An algorithm for hiding and recovering data using matrices

2018/03/12 by S. S. Mizrahi, Mizrahi, Salomon S., D. Galetti +1
Computer Science · Engineering · Mathematics · #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Geometric and Algebraic Topology #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1803.05003

openalex publication_date 2018/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an algorithm for the recovery of a matrix \mathbbM % (non-singular ∈ ℂ^{N× N}) by only being aware of two of its powers, \mathbbM_k₁:=\mathbbM^k₁ and \mathbbM% _k₂:=\mathbbM^k₂ (k₁>k₂) whose exponents are positive coprime numbers. The knowledge of the exponents is the key to retrieve matrix \mathbbM out from the two matrices \mathbbM_k_i. The procedure combines products and inversions of matrices, and a few computational steps are needed to get \mathbbM, almost independently of the exponents magnitudes. Guessing the matrix \mathbbM from the two matrices \mathbbM_k_i, without the knowledge of k₁ and k₂, is comparatively highly consuming in terms of number of operations. If a private message, contained in \mathbbM, 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.

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