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<p>We give an alternative derivation of (<i>N</i>,&#xa0;<i>N</i>)-isogenies between fast Kummer surfaces which complements existing works based on the theory of theta functions. We use this framework to produce explicit formulæ for the case of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40993_2024_600_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(N=3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, and show that the resulting algorithms are more efficient than all prior (3,&#xa0;3)-isogeny algorithms.</p>

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Efficient (3, 3)-isogenies on fast Kummer surfaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月11日

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  • Maria Corte-Real Santos,
  • Craig Costello,
  • Benjamin Smith

摘要

We give an alternative derivation of (N, N)-isogenies between fast Kummer surfaces which complements existing works based on the theory of theta functions. We use this framework to produce explicit formulæ for the case of \(N=3\) N = 3 , and show that the resulting algorithms are more efficient than all prior (3, 3)-isogeny algorithms.