Abstract. We apply internal perturbation [3] to the matrix-type cryptosystems [Cn] and HM constructed in [9]. Using small instances of these variants, we investigate the existence of linearization equations and degree 2 equations that could be used in a XL attack. Our results indicate that these new variants may be suitable for use in practical implementations. We propose a specific instance for practical implementation, and estimate its performance and security.
Zhiping Wu, Jintai Ding, Jason E. Gower, Dingfeng