Welcome to the resource topic for 2004/305
Title:
A note on efficient computation of cube roots in characteristic 3
Authors: Paulo S. L. M. Barreto
Abstract:The cost of the folklore algorithm for computing cube roots in \F_{3^m} in standard polynomial basis is less that one multiplication, but still O(m^2). Here we show that, if \F_{3^m} is represented in trinomial basis as \F_3[x]/(x^m + ax^k + b) with a, b = \pm 1, the actual cost of computing cube roots in \F_{3^m} is only O(m).
ePrint: https://eprint.iacr.org/2004/305
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