A Linear Algebraic Threshold Essential Secret Image Sharing Scheme

Mohammad Ghebleh, Ali Kanso and Abdullah Alazemi
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Mohammad Ghebleh: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Ali Kanso: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Abdullah Alazemi: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Mathematics, 2022, vol. 10, issue 5, 1-16

Abstract: A secret sharing scheme allocates to each participant a share of a secret in such a way that authorized subsets of participants can reconstruct the secret, while shares of unauthorized subsets of participants provide no useful information about the secret. For positive integers r , s , t , n with r ⩽ s ⩽ t ⩽ n , an ( r , s , t , n ) –threshold essential secret sharing scheme is an algorithm that decomposes a secret S into n shares, s of which are essential, in a way that authorized subsets are precisely those with at least t members, at least r of whom are essential. This work proposes a lossless linear algebraic ( r , s , t , n ) –threshold essential secret image sharing scheme that decomposes the secret, S , into equally-sized shares, each of size 1 / t the size of S . For each block, B , of S , the scheme assigns to the n participants distinct signature vectors v 1 , v 2 , … , v n in the vector space F 2 α t , where α is a suitable positive integer, typically between 2 and 5, inclusive. These signature vectors must adhere to some admissibility conditions in order to satisfy the secret sharing threshold properties. The decomposition of B into n shares is obtained by partitioning B into t vectors, then computing the share y j of the j th participant ( 1 ≤ j ≤ n ), as a linear combination of these parts with coefficients from the signature v j . The presented simulations showcase the effectiveness and robustness of the proposed scheme against standard statistical and security attacks. They further demonstrate its superiority with respect to existing schemes.

Keywords: secret sharing; threshold secret sharing; essential secret sharing; secret image sharing; admissible tracks; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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