Berlekamp–Rabin algorithm: Difference between revisions

Revision as of 21:56, 4 December 2019

Revision as of 21:56, 4 December 2019

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== History ==

The method was proposed by [[Elwyn Berlekamp]] in his 1970 work<ref name=":0" /> on polynomial factorization over finite fields. His original work lacked a formal [[Correctness (computer science)|correctness]] proof<ref name=":1" /> and was later refined and modified for arbitrary finite fields by [[Michael O. Rabin|Michael Rabin]].<ref name=":1" /> In 1986 René Peralta proposed a similar algorithm<ref>{{cite journal |author = Tsz-Wo Sze |editor= |title= On taking square roots without quadratic nonresidues over finite fields |journal= Mathematics of Computation|year= 2011 |volume= 80 |issue= 275 |pages = 1797–1811 |series= |issn = 00255718 |doi = 10.1090/s0025-5718-2011-02419-1 |bibcode = |arxiv =0812.2591 |pmid = |ref= |language= |quote= }}</ref> for finding square roots in <math>\mathbb Z_p</math>.<ref>{{cite journal |author = R. Peralta |editor= |title= A simple and fast probabilistic algorithm for computing square roots modulo a prime number (Corresp.) |journal= IEEE Transactions on Information Theory Date|date=November 1986 |volume= 32 |issue= 6 |pages = 846–847 |series= |issn = 00189448 |doi = 10.1109/TIT.1986.1057236 |bibcode = |arxiv = |pmid = |ref= |language= |quote= |year= 1986}}</ref> In 2000 Peralta's method was generalized for cubic equations.<ref>{{cite journal |author = C Padró, G Sáez |editor= |title= Taking cube roots in Zm |journal= Applied Mathematics Letters |date=August 2002 |volume= 15 |issue= 6 |pages = 703–708 |series= |issn = 08939659 |doi = 10.1016/s0893-9659(02)00031-9 |bibcode = |arxiv = |pmid = |ref= |language= |quote= }}</ref>

== Statement of problem==