{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:44:29Z","timestamp":1776840269526,"version":"3.51.2"},"reference-count":32,"publisher":"American Mathematical Society (AMS)","issue":"355","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/S022503\/1"],"award-info":[{"award-number":["EP\/S022503\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis upper N comma upper N right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(N,N)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -isogenies, for any odd\u00a0\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N\">\n                        <mml:semantics>\n                          <mml:mi>N<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">N<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , both on the general Kummer surface and on the Fast model.\n                  <\/p>","DOI":"10.1090\/mcom\/4036","type":"journal-article","created":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T09:38:03Z","timestamp":1728466683000},"page":"2575-2612","source":"Crossref","is-referenced-by-count":3,"title":["Isogenies on Kummer Surfaces"],"prefix":"10.1090","volume":"94","author":[{"given":"Maria","family":"Corte-Real Santos","sequence":"first","affiliation":[]},{"given":"E.","family":"Flynn","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,11,7]]},"reference":[{"key":"1","unstructured":"[Bis11] G. Bisson, Endomorphism rings in cryptography, Ph.D. Thesis, Institut National Polytechnique de Lorraine-INPL, Technische Universiteit Eindhoven, 2011."},{"key":"2","unstructured":"[BCR10] G. Bisson, R. Cosset, and D. Robert, AVIsogenies v0.7 (abelian varieties and isogenies), Magma Package for Explicit Isogenies Between Abelian Varieties, 2021, \\url{https:\/\/www.math.u-bordeaux.fr\/ damienrobert\/avisogenies\/}."},{"issue":"3-4","key":"3","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma, Wieb","year":"1997","journal-title":"J. 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Cryptol.","ISSN":"https:\/\/id.crossref.org\/issn\/1862-2976","issn-type":"print"},{"issue":"4","key":"7","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/0196-8858(86)90023-0","article-title":"Sequences of numbers generated by addition in formal groups and new primality and factorization tests","volume":"7","author":"Chudnovsky, D. V.","year":"1986","journal-title":"Adv. in Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0196-8858","issn-type":"print"},{"key":"8","isbn-type":"print","first-page":"465","article-title":"Fast, uniform scalar multiplication for genus 2 Jacobians with fast Kummers","author":"Chung, Ping Ngai","year":"2017","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319694535"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[CCS24] M. Corte-Real Santos, C. Costello, and B. Smith. Efficient (3,3)-isogenies on fast Kummer surfaces, 2024, \\url{https:\/\/arxiv.org\/pdf\/2402.01223.pdf}.","DOI":"10.1007\/s40993-024-00600-y"},{"key":"10","unstructured":"[CF24] M. Corte-Real Santos and E. V. Flynn, Github repository, 2024, \\url{https:\/\/github.com\/mariascrs\/NN_{i}sogenies}."},{"key":"11","unstructured":"[Cos11] R. Cosset, Applications of theta functions for hyperelliptic curve cryptography, Ph.D. Thesis, Universit\u00e9 Henri Poincar\u00e9 - Nancy I, November 2011."},{"issue":"294","key":"12","doi-asserted-by":"publisher","first-page":"1953","DOI":"10.1090\/S0025-5718-2014-02899-8","article-title":"Computing (\u2113,\u2113)-isogenies in polynomial time on Jacobians of genus 2 curves","volume":"84","author":"Cosset, Romain","year":"2015","journal-title":"Math. 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