An algorithm for hiding and recovering data using matrices

03/12/2018

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by   Salomon S. Mizrahi, et al.

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We present an algorithm for the recovery of a matrix M (non-singular ∈ C^N× N) by only being aware of two of its powers, M_k_1:=M^k_1 and M _k_2:=M^k_2 (k_1>k_2) whose exponents are positive coprime numbers. The knowledge of the exponents is the key to retrieve matrix M out from the two matrices M_k_i. The procedure combines products and inversions of matrices, and a few computational steps are needed to get M, almost independently of the exponents magnitudes. Guessing the matrix M from the two matrices M_k_i, without the knowledge of k_1 and k_2, is comparatively highly consuming in terms of number of operations. If a private message, contained in M, has to be conveyed, the exponents can be encrypted and then distributed through a public key method as, for instance, the DF (Diffie-Hellman), the RSA (Rivest-Shamir-Adleman), or any other.