Cryptology ePrint Archive: Report 2004/360

Equivalent Keys in HFE, C$^*$, and variations

Christopher Wolf and Bart Preneel

Abstract: In this article, we investigate the question of equivalent keys for two $\mathcal{M}$ultivariate $\mathcal{Q}$uadratic public key schemes HFE and C$^{*--}$ and improve over a previously known result, to appear at PKC 2005. Moreover, we show a new non-trivial extension of these results to the classes HFE-, HFEv, HFEv-, and C$^{*--}$, which are cryptographically stronger variants of the original HFE and C$^*$ schemes. In particular, we are able to reduce the size of the private --- and hence the public --- key space by at least one order of magnitude. While the results are of independent interest themselves, we also see applications both in cryptanalysis and in memory efficient implementations.

Category / Keywords: public-key cryptography / Multivariate Quadratic Equations, Public Key signature, Hidden Field Equations, HFE, HFE-, HFEv, HFEv-, C$^*$, C$^{*--}$

Publication Info: Proceedings of Mycrypt 2005, LNCS 3715, pages 33-49. Serge Vaudenay, editor, Springer, 2005.

Date: received 16 Dec 2004, last revised 9 Aug 2005

Contact author: Christopher Wolf at esat kuleuven ac be

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Version: 20050809:120138 (All versions of this report)

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