Analysis of Intermediate Field Systems

Olivier Billet; Jacques Patarin; Yannick Seurin

Paper 2009/542

Analysis of Intermediate Field Systems

Olivier Billet, Jacques Patarin, and Yannick Seurin

Abstract

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 Groebner 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): yannick seurin @ m4x org
History: 2009-11-08: received
Short URL: https://ia.cr/2009/542
License: CC BY

BibTeX

@misc{cryptoeprint:2009/542,
      author = {Olivier Billet and Jacques Patarin and Yannick Seurin},
      title = {Analysis of Intermediate Field Systems},
      howpublished = {Cryptology ePrint Archive, Paper 2009/542},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/542}},
      url = {https://eprint.iacr.org/2009/542}
}