Remarks on the Attack of Fouque et al. against the {\ell}IC Scheme

Naoki Ogura; Shigenori Uchiyama

Paper 2008/208

Remarks on the Attack of Fouque et al. against the {\ell}IC Scheme

Naoki Ogura and Shigenori Uchiyama

Abstract

In 2007, $ℓ$ -Invertible Cycles ( $ℓ$ IC) was proposed by Ding et al. This is one of the most efficient trapdoors for encryption/signature schemes, and of the mixed field type for multivariate quadratic public-key cryptosystems. Such schemes fit on the implementation over low cost smart cards or PDAs. In 2008, Fouque et al. proposed an efficient attack against the IC signature scheme by using Gröbner basis algorithms. However, they only explicitly dealt with the odd case, i.e. is odd, but the even case; they only implemented their proposed attack in the odd case. In this paper, we propose an another practical attack against the IC encryption/signature scheme. Our proposed attack does not employ Gröbner basis algorithms, and can be applied to the both even and odd cases. We show the efficiency of the attack by using some experimental results. Furthermore, the attack can be also applied to the IC- scheme. To the best of our knowledge, we for the first time show some experimental results of a practical attack against the IC- scheme for the even case.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: -Invertible Cycles SFLASH
Contact author(s): ogura-naoki @ ed tmu ac jp
History: 2008-05-21: revised; 2008-05-21: received; See all versions
Short URL: https://ia.cr/2008/208
License: CC BY

BibTeX

@misc{cryptoeprint:2008/208,
      author = {Naoki Ogura and Shigenori Uchiyama},
      title = {Remarks on the Attack of Fouque et al. against the {\ell}{IC} Scheme},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/208},
      year = {2008},
      url = {https://eprint.iacr.org/2008/208}
}