Cryptology ePrint Archive: Report 2007/203

Kipnis-Shamir's Attack on HFE Revisited

Xin Jiang and Jintai Ding and Lei Hu

Abstract: In this paper, we show that the claims in the original Kipnis-Shamir's attack on the HFE cryptosystems and the improved attack by Courtois that the complexity of the attacks is polynomial in terms of the number of variables are invalid. We present computer experiments and a theoretical argument using basic algebraic geometry to explain why it is so. Furthermore we show that even with the help of the powerful new Gr\"{o}bner basis algorithm like $F_4$, the Kipnis-Shamir's attack still should be exponential not polynomial. This again is supported by our theoretical argument.

Category / Keywords: public-key cryptography /

Date: received 30 May 2007

Contact author: ding at math uc edu

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Version: 20070531:185642 (All versions of this report)

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