Journal of Cryptology

, Volume 26, Issue 2, pp 246-250

First online:

A Note on the Bivariate Coppersmith Theorem

  • Jean-Sébastien CoronAffiliated withUniversité du Luxembourg Email author 
  • , Alexey KirichenkoAffiliated withF-Secure Corporation
  • , Mehdi TibouchiAffiliated withNTT Information Sharing Platform Laboratories

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In 1997, Coppersmith proved a famous theorem for finding small roots of bivariate polynomials over ℤ, with important applications to cryptography.

While it seems to have been overlooked until now, we found the proof of the most commonly cited version of this theorem to be incomplete. Filling in the gap requires technical manipulations which we carry out in this paper.

Key words

Coppersmith’s theorem Bivariate polynomials Small roots