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Fast Ideal Cubing in Quadratic Number and Function Fields

Laurent Imbert 1 Michael Jacobson Jr 2 Arthur Schmidt 2
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We present algorithms for computing the cube of an ideal in an imaginary quadratic number field or function field. In addition to a version that computes a non-reduced output, we present a variation based on Shanks' NUCOMP algorithm that computes a reduced output and keeps the sizes of the intermediate operands small. Extensive numerical results are included demonstrating that in many cases our formulas, when combined with double base chains using binary and ternary exponents, lead to faster exponentiation.
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Submitted on : Wednesday, May 19, 2010 - 1:00:10 AM
Last modification on : Friday, October 22, 2021 - 3:07:18 PM

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Laurent Imbert, Michael Jacobson Jr, Arthur Schmidt. Fast Ideal Cubing in Quadratic Number and Function Fields. Advances in Mathematics of Communications, AIMS, 2010, 4 (2), pp.237-260. ⟨10.3934/amc.2010.4.237⟩. ⟨lirmm-00484731⟩



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