High order linearization equation (HOLE) attack on multivariate public key cryptosystems

Authors:
Jintai Ding;Lei Hu;Xuyun Nie;Jianyu Li;John Wagner
Affiliations:
Department of Mathematical Sciences, University of Cincinnati, Fachbereich Informatik, Technische Universität Darmstadt, Cincinnati, OH;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing, China;Department of Mathematical Sciences, University of Cincinnati, Fachbereich Informatik, Technische Universität Darmstadt, Cincinnati, OH
Venue:
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Year:
2007

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Abstract

In the CT-track of the 2006 RSA conference, a new multivariate public key cryptosystem, which is called the Medium Field Equation (MFE) multivariate public key cryptosystem, is proposed by Wang, Yang, Hu and Lai. We use the second order linearization equation attack method by Patarin to break MFE. Given a ciphertext, we can derive the plaintext within 223 F216-multiplications, after performing once for any given public key a computation of complexity less than 252. We also propose a high order linearization equation (HOLE) attack on multivariate public key cryptosystems, which is a further generalization of the (first and second order) linearization equation (LE). This method can be used to attack extensions of the current MFE.