Technical Report CS-2000-01

Title: Cryptanalysis of Patarin's 2-Round Public Key System with S Boxes (2R)
Authors: Eli Biham
Abstract: In a series of papers Patarin proposes new efficient public key systems. A very interesting proposal, called {\it 2-Round Public Key System with S Boxes}, or {\it 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 $2^{30}$ steps, and the more secure 128-bit blocks variant with complexity about $2^{60}$ 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.
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