Journal of Cryptology

, Volume 26, Issue 2, pp 246–250

A Note on the Bivariate Coppersmith Theorem

  • Jean-Sébastien Coron
  • Alexey Kirichenko
  • Mehdi Tibouchi

DOI: 10.1007/s00145-012-9121-x

Cite this article as:
Coron, JS., Kirichenko, A. & Tibouchi, M. J Cryptol (2013) 26: 246. doi:10.1007/s00145-012-9121-x


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 theoremBivariate polynomialsSmall roots

Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Jean-Sébastien Coron
    • 1
  • Alexey Kirichenko
    • 2
  • Mehdi Tibouchi
    • 3
  1. 1.Université du LuxembourgLuxembourgLuxembourg
  2. 2.F-Secure CorporationHelsinkiFinland
  3. 3.NTT Information Sharing Platform LaboratoriesMusashino-shi, TokyoJapan