پیشنهاد و مقایسه دو ﻃﺮح ﺗﺴﻬﯿﻢ ﭼﻨﺪ راز ﺗﺼﺪﯾﻖ ﭘﺬﯾﺮ: یک طرح ﺧﻄﯽ ﺑﺎ اﻣﻨﯿﺖ اﺳﺘﺎﻧﺪارد و یک طرح مشبکه مبنا

[1]     A. Shamir‎, “How to Share a Secret,” ‎Communications of the ACM‎, vol.‎ 22, no. 11, pp. ‎612-613‎, ‎1979‎.##

[2]     G. Blakley‎, “Safeguarding Cryptographic Keys,” ‎In Proc. AFIPS 1979 National‎ Computer Conf.‎, ‎pp‎. ‎313–317‎, ‎June 1979‎.##

[3]     Z. Eslami, ‎S. Kabiri Rad, “A New Verifiable Multi-Secret Sharing Scheme‎ Based on Bilinear Maps‎,” ‎Wirel‎. ‎Pers‎. ‎Commun.‎, ‎63‎, ‎pp‎. ‎459–467‎, ‎2012‎.##

[4]     Ch. Hsu‎, Q. Cheng‎, X. Tang‎, ‎et al, “An Ideal Multi-Secret Sharing Scheme Based on MSP‎,” ‎Inf‎. ‎Sci.‎, ‎181‎, ‎pp‎. ‎1403–1409‎, ‎2011‎.##

[5]     J. ‎Zhang‎, F. Zhang, “Information-theoretical Secure Verifiable Secret Sharing‎ with Vector Space Access Structures over Bilinear Groups and its Application,” Future Gener‎. ‎Comput‎. ‎Syst.‎ 52‎, ‎pp‎. ‎109–115‎, ‎2015‎.##

[6]     M. Ben-Or‎, Sh. Goldwasser‎, ‎A. Wigderson, “Completeness Theorems for Non-cryptographic Fault-Tolerant Distributed Computation (Extended Abstract),”‎ ‎ STOC‎, ‎p‎p. ‎1–10‎, ‎1988‎.##

[7]     D. Chaum‎, ‎C. Crepeau‎, I. ‎Damgard, “Multiparty Unconditionally Secure Protocols (Extended Abstract),” ‎ ‎STOC‎, ‎pp‎. ‎11–19‎, ‎1988‎.##

[8]     B Chor‎, ‎Sh. Goldwasser‎, ‎S Micali, ‎B. Awerbuch‎, “Verifiable Secret Sharing and Achieving Simultaneity in the Presence of Faults (Extended Abstract),” ‎ ‎FOCS‎, p‎p‎. ‎383–395‎, ‎1985‎.##

[9]     C. Ma, X. Ding, “Proactive Verifiable Linear Integer Secret Sharing Scheme,” Information and Communications Security‎, (LNCS‎, ‎5927)‎, ‎pp‎. ‎439–448‎, ‎2009‎.##

[10]  S. Mashhadi‎‎, M. Hadian‎, “Two Verifiable Multi Secret Sharing Schemes Based‎ on Nonhomogeneous Linear Recursion and LFSR Public-Key Cryptosystem‎,” Inf‎. ‎Sci.‎, ‎ 294‎, ‎pp‎. ‎31–40‎, ‎2015‎.##

[11]  T. S. Wu‎‎, Y. M. Tseng‎, “Publicly Verifiable Multi-Secret Sharing Scheme‎ from Bilinear Pairings,” ‎IET Inf‎. ‎Sec.‎, ‎7‎, ‎pp‎. ‎239–246‎, ‎2013‎.##

[12]  C. Lin‎, ‎L. Harn, “Unconditionally Secure Verifiable Secret Sharing Scheme‎,” AISS‎: ‎Adv‎. ‎Inf‎. ‎Sci‎. ‎Serv‎. ‎Sci.‎, ‎4‎, ‎pp‎. ‎514–518, 2012‎.##

[13]  D. R. ‎Stinson, R. ‎Wei “Unconditionally Secure Proactive Secret Sharing‎ Scheme with Combinatorial Structures‎, ‎Selected Areas in Cryptography‎,” Selected Areas in Cryptography‎: ‎SAC'99‎, ‎(LNCS‎, ‎1758)‎, ‎pp‎. ‎200–214‎, ‎2000‎.##

[14]  M. Fatemi‎, R. Ghasemi, T. ‎Eghlidos, M. R. Aref, “Efficient Multistage Secret‎ Sharing Scheme Using Bilinear Map,” ‎IET Inf‎. ‎Sec.‎, ‎8‎, ‎pp‎. ‎224–229‎, ‎2014‎.##

