Cryptanalysis of Patarin’s 2-Round Public Key System with S Boxes (2R)

In a series of papers Patarin proposes new efficient public key systems. A very interesting proposal, called 2-Round Public Key System with S Boxes, or 2R, is based on the difficulty of decomposing the structure of several rounds of unknown linear transformations and S boxes. This difficulty is due to the difficulty of decomposing compositions of multivariate binary functions. In this paper we present a novel attack which breaks the 64-bit block variant with complexity about 230 steps, and the more secure 128-bit blocks variant with complexity about 260 steps. It is interesting to note that this cryptanalysis uses only the ciphertexts of selected plaintexts, and does not analyze the details of the supplied encryption code.