynomials over finite fields are compared from the point of view of asymptotic complexity, and from a more realistic point of view: how well actual implementations perform on "moderately" sized inputs. 1 Introduction The purpose of this paper is to examine several algorithms for factoring polynomials over finite fields, from both the point of view of asymptotic complexity, and from a more realistic point of view: how well actual implementations perform on... (Update)
Context of citations to this paper: More
.... Shoup 1995, Fleischmann Roelse 1996) At the heart of these achievements lies the systematic use of fast arithmetic, pioneered by Shoup (1993) . This Extended Abstract presents a first step towards applying fast methods in symbolic summation, namely to two problems that...
...1991, Cantor 1989) and repeated squaring. We may always assume an exponent to be less than q n . Implementation reports are in Shoup (1993) and von zur Gathen and Gerhard (1999) Section 9.7. Fast polynomial factorization software is also discussed in Montgomery (1991) and...
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0.3: A New Polynomial Factorization Algorithm and its Implementation - Shoup (1996) (Correct)
0.3: Efficient Computation of Minimal Polynomials in Algebraic.. - Shoup (1999) (Correct)
0.2: On Fast and Provably Secure Message Authentication Based on.. - Shoup (1996) (Correct)
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0.2: Subquadratic-Time Factoring of Polynomials over Finite Fields - Kaltofen, Shoup (1995) (Correct)
0.2: Polynomial Factorization Challenges - Zimmermann, Bernardin, Monagan (1996) (Correct)
0.2: Computing Frobenius Maps And Factoring Polynomials - Gathen, Shoup (1992) (Correct)
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3: Subquadratic-time factoring of polynomials over finite fields - Kaltofen, Shoup - 1995
3: A new polynomial factorization algorithm and its implementation - Shoup - 1996
3: RFC1036: Standard for interchange of USENET messages (context) - Adams - 1987
BibTeX entry: (Update)
V. Shoup, Factoring polynomials over finite fields: asymptotic complexity vs. reality. In Proc. Int. IMACS Symp. on Symbolic Computation, New Trends and Developments, Lille, France, 1993, 124--129. http://citeseer.ist.psu.edu/shoup93factoring.html More
@misc{ shoup93factoring,
author = "V. Shoup",
title = "Factoring polynomials over finite fields: asymptotic complexity vs",
text = "V. Shoup, Factoring polynomials over finite fields: asymptotic complexity
vs. reality. In Proc. Int. IMACS Symp. on Symbolic Computation, New Trends
and Developments, Lille, France, 1993, 124--129.",
year = "1993",
url = "citeseer.ist.psu.edu/shoup93factoring.html" }
Citations (may not include all citations):2003 The Art of Computer Programming (context) - Knuth - 1981
69 Factoring polynomials over large finite fields (context) - Berlekamp - 1970
42 Fast algorithms for manipulating formal power series (context) - Brent, Kung - 1978
39 A new algorithm for factoring polynomials over finite fields (context) - Cantor, Zassenhaus - 1981
27 Computing Frobenius maps and factoring polynomials - Gathen, Shoup - 1992
4 Solving sparse linear systems over finite fields (context) - Wiedemann - 1986
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