Random polynomials and polynomial factorization

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1099, Issue , 1996, Pages 232-243

  Flajolet, Philippe ^a   Gourdon, Xavier ^a   Panario, Daniel ^b  

^a INRIA ROCQUENCOURT   (France)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; FACTORIZATION;

AVERAGE-CASE ANALYSIS; FINITE FIELDS; GENERATING FUNCTIONS; POLYNOMIAL FACTORIZATION; RANDOM POLYNOMIALS; SINGULARITY ANALYSIS;

POLYNOMIALS;

EID: 84947786774     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61440-0_131     Document Type: Conference Paper

References (24)

1. Berlekamp, E. R. Algebraic Coding Theory. Mc Graw-HШ, 1968. Revised edition, 1984.
2. buchmann, J. Complexity of algorithms in number theory. In Number Theory: Proceeding! of the First Conference of the Canadian Number Theory Association (1990), Walter de Gruyter, pp. 37—53.
3. Cantor, D. G., and zassenhauss, H. A new algorithm for factoring polynomials over finite fields. Mathematics of Computation 36 (1981), 587-592.
4. CAR, M. Factorisation dans Comptes-Rendus de VAcadémie des Sciences 294 (Ser. I) (1982), 147-150.
5. CARLITZ, L. The arithmetic of polynomials in a Galois field. American Journal of Mathematics 54 (1932), 39-50.
6. Chor, B., and Rivest, R. A knapsack type public key cryptosystem based on on arithmetics over finite fields. IEEE Transactions on Information Theory 34 (1988), 901-909.
7. COMTET, L. Advanced Combinatorics. Reidel, Dordrecht, 1974.
8. DEDEKIND, R. Abriss einer Theorie der höhern Congruenzen in Bezug auf einen reellen Primzahlmodulus. Journal für die reine und angewandte Mathematik 54 (1857), 1-26.
9. FLAJOLET, P., and Odlyzko, A. M. Singularity analysis of generating functions. SIAM Journal on Discrete Mathematics 3, 2 (1990), 216-240.
10. FLAJOLET, P., and soria, M. Gaussian limiting distributions for the number of components in combinatorial structures. Journal of Combinatorial Theory, Series A 53 (1990), 165-182.
11. Gauss, C. F. Untersuchungen über höhere Mathematik. Chelsea, New York, 1889.
12. geddes, К. O., czapor, S. R., and Labahn, G. Algorithms for Computer Algebra. Kluwer Academic Publishers, Boston, 1992.
13. greene, D. H., and KNUTH, D. E. Mathematics for the analysis of algorithms, seconded. Birkhauser, Boston, 1982.
14. knopfmacher, J., and knopfmacher, A. Counting irreducible factors of polynomials over a finite field. Discrete Mathematics 112 (1993), 103-118.
15. knuth, D. E. The Art of Computer Programming, vol.3: Sorting and Searching. Addison-Wesley, 1973.
16. knuth, D. E. The Art of Computer Programming, 2nd ed., vol. 2: Seminumerical Algorithms. Addison-Wesley, 1981.
17. knuth, D. E., and pardo, L. T. Analysis of a simple factorization algorithm. Theoretical Computer Science 3 (1976), 321-348.
18. lenstra, H. W. On the Chor Rivest cryptosystem. Journal ofCryptologyS (1991), 149-155.
19. LIDL, R., and NIEDERREITER, Η. Finite Fields, vol. 20 of Encyclopedia of Mathematics and its Applications. Addison-Wesley, 1983.
20. ODLYZKO, A. M. Discrete logarithms and their cryptographic significance. In Advances in Cryptology (1985), Lecture Notes in Computer Science, Springer Verlag, pp. 224-314.
21. ODLYZKO, A. M. Asymptotic enumeration methods. In Handbook of Combinatorics, M. G. R. Graham and L. Lovasz, Eds., vol. II. Elsevier, Amsterdam, 1995, pp. 1063-1229.
22. postnikov, A. G. Tauberian theory and its applications, vol. 144 of Proceedings of the Steklov Institute of Mathematics. American Mathematical Society, 1980.
23. Shepp, L. Α., and Lloyd, S. P. Ordered cycle lengths in a random permutation. Transactions of the American Mathematical Society 121 (1966), 340-357.
24. Shoup, V. A new polynomial factorization algorithm and its implementation. Preprint, 1994.