Recovering a sum of two squares decomposition

Jaime Gutierrez , Ibeas Alvar , Antoine Joux (1)

1 ALMASTY - ALgorithms for coMmunicAtion SecuriTY

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 $N^{1/4}$.

Domaines: Informatique [cs]

Jaime Gutierrez, Ibeas Alvar, Antoine Joux. Recovering a sum of two squares decomposition. Journal of Symbolic Computation, 2014, 64, pp.16-21. ⟨10.1016/j.jsc.2013.12.003⟩. ⟨hal-01198937⟩