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## A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing

#### İbrahim OZBEK [1] , Fatih TEMİZ [2] , İrfan SİAP [3]

Secret sharing scheme is an efficient method to hide secret key or secret image by partitioning it into parts such that some predetermined subsets of partitions can recover the secret but remaining subsets cannot. In 1979, the pioneer construction on this area was given by Shamir and Blakley independently. After these initial studies, Asmuth-Bloom and Mignotte have proposed a different $(k,n)$ threshold modular secret sharing scheme by using the Chinese remainder theorem. In this study, we explore the generalization of Mignotte's scheme to Euclidean domains for which we obtain some promising results. Next, we propose new algorithms to construct threshold secret image sharing schemes by using Mignotte's scheme over polynomial rings. Finally, we compare our proposed scheme to the existing ones and we show that this new method is more efficient and it has higher security.
Mignotte sequences, Secret image sharing, Secret sharing scheme, Euclidean domain
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Primary Language en Engineering Articles Author: İbrahim OZBEK Orcid: 0000-0001-5477-0463Author: Fatih TEMİZ (Primary Author) Orcid: 0000-0002-9702-1531Author: İrfan SİAP Publication Date : September 13, 2019
 Bibtex @research article { jacodesmath617239, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2019}, volume = {6}, pages = {147 - 161}, doi = {10.13069/jacodesmath.617239}, title = {A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing}, key = {cite}, author = {Ozbek, İbrahim and Temi̇z, Fatih and Si̇ap, İrfan} } APA Ozbek, İ , Temi̇z, F , Si̇ap, İ . (2019). A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing . Journal of Algebra Combinatorics Discrete Structures and Applications , 6 (3) , 147-161 . DOI: 10.13069/jacodesmath.617239 MLA Ozbek, İ , Temi̇z, F , Si̇ap, İ . "A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing" . Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 147-161 Chicago Ozbek, İ , Temi̇z, F , Si̇ap, İ . "A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing". Journal of Algebra Combinatorics Discrete Structures and Applications 6 (2019 ): 147-161 RIS TY - JOUR T1 - A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing AU - İbrahim Ozbek , Fatih Temi̇z , İrfan Si̇ap Y1 - 2019 PY - 2019 N1 - doi: 10.13069/jacodesmath.617239 DO - 10.13069/jacodesmath.617239 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 147 EP - 161 VL - 6 IS - 3 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.617239 UR - https://doi.org/10.13069/jacodesmath.617239 Y2 - 2019 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing %A İbrahim Ozbek , Fatih Temi̇z , İrfan Si̇ap %T A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing %D 2019 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 6 %N 3 %R doi: 10.13069/jacodesmath.617239 %U 10.13069/jacodesmath.617239 ISNAD Ozbek, İbrahim , Temi̇z, Fatih , Si̇ap, İrfan . "A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing". Journal of Algebra Combinatorics Discrete Structures and Applications 6 / 3 (September 2019): 147-161 . https://doi.org/10.13069/jacodesmath.617239 AMA Ozbek İ , Temi̇z F , Si̇ap İ . A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(3): 147-161. Vancouver Ozbek İ , Temi̇z F , Si̇ap İ . A generalization of the Mignotte’s scheme over Euclidean domains and applications to secret image sharing. Journal of Algebra Combinatorics Discrete Structures and Applications. 2019; 6(3): 147-161.

Authors of the Article
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