The polynomial composition problem in (Z/nZ)[X]

  • Authors:
  • Marc Joye;David Naccache;Stéphanie Porte

  • Affiliations:
  • Thomson R&D, Security Competence Center, Cesson-Sévigné Cedex, France;Ecole normale supérieure, Département d'informatique, Paris Cedex 05, France;Smart Consulting, La Ciotat, France

  • Venue:
  • CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
  • Year:
  • 2010

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Abstract

Let n be an RSA modulus and let $\mathcal {P},\mathcal{Q} \in (\mathbb{Z}/n\mathbb{Z})[X]$. This paper explores the following problem: Given polynomials $\mathcal{Q}$ and $\mathcal{Q}(\mathcal{P})$, find polynomial $\mathcal{P}$. We shed light on the connections between the above problem and the RSA problem and derive from it new zero-knowledge protocols suited to smart-card applications.