A new variant of the matsumoto-imai cryptosystem through perturbation

Abstract

Though the multivariable cryptosystems first suggested by Matsumoto and Imai was defeated by the linearization method of Patarin due to the special properties of the Matsumoto-Imai (MI) cryptosystem, many variants and extensions of the MI system were suggested mainly by Patarin and his collaborators. In this paper, we propose a new variant of the MI system, which was inspired by the idea of "perturbation". This method uses a set of r (a small number) linearly independent linear functions zi = ∑j=1n αijxj+βi, i=1, .., r, over the variables xi, which are variables of the MI system. The perturbation is performed by adding random quadratic function of Zi to the MI systems. The difference between our idea and a very similar idea of the Hidden Field Equation and Oil-Vinegar system is that our perturbation is internal, where we do not introduce any new variables, while the Hidden Field Equation and Oil-Vinegar system is an "external" perturbation of the HFE system, where a few extra (external) new variables are introduced to perform the perturbation. A practical implementation example of 136 bits, its security analysis and efficiency analysis are presented. The attack complexity of this perturbed Matsumoto-Imai cryptosystem is estimated. Keywords: open-key, multivariable, quadratic polynomials, perturbation © International Association for Cryptologic Research 2004.