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Differential Properties of the HFE Cryptosystem



Taylor Daniels, Daniel Smith-Tone


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.
Conference Dates
October 1-3, 2014
Conference Location
Waterloo, CA
Conference Title
PQCrypto 2014: The 6th International Conference on Post-Quantum Cryptography


MPKC, cryptostystem, HFE<sup>-</sup> systems, differential properties


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],, (Accessed June 25, 2024)


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Created September 30, 2014, Updated October 12, 2021