Differential Properties of the HFE Cryptosystem

Published

October 1, 2014

Author(s)

Taylor Daniels, Daniel Smith-Tone

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.

Volume

8772

Conference Dates

October 1-3, 2014

Conference Location

Waterloo, CA

Conference Title

PQCrypto 2014: The 6th International Conference on Post-Quantum Cryptography

Pub Type

Conferences

Download Paper

https://doi.org/10.1007/978-3-319-11659-4_4

Local Download

Keywords

MPKC, cryptostystem, HFE^- systems, differential properties

Citation

Daniels, T. and Smith-Tone, D. (2014), Differential Properties of the HFE Cryptosystem, PQCrypto 2014: The 6th International Conference on Post-Quantum Cryptography, Waterloo, CA, [online], https://doi.org/10.1007/978-3-319-11659-4_4, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=926104 (Accessed October 12, 2025)