In this paper, we show the claims in the original Kipnis-Shamir 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 Gröbner basis algorithm like F 4, the Kipnis-Shamir attack still should be exponential but not polynomial. This again is supported by our theoretical argument. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Jiang, X., Ding, J., & Hu, L. (2008). Kipnis-Shamir attack on HFE revisited. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4990 LNCS, pp. 399–411). https://doi.org/10.1007/978-3-540-79499-8_31
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