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Category / Keywords: public-key cryptography / digital signatures, provable security, short signatures, multivariate cryptography, HFE, Quartz, Sflash, algebraic attacks, multivariate polynomial equations, Grobner bases Date: received 17 Jun 2004, last revised 15 Jun 2005 Contact author: courtois at minrank org Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Note: On the margin of this paper: The recent HFE paper by Faugère and Joux heavily misrepresents the actual state of contributions, regarding the security of HFE systems. All the attacks Faugère et al. attribute to themselves, were already known and published in not less than 5 previously published papers (!), by Patarin himself, Shamir and Kipnis, Courtois, Daum and Felke. The details are found in Section 8.2. of this draft. Version: 20050615:164807 (All versions of this report) Short URL: ia.cr/2004/143 Discussion forum: Show discussion | Start new discussion