Analysis of Intermediate Field Systems.
Olivier Billet, Jacques Patarin, Yannick Seurin · IACR Cryptology ePrint Archive · 2009
We study a new generic trapdoor for public key multivariate cryptosystems, called IFS for Intermediate Field Systems, which can be seen as dual to HFE. This new trapdoor relies on the possibility to invert a system of quadratic multivariate equations with few (logarithmic with respect to the security parameter) unknowns on an intermediate field thanks to Grobner bases algorithms. We provide a comprehensive study of the security of this trapdoor and show that it is equivalent to the security provided by HFE. Therefore, while insecure in its basic form, this trapdoor may reveal quite attractive when used with, e.g., the minus modifier.