Search for equivalent keys of the mceliece - sidelnikov cryptosystem built on the reed - muller binary codes

A new method is proposed for recovering equivalent secret keys of the McEliece - Sidelnikov cryptosystem built on the Reed - Muller binary codes. It is proved that using the superposition of Schur product and taking the orthogonal code we can obtain from the code with generating matrix (R||HR) the code belonging to the Cartesian product of codes RM(m - r (\\m/r] - 1) - 1,m) x RM(m - r(\\m/r \\ - 1) - 1,m). Here, R is the generating matrix of the Reed - Muller code of order r and length 2^m. Thus, proposed method reduces the problem of recovering equivalent secret keys of the McEliece - Sidel-nikov cryptosystem to two problems of finding the equivalent secret key of the McEliece cryptosystem. It is proved that the offered algorithm works in a polynomial time. Numerical experiments confirm the theoretical results.

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