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 \(z_i=\sum_{j=1}^n \alpha_{ij} x_j+\beta_i,\) i=1,..,r, over the variables x i , which are variables of the MI system. The perturbation is performed by adding random quadratic function of z i 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.
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Ding, J. (2004). A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation. In: Bao, F., Deng, R., Zhou, J. (eds) Public Key Cryptography – PKC 2004. PKC 2004. Lecture Notes in Computer Science, vol 2947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24632-9_22
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DOI: https://doi.org/10.1007/978-3-540-24632-9_22
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