Cryptanalysis of Rational Multivariate Public Key Cryptosystems

Jintai Ding; John Wagner

Paper 2007/367

Cryptanalysis of Rational Multivariate Public Key Cryptosystems

Jintai Ding and John Wagner

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: multivariate public key cryptosystems rational polynomials map decomposition
Contact author(s): ding @ math uc edu
History: 2007-09-19: received
Short URL: https://ia.cr/2007/367
License: CC BY

BibTeX

@misc{cryptoeprint:2007/367,
      author = {Jintai Ding and John Wagner},
      title = {Cryptanalysis of Rational Multivariate Public Key Cryptosystems},
      howpublished = {Cryptology ePrint Archive, Paper 2007/367},
      year = {2007},
      note = {\url{https://eprint.iacr.org/2007/367}},
      url = {https://eprint.iacr.org/2007/367}
}