Recovering a sum of two squares decomposition

  • Authors:
  • Jaime Gutierrez;Álvar Ibeas;Antoine Joux

  • Affiliations:
  • Dep. Matemática Aplicada y CC. Computación, Universidad de Cantabria, Spain;Dep. Matemática Aplicada y CC. Computación, Universidad de Cantabria, Spain;Chaire de Cryptologie de la Fondation Partenariale de l'UPMC, UPMC/LIP6, UMR CNRS 7606, Inria Paris-Rocquencourt, France

  • Venue:
  • Journal of Symbolic Computation
  • Year:
  • 2014

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Abstract

We present an algorithm that recovers a decomposition of an integer N as sum of two squares from an approximation to one of the summands. It is based on Coppersmith's linearization technique which, applied directly to this problem, requires an approximation error smaller than N^1^/^6. Our algorithm performs a two-round linearization and allows approximation errors up to N^1^/^4.