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Differential Properties of the HFE Cryptosystem

  • Taylor Daniels
  • Daniel Smith-Tone
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8772)

Abstract

Multivariate Public Key Cryptography (MPKC) has been put forth as a possible post-quantum family of cryptographic schemes. These schemes lack provable security in the reduction theoretic sense, and so their security against yet undiscovered attacks remains uncertain. The effectiveness of differential attacks on various field-based systems has prompted the investigation of differential properties of multivariate schemes to determine the extent to which they are secure from differential adversaries. Due to its role as a basis for both encryption and signature schemes we contribute to this investigation focusing on the HFE cryptosystem. We derive the differential symmetric and invariant structure of the HFE central map and that of HFE  − and provide a collection of parameter sets which make these HFE systems provably secure against a differential symmetric or differential invariant attack.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Taylor Daniels
    • 1
  • Daniel Smith-Tone
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  2. 2.National Institute of Standards and TechnologyGaithersburgUSA

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