High Order Linearization Equation (HOLE) Attack on Multivariate Public Key Cryptosystems

Jintai Ding; Lei Hu; Xuyun Nie; Jianyu li; John Wagner

Paper 2006/336

High Order Linearization Equation (HOLE) Attack on Multivariate Public Key Cryptosystems

Jintai Ding, Lei Hu, Xuyun Nie, Jianyu li, and John Wagner

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 -operations, after performing once for any public key a computation of complexity less than . 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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: multivariate PKC algebraic cryptanalysis high order linearization equation
Contact author(s): ding @ math uc edu
History: 2006-10-05: received
Short URL: https://ia.cr/2006/336
License: CC BY

BibTeX

@misc{cryptoeprint:2006/336,
      author = {Jintai Ding and Lei Hu and Xuyun Nie and Jianyu li and John Wagner},
      title = {High Order Linearization Equation ({HOLE}) Attack on Multivariate Public Key Cryptosystems},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/336},
      year = {2006},
      url = {https://eprint.iacr.org/2006/336}
}