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Fast Algorithm of Square Rooting in Some Finite Fields of Odd Characteristic
Moscow State University, Russia.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
2018 (engelsk)Inngår i: Moscow University Mathematics Bulletin, ISSN 0027-1322, Vol. 73, nr 5, s. 176-181Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

It was proved that the complexity of square root computation in the Galois field GF(3 (s) ), s = 2 (k) r, is equal to O(M(2 (k) )M(r)k + M(r) log(2) r) + 2 (k) kr (1+o(1)), where M (n) is the complexity of multiplication of polynomials of degree n over fields of characteristics 3. The complexity of multiplication and division in the field GF(3 (s) ) is equal to O(M(2 (k) )M(r)) and O(M(2 (k) )M(r)) + r (1+o(1)), respectively. If the basis in the field GF(3 (r) ) is determined by an irreducible binomial over GF(3) or is an optimal normal basis, then the summands 2 (k) kr (1+o(1)) and r (1+o(1)) can be omitted. For M(n) one may take n log(2) n psi(n) where psi(n) grows slower than any iteration of the logarithm. If k grow and r is fixed, than all the estimates presented here have the form O (r) (M (s) log (2) s) = s (log (2) s)(2) psi(s).

sted, utgiver, år, opplag, sider
Cham: Springer, 2018. Vol. 73, nr 5, s. 176-181
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-70427DOI: 10.3103/S0027132218050029ISI: 000450666000002OAI: oai:DiVA.org:kau-70427DiVA, id: diva2:1268598
Tilgjengelig fra: 2018-12-06 Laget: 2018-12-06 Sist oppdatert: 2018-12-13bibliografisk kontrollert

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