Abstract
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.
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Jiang, X., Ding, J., Hu, L. (2008). Kipnis-Shamir Attack on HFE Revisited. In: Pei, D., Yung, M., Lin, D., Wu, C. (eds) Information Security and Cryptology. Inscrypt 2007. Lecture Notes in Computer Science, vol 4990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79499-8_31
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DOI: https://doi.org/10.1007/978-3-540-79499-8_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79498-1
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