International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Paper: Cryptanalysis of Rational Multivariate Public Key Cryptosystems

Authors:
Jintai Ding
John Wagner
Download:
URL: http://eprint.iacr.org/2007/367
Search ePrint
Search Google
Abstract: In 1989, Tsujii, Fujioka, and Hirayama proposed a family of multivariate public key cryptosystems, where the public key is given as a set of multivariate rational functions of degree 4\cite{Tsujii-Fujioka:89}. These cryptosystems are constructed via composition of two quadratic rational maps. In this paper, we present the cryptanalysis of this family of cryptosystems. The key point of our attack is to transform a problem of decomposition of two rational maps into a problem of decomposition of two polynomial maps. We develop a new improved 2R decomposition method and other new techniques, which allows us to find an equivalent decomposition of the rational maps to break the system completely. For the example suggested for practical applications, it is extremely fast to perform the computation to derive an equivalent private key, and it requires only a few seconds on a standard PC.
BibTeX
@misc{eprint-2007-13647,
  title={Cryptanalysis of Rational Multivariate Public Key Cryptosystems},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / multivariate public key cryptosystems, rational polynomials, map decomposition},
  url={http://eprint.iacr.org/2007/367},
  note={ ding@math.uc.edu 13769 received 13 Sep 2007},
  author={Jintai Ding and John Wagner},
  year=2007
}