Cryptology ePrint Archive: Report 2004/361

Superfluous Keys in Multivariate Quadratic Asymmetric Systems

Christopher Wolf and Bart Preneel

Abstract: In this article, we show that public key schemes based on multivariate quadratic equations allow many equivalent, and hence superfluous private keys. We achieve this result by investigating several transformations to identify these keys and show their application to Hidden Field Equations (HFE), C$^*$, and Unbalanced Oil and Vinegar schemes (UOV). In all cases, we are able to reduce the size of the private --- and hence the public --- key space by at least one order of magnitude. We see applications of our technique both in cryptanalysis of these schemes and in memory efficient implementations.

Category / Keywords: public-key cryptography / Multivariate Quadratic Equations, Public Key Schemes, Equivalent Keys

Date: received 16 Dec 2004, last revised 28 Jan 2005

Contact author: christopher wolf at esat kuleuven ac be

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Version: 20050128:083727 (All versions of this report)

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