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• W1849802011 abstract "In this paper, we investigate the difficulty of one of the most relevant problems in multivariate cryptography – namely MinRank – about which no real progress has been reported since [9, 19]. Our starting point is the Kipnis-Shamir attack [19]. We first show new properties of the ideal generated by Kipnis-Shamir’s equations. We then propose a new modeling of the problem. Concerning the practical resolution, we adopt a Gröbner basis approach that permitted us to actually solve challenges A and B proposed by Courtois in [8]. Using the multi-homogeneous structure of the algebraic system, we have been able to provide a theoretical complexity bound reflecting the practical behavior of our approach. Namely, when r ′ the dimension of the matrices minus the rank of the target matrix in the MinRank problem is constant, then we have a polynomial time attack $mathcal{O}left( lnleft( qright) ,n^{3,r^{prime2}}right) $ . For the challenge C [8], we obtain a theoretical bound of 266.3 operations." @default.
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• W1849802011 date "2008-08-20" @default.
• W1849802011 modified "2023-10-10" @default.
• W1849802011 title "Cryptanalysis of MinRank" @default.
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• W1849802011 doi "https://doi.org/10.1007/978-3-540-85174-5_16" @default.
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