Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / multivariate public key cryptosystems, rational polynomials, map decomposition

Date: received 13 Sep 2007

Contact author: ding at math uc edu

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Version: 20070919:211049 (All versions of this report)

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