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Abstract: . We present a new algorithm for finding an irreducible polynomial of specified degree over a finite field. Our algorithm is deterministic, and it runs in polynomial time for fields of small characteristic. We in fact prove the stronger result that the problem of finding irreducible polynomials of specified degree over a finite field is deterministic polynomial time reducible to the problem of factoring polynomials over the prime field. 1980 Mathematics Subject Classification (1985 revision).... (Update)
Context of citations to this paper: More
...the problem of constructing an irreducible polynomial of degree 2 for any given integer e. The last problem is considered by Lenstra [4] and Shoup [7]. Let 2 be the highest power of 2 in p 1. Then 2 is the highest power of 2 in p 1. Let # # F p 2 be of . Then it is known...
.... the composed sums and multiplications are used for constructing irreducible polynomials of large degree over finite fields, see [7, 8, 23] and [24] These operations, in particular composed sums and composed products, actually appear as basic subroutines in many other...
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9: The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
8: Small-bias probability spaces: Efficient constructions and applications - Naor, Naor - 1993
8: Finding irreducible polynomials over finite fields (context) - Adleman, Jr - 1986
BibTeX entry: (Update)
V. Shoup. New algorithms for finding irreducible polynomials over finite fields. Math. Comp., 54(189):435--447, 1990. http://citeseer.ist.psu.edu/shoup90new.html More
@inproceedings{ shoup88new,
author = "Victor Shoup",
title = "New Algorithms for Finding Irreducible Polynomials over Finite Fields",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "283-290",
year = "1988",
url = "citeseer.ist.psu.edu/shoup90new.html" }
Citations (may not include all citations):1450 The Design and Analysis of Computer Algorithms (context) - Aho, Hopcroft et al. - 1974
182 Algebraic Coding Theory (context) - Berlekamp - 1968
69 Factoring polynomials over large finite fields (context) - Berlekamp - 1970
40 Probabilistic algorithms in finite fields - Rabin - 1980
38 A knapsack type public key cryptosystem based on arithmetic .. - Chor, Rivest - 1984
32 A time-randomness tradeoff for oblivious routing (context) - Krizanc, Peleg et al. - 1988
23 Finding irreducible polynomials over finite fields (context) - Adleman, Lenstra - 1986
20 the deterministic complexity of factoring polynomials over f.. - Shoup - 1988
18 Realistic analysis of some randomized algorithms (context) - Bach - 1987
15 Theory of Equations (context) - Uspensky - 1948
14 Factorization of multivariate polynomials over finite fields (context) - Gathen, Kaltofen - 1985
14 Schnelle Multiplikation von Polynomen uber Korpern der Chara.. (context) - Schonhage - 1977
12 Randomized algorithms and pseudorandom numbers (context) - Karloff, Raghaven - 1988
10 Factoring polynomials and primitive elements for special pri.. (context) - Gathen - 1987
9 A bound for the least prime ideal in the Chebotarev density .. (context) - Lagarias, Montgomery et al. - 1979
9 nd edition (context) - Lang - 1984
9 Improving an algorithm for factoring polynomials over a fini.. (context) - Camion - 1983
8 Riemann Hypothesis and finding roots over finite fields (context) - Huang - 1985
7 Very fast parallel matrix and polynomial arithmetic (context) - Eberly - 1984
4 A general method of synthesizing irreducible polynomials ove.. (context) - Varshamov - 1984
3 Irreducible polynomials over finite fields (context) - Gathen - 1986
3 Factoring polynomials using fewer random bits - Bach, Shoup - 1988
2 Finding witnesses using fewer random bits (context) - Shoup - 1987
2 Springer-Verlag Lecture Notes in Mathematics No (context) - Schmidt, Finite - 1976
1 Efficient factorization of polynomials over finite fields an.. (context) - Evdokimov - 1986
1 th edition (context) - van der Waerden, Volume - 1970
The graph only includes citing articles where the year of publication is known.
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