[15]  J. Herranz‎, ‎ A. Ruiz‎‎, ‎G. Sáez‎, “Sharing Many Secrets with Computational‎ Provable Security‎,” ‎Inf‎. ‎Proc‎. ‎Lett.‎, ‎113‎, ‎pp‎. ‎572–579‎, ‎2013‎.##

[16]  S. Mashhadi, “How to Fairly Share Multiple Secrets Stage by Stage” ‎, ‎Wirel‎. Pers‎. ‎Commun.‎, ‎90‎, ‎pp‎. ‎93–107‎, ‎2016‎.##

[17]  L. J. Pang, Y. M. ‎Wang‎, “A New (t‎, ‎n) Multi-Secret Sharing Scheme Based on Shamir’s Secret‎ Sharing‎,” ‎Applied Mathematics and Computation‎, vol. ‎167‎, ‎pp. 840-848‎, ‎2005‎.##

[18]  T. Y. Chang‎, M. S.  ‎Hwang‎, ‎W. P. Yang‎, ‎ “A New Multi-Stage Secret Sharing‎ Scheme Using One-Way Function,” ACM SIGOPS Oper‎. ‎Syst.‎, ‎39‎, ‎pp‎. ‎48–55, 2005‎.##

[19]  J. He‎‎, E.‎ Dawson‎, “Multistage Secret Sharing Based on One-Way Function‎,” Electron‎. ‎Lett.‎, vol. ‎30‎, ‎pp‎. ‎1591–1592‎, ‎1994‎.##

[20]  H. X. Li‎‎, ‎C. T. Cheng‎‎, L. J. ‎Pang‎‎, “An Improved Multi-Stage (t‎, ‎n)-Threshold‎ Secret Sharing Scheme‎,” ‎WAIM‎, ‎ (LNCS‎, ‎3739)‎, ‎pp‎. ‎267–274‎, ‎2005‎.##

[21]  P. W. Shor, “Algorithms for Quantum Computation‎: ‎Discrete Logarithms and‎ Factoring‎,” ‎Proc. of the 35th Annual Symposium on Foundations of‎ Computer Science‎, ‎Washington‎, ‎DC‎, ‎USA‎: ‎IEEE Computer Society‎, pp‎. ‎124-134‎, ‎1994‎.##

[22]  R‎. ‎J‎. ‎McEliece‎, “A Public-Key Cryptosystem Based on Algebraic Coding Theory‎,” DSN Progress Report‎, ‎vol‎. ‎42‎, ‎no‎. ‎44‎, ‎pp‎. ‎114-116‎, ‎1978‎.##

[23]  D‎. ‎Bernstein‎, ‎J‎. ‎Buchmann‎, ‎E‎. ‎Dahmen‎, “Post-Quantum Cryptography,”‎ Springer‎, ‎2009‎.##

[24]  M‎. ‎Ajtai‎, “Generating Hard Instances Of Lattice Problems (Extended Abstract),”‎ Proc. of the Twenty-Eighth Annual ACM Symposium on Theory of‎ Computing‎, ‎New York‎, ‎NY‎, ‎USA‎: ‎ACM‎‎, ‎pp‎. ‎99-108,  1996.##

[25]  O‎. ‎Goldreich‎, ‎S‎. ‎Goldwasser‎, ‎S‎. ‎Halevi, “Public-key Cryptosystems from Lat‎Tice Reduction Problems,” ‎Advances in Cryptology CRYPTO 97‎, ‎ser‎. ‎Lecture‎ Notes in Computer Science‎, ‎J‎. ‎Kaliski‎, ‎BurtonS.‎, ‎Ed‎. ‎Springer Berlin Hei‎delberg‎, ‎vol‎. ‎1294‎, ‎pp‎. ‎112-131‎, ‎1997‎.##

[26]  Georgescu‎, “A Lwe-Based Secret Sharing Scheme‎,” ‎IJCA Special Issue on‎ Network Security and Cryptography‎, ‎ ‎no‎. ‎3‎, ‎pp‎. ‎27-29‎, ‎December‎, ‎published by Foundation of Computer Science‎, ‎New York‎, ‎USA‎, ‎2011‎.

