%0 Conference Proceedings %T Cryptanalysis of MinRank %+ Solvers for Algebraic Systems and Applications (SALSA) %+ Unité de Mathématiques Appliquées (UMA) %+ Algorithmique, Langage et Information (ALI) %A Faugère, Jean-Charles %A Levy-Dit-Vehel, Françoise %A Perret, Ludovic %< avec comité de lecture %( Advances in Cryptology – CRYPTO 2008 %B CRYPTO 2008 - 28th Annual International Cryptology Conference %C Santa Barbara, CA, United States %I Springer %3 Lecture Notes in Computer Science %V 5157 %P 280-296 %8 2008-08-17 %D 2008 %R 10.1007/978-3-540-85174-5_16 %Z Mathematics [math] %Z Computer Science [cs]/Cryptography and Security [cs.CR]Conference papers %X 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 O(ln(q)n3r′2) . For the challenge C [8], we obtain a theoretical bound of 266.3 operations. %G English %L hal-00976374 %U https://ensta-paris.hal.science/hal-00976374 %~ UPMC %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-ROCQ %~ INSMI %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ LIP6 %~ INRIA2 %~ UPMC_POLE_1 %~ SORBONNE-UNIVERSITE %~ SU-SCIENCES %~ SU-TI %~ ALLIANCE-SU