1
Ph.D. student, Department of Mathematics, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran
2
Associate Professor, Faculty and Research Institute of Information and Communication Technology, Imam Hossein University (AS), Tehran, Iran
3
Assistant Professor of Mathematics Department, Khorramabad Branch, Islamic Azad University, Khorramabad, Iran
4
Associate Professor, Information Science Research Institute, Iran Information Science and Technology Research Institute (Irandak), Tehran, Iran
Abstract
The Secret sharing is one of the fascinating topics of cryptography, which is widely used in information security. The aim of secret sharing is a process in which one or more secrets are shared between a number of qualified participants or with different credentials. In times when there is a need to recover a secret, a number of people, whom we call authorized people, collect their shares to recover the desired secret. So far, various types of secret sharing schemes based on interpolation have been proposed. In these secret sharing plans, different interpolations have been used, depending on the structural needs of the plan. In this article, some secret sharing schemes based on interpolation are introduced and reviewed. Then by analyzing and comparing the characteristics of these schemes, we conclude that the two secret sharing schemes based on Berkhoff interpolation have better efficiency than the other reviewed schemes.
Shamir, “ How to share a secret”, Communications of the ACM, 22(11), pp. 612-613, 1979.
R. Blakley, “Safeguarding cryptographic keys”, In Proceedings of the National Computer Conference, Vol. 48. No. 313, 1979.
Shamir, “How to share a secret”, Communications of the ACM, 22(11): 612- 613, 1979.
Harn, “Efficient sharing (broadcasting) of multiple secrets”, IEE Proceedings Computers and Digital Techniques, 142(3): 237-240, 1995.
Nikov, S. Nikov, B. Preneel, and J. Vandewalle., “Applying general access structure to proactive secret sharing schemes”, IACR Cryptology ePrint Archive, 141, 2002.
He, and E. Dawson,”Multistage secret sharing based on one-way function”. Electronics Letters, 30(19): 1591–1592, 1994.
, Pilaram and T. Eghlidos, “An efficient lattice based multi-stage secret sharing scheme”, IEEE Transactions on Dependable and Secure Computing, 14(1): 2–8, 2017.
Nojoumian, D. R. Stinson, and M. Grainger, “Unconditionally secure social secret sharing scheme”, IET Information Security, 4(4): 202–211, 2010.
Shamir, “How to share a secret”, Communications of the ACM, 22(11): 612- 613, 1979.
Farras, and C. Padro, “Ideal hierarchical secret sharing schemes”, Information Theory, IEEE Transactions on, 58(5):3273–3286, 2012.
J. Simmons, “How to (really) share a secret”, In Proceedings on Advances in Cryptology, CRYPTO ’88: 390–448, 1990.
F. Brickell, “Some ideal secret sharing schemes”, In Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques on Advances in Cryptology, EUROCRYPT’89: 468–475, 1990.
Tassa, and N. Dyn, “ Multi partite Secret Sharing by bivariate interpolation”, Journal of, Cryptology, 22(2): 227–258, 2009.
Atkinson, and A. Sharma, “A partial characterization of poised hermite–birkhoff interpolation problems”, SIAM Journal on Numerical Analysis, 6: 230–235, 1969.
Lorentz, K. Jetter, S. D. Riemenschneider, ”Birkhoff Interpolation.Encyclopedia of Mathematics and its Applications”, Vol.19. ISBN: 0-201-13518-3, 1984.
Beimel, T. Tassa, and E. Weinreb, “ Characterizing ideal weighted threshold secret sharing”, In Second Theory of Cryptography Conference, TCC 2005. Lecture Notes in Computer Sci. 3378: 600–619, 2005.
Morillo, C. Padro, G. Saez, and J. L. Villar,”Weighted threshold secret sharing schemes”, Information Processing Letters, 70(5): 211 – 216, 1999.
E. Ebrahimi Kiasari, A. Mirghadri, N. Pakniat, and M. Nazari, “Proactive multi-secret sharing scheme based on lagrange interpolation and chinese remainder theorem”, Journal of New Researches in Mathematics, 28:145-156, 2021.
E. Ebrahimi Kiasari, A. Mirghadri, N. Pakniat, and M. Nazari, “A new social multi-secret sharing scheme using Birkhoff interpolation and Chinese remainder theorem”, The ISC Int'l Journal of Information Security, Volume 15, Number 1, pp. 125–135, 2022.
Eslami, N. Pakniat, and M. Nojoumian, “Ideal social secret sharing using Birkhoff interpolation method”, Security and Communication Networks, 9(18):4973– 4982, 2016.
Pakniat, and Z. Eslami, “Verifiable social multi-secret sharing secure in active adversarial model. Journal of Computing and Security, 4(1): 3–12, 2017.
Ebrahimi Kiasari,M E , Mir Qadri,A R , nazari,M and Pakniat,N . (2024). Survey and analysis of several secret sharing schemes based on interepulation methods. Electronic and Cyber Defense, 12(1), 11-20.
MLA
Ebrahimi Kiasari,M E , , Mir Qadri,A R , , nazari,M , and Pakniat,N . "Survey and analysis of several secret sharing schemes based on interepulation methods", Electronic and Cyber Defense, 12, 1, 2024, 11-20.
HARVARD
Ebrahimi Kiasari M E, Mir Qadri A R, nazari M, Pakniat N. (2024). 'Survey and analysis of several secret sharing schemes based on interepulation methods', Electronic and Cyber Defense, 12(1), pp. 11-20.
CHICAGO
M E Ebrahimi Kiasari, A R Mir Qadri, M nazari and N Pakniat, "Survey and analysis of several secret sharing schemes based on interepulation methods," Electronic and Cyber Defense, 12 1 (2024): 11-20,
VANCOUVER
Ebrahimi Kiasari M E, Mir Qadri A R, nazari M, Pakniat N. Survey and analysis of several secret sharing schemes based on interepulation methods. Electronic and Cyber Defense. 2024;12(1):11-20 (In Persian).