[27]  R‎. ‎El Bansarkhani‎, ‎M‎. ‎Meziani‎, ‎“An Efficient Lattice-Based Secret Sharing‎ Construction‎,” ‎Information Security Theory and Practice‎. ‎Security‎, ‎Privacy‎ and Trust in Computing Systems and Ambient Intelligent Ecosystems‎, ser‎. ‎Lecture Notes in Computer Science‎, ‎I‎. ‎Askoxylakis‎, ‎H‎. ‎Phls‎, ‎and J‎. Posegga‎, ‎Eds‎. ‎Springer Berlin Heidelberg‎, ‎vol‎. ‎7322‎, ‎pp‎. ‎160-168‎, ‎2012‎.##

[28]  J. Shao‎, ‎Z. F. Cao, “A New Efficient (t‎, ‎n) Verifiable Multi-Secret Sharing (VMSS) Based on YCH‎ Scheme‎,” ‎Applied Mathematics and Computation‎, ‎168‎, ‎pp. 135–140‎, ‎2005‎.##

[29]  M. ‎Tadayon‎, ‎H.‎ ‎Khanmohammadi‎‎, M. Haghighi‎, “Dynamic and Verifiable‎ Multi-Secret Sharing Scheme Based on Hermite Interpolation and Bilinear‎ Maps‎,” ‎IET Inf‎. ‎Sec.‎, ‎9‎, ‎pp‎. ‎234–239‎, ‎2015‎.##

[30]  Ch. Hsu‎, ‎L. Harn‎, G. Cui, “An Ideal Multi-Secret Sharing Scheme Based on Connectivity of Graphs‎,” Wireless Personal Communication, 77, pp. 383-394, 2014##.

[31]  Ch. Hsu‎, G. Cui‎, Q. Cheng‎, J. Chen, “A Novel Linear Multi-Secret Sharing Scheme for Group Communication in Wireless Mesh Networks‎,” Network and Computer Applications‎, 34, pp. 464-468, 2011‎.##

[32]  M. Liu‎, L. ‎Xiao‎, ‎Z. Zhang‎, “Linear Multi-Secret Sharing Schemes Based on Multi-Party‎ Computation‎,” ‎Finite Fields and Their Applications‎, vol. ‎12‎, ‎pp. 704-13‎, ‎2006‎.##

[33]  S. Mashhadi, M. Hadian Dehkordi, N. Kiamari, “Provably Secure Verifiable Multi-Stage Secret Sharing Scheme Based on Monotone Span Program‎,” IET Information Security, vol. 11, pp.326-331, 2017.##

[34]  S. Mashhadi, “Computationally-Secure Multiple Secret Sharing‎: ‎Models‎, Schemes‎, ‎and Formal Security Analysis‎,” ‎The ISC Int‎. ‎J‎. ‎Inf‎. ‎Sec.‎, vol. ‎7‎, ‎pp‎. 1–10‎, ‎2015‎.##

[35]  M‎. ‎Karchmer‎, ‎A‎. ‎Wigderson‎, ‎“On Span Programs‎,” ‎ In Proceedings of the‎ Eighth Annual Conf. On Structure in Complexity‎, ‎San Diego‎, ‎CA‎, ‎pp‎. ‎102-111‎, ‎May 1993‎.##

[36]  D‎. ‎Micciancio‎, ‎S‎. ‎Goldwasser‎, “Complexity of Lattice Problems‎: ‎A Cryp‎tographic Perspective‎,” ‎Ser‎. ‎Milken Institute Series on Financial Inno‎vation and Economic Growth‎. ‎Springer US‎, ‎2002‎. ‎[Online]‎. ‎Available‎: http://books.google.com/books?id=N4lHlGwy1AUC##

[37]  O. Regev‎, ‎ “On Lattices‎, ‎Learning with Errors‎, ‎Random Linear Codes‎, ‎and‎ Cryptography‎,” ‎J‎. ‎ACM‎, ‎56(6):34:134:40‎, ‎September 2009‎.##

[38]  J. ‎Hoffstein‎, ‎J‎. ‎Pipher‎, ‎J‎. ‎Silverman‎, ‎Ntru “A Ring-Based Public Key Cryp‎Tosystem‎,” ‎Algorithmic Number Theory‎, ‎Ser‎. ‎Lecture Notes in Computer‎ Science‎, ‎1423, pp.267-288, 1998.##

[39]  M.H. Dehkordi, R. Ghasemi, “A Lightweight Public Verifiable Multi Secret Sharing Scheme Using Short Integer Solution,” In Wireless Personal Communi- Cations, Springer, pp. 1459–1469, 2016.##

[40]  H. Pilaram, T. Eghlidos “An Efficient Lattice Based Multi-stage IEEE Transactions on Dependable and Secure Computing, vol. 14, no. 1, pp.2-8‎, 2015‎.##

[41]  B. Rajabi, Z. Eslami, “A Verifiable Threshold Secret Sharing Scheme Based on Lattices‎,” Information Sciences, Vol. 501 pp.655–661, 2019.##