Square-Vinegar Signature Scheme

Authors:
John Baena;Crystal Clough;Jintai Ding
Affiliations:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA 45220 and Department of Mathematics, National University of Colombia, Medellin, Colombia;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA 45220;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA 45220
Venue:
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Year:
2008

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Abstract

We explore ideas for speeding up HFE-based signature schemes. In particular, we propose an HFEv驴 system with odd characteristic and a secret map of degree 2. Changing the characteristic of the system has a profound effect, which we attempt to explain and also demonstrate through experiment. We discuss known attacks which could possibly topple such systems, especially algebraic attacks. After testing the resilience of these schemes against F4, we suggest parameters that yield acceptable security levels.