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Application of Homomorphism to Secure Image Sharing

Abstract : In this paper, we present a new approach for sharing images between l players by exploiting the additive and multiplicative homomorphic properties of two well-known public key cryptosystems, i.e. RSA and Paillier. Contrary to the traditional schemes, the proposed approach employs secret sharing in a way that limits the in fl uence of the dealer over the protocol and allows each player to participate with the help of his key-image. With the proposed approach, during the encryption step, each player encrypts his own key-image using the dealer's public key. The dealer encrypts the secret-to-be-shared image with the same public key and then, the l encrypted key-images plus the encrypted to-be shared image are multiplied homomorphically to get another encrypted image. After this step, the dealer can safely get a scrambled image which corresponds to the addition or multiplication of the l +1 original images ( l key-images plus the secret image) because of the additive homomorphic property of the Paillier algorithm or multiplicative homomorphic property of the RSA algorithm. When the l players want to extract the secret image, they do not need to use keys and the dealer has no role. Indeed, with our approach, to extract the secret image, the l players need only to subtract their own key-image with no speci fi c order from the scrambled image. Thus, the proposed approach provides an opportunity to use operators like multiplication on encrypted images for the development of a secure privacy preserving protocol in the image domain. We show that it is still possible to extract a visible version of the secret image with only l -1 key-images (when one key-image is missing) or when the l key-images used for the extraction are different from the l original key-images due to a lossy compression for example. Experimental results and security analysis verify and prove that the proposed approach is secure from cryptographic viewpoint.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00818389
Contributor : William Puech <>
Submitted on : Tuesday, May 14, 2013 - 11:19:54 AM
Last modification on : Monday, September 14, 2020 - 12:09:29 PM
Long-term archiving on: : Tuesday, April 4, 2017 - 12:58:53 AM

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Naveed Islam, William Puech, Khizar Hayat, Robert Brouzet. Application of Homomorphism to Secure Image Sharing. Optics Communications, Elsevier, 2011, 284 (19), pp.4412-4429. ⟨10.1016/j.optcom.2011.05.079⟩. ⟨lirmm-00818389⟩

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