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How to share a secret. (English) Zbl 0414.94021


MSC:

94A62 Authentication, digital signatures and secret sharing
94A60 Cryptography
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[1] Blakley G R. Safeguarding cryptographic keys. In: Proceedings of the 1979 AFIPS National Computer Conference, Monval, 1979. 313-317
[2] Shamir A. How to share a secret. Commun ACM, 1979, 22: 612-613 · Zbl 0414.94021
[3] Wang Y J, Wong D S, Wu Q H, et al. Practical distributed signatures in the standard model. In: Proceedings of the Cryptographer’s Track at the RSA Conference, San Francisco, 2014. 307-326 · Zbl 1337.94103
[4] Deng H, Wu Q H, Qin B, et al. Ciphertext-policy hierarchical attribute-based encryption with short ciphertexts. Inform Sci, 2014, 275: 370-384 · Zbl 1341.68043
[5] Deng H, Wu Q H, Qin B, et al. Who is touching my cloud. In: Proceedings of the 19th European Symposium on Research in Computer Security, Part I, Wroclaw, 2014. 362-379
[6] Liu W R, Liu J W, Wu Q H, et al. Practical direct chosen ciphertext secure key-policy attribute-based encryption with public ciphertext test. In: Proceedings of the 19th European Symposium on Research in Computer Security, Part II, Wroclaw, 2014. 91-108 · Zbl 1443.94071
[7] Tang C M, Gao S H. Leakproof secret sharing protocols with applications to group identification scheme. Sci China Inf Sci, 2012, 55: 1172-1185 · Zbl 1245.94103
[8] McEliece R J, Sarwate D V. On sharing secrets and Reed-Solomon codes. Commun ACM, 1981, 24: 583-584
[9] Feldman J, Malkin T, Servedio R A, et al. Secure network coding via filtered secret sharing. In: Proceedings of 42nd Annual Allerton Conference on Communication, Control, and Computing, Illinois, 2004. 30-39
[10] Ding L H, Wu P, Wang H, et al. Lifetime maximization routing with network coding in wireless multihop networks. Sci China Inf Sci, 2013, 56: 022303
[11] Zheng J, Li J D, Liu Q, et al. Performance analysis of three multi-radio access control policies in heterogeneous wireless networks. Sci China Inf Sci, 2013, 56: 122305
[12] Zhang Z F, Liu M L. Rational secret sharing as extensive games. Sci China Inf Sci, 2013, 56: 032107
[13] Beimel A. Secret-sharing schemes: a survey. In: Proceedings of the 3rd International Workshop on Coding and Cryptology, Qingdao, 2011. 11-46 · Zbl 1272.94074
[14] Karnin E D, Greene J W, Hellman M E. On secret sharing systems. IEEE Trans Inform Theory, 1983, 29: 35-41 · Zbl 0503.94018
[15] Benaloh J, Leichter J. Generalized secret sharing and monotone functions. In: Proceedings of Advances in Cryptology—CRYPTO’88, Santa Barbara, 1988. 27-35 · Zbl 0715.94003
[16] Brickell E F. Some ideal secret sharing schemes. In: Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques on Advances in Cryptology, Houthalen, 1989. 468-475
[17] Ito M, Saito A, Nishizeki T. Secret sharing scheme realizing general access structure. In: IEEE/IEICE Global Telecommunications Conference, Tokyo, 1987. 99-102
[18] Capocelli R M, de Santis A, Gargano L, et al. On the size of shares of secret sharing schemes. J Cryptol, 1993, 6: 157-168 · Zbl 0786.68030
[19] Csirmaz L. The size of a share must be large. J Cryptol, 1997, 10: 223-231 · Zbl 0897.94012
[20] Farràs O, Metcalf-Burton J R, Padrró C, et al. On the optimization of bipartite secret sharing schemes. Des Codes Cryptogr, 2012, 63: 255-271 · Zbl 1236.94075
[21] Martí-Farré J, Padrró C. On secret sharing schemes, matroids and polymatroids. J Math Cryptol, 2010, 4: 95-120 · Zbl 1201.94111
[22] Padró C, Sáez G. Secret sharing schemes with bipartite access structure. IEEE Trans Inform Theory, 2000, 46: 2596-2604 · Zbl 0999.94031
[23] Padró C, Vázquez L, Yang A. Finding lower bounds on the complexity of secret sharing schemes by linear programming. Discrete Appl Math, 2013, 161: 1072-1084 · Zbl 1262.68049
[24] Beimel A, Livne N. On matroids and non-ideal secret sharing. IEEE Trans Inform Theory, 2008, 54: 482-501 · Zbl 1112.94024
[25] Beimel A, Livne N, Padró C. Matroids can be far from ideal secret sharing. In: Proceedings of the 5th Conference on Theory of Cryptography, New York, 2008. 194-212 · Zbl 1162.94337
[26] Beimel A, Orlov I. Secret sharing and non-shannon information inequalities. IEEE Trans Inform Theory, 2011, 57: 539-557 · Zbl 1213.94150
[27] Stinson D R. An explication of secret sharing schemes. Des Codes Cryptogr, 1992, 2: 357-390 · Zbl 0793.68111
[28] Beimel A, Weinreb E. Monotone circuits for monotone weighted threshold functions. Inf Process Lett, 2006, 97: 12-18 · Zbl 1184.68227
[29] Morillo P, Padró C, Sáez G, et al. Weighted threshold secret sharing schemes. Inf Process Lett, 1999, 70: 211-216 · Zbl 0998.94546
[30] Beimel A, Tassa T, Weinreb E. Characterizing ideal weighted threshold secret sharing. SIAM J Discrete Math, 2008, 22: 360-397 · Zbl 1161.94005
[31] Farràs O, Padró C. Ideal hierarchical secret sharing schemes. IEEE Trans Inform Theory, 2012, 58: 3273-3286 · Zbl 1365.94479
[32] Simmons G J. How to (really) share a secret. In: Proceedings of Advances in Cryptology—CRYPTO’88, Santa Barbara, 1988. 390-448
[33] Tassa T, Dyn N. Multipartite secret sharing by bivariate interpolation. J Cryptol, 2009, 22: 227-258 · Zbl 1159.94373
[34] Farràs O, Padró C, Xing C, et al. Natural generalizations of threshold secret sharing. IEEE Trans Inform Theory, 2014, 60: 1652-1664 · Zbl 1360.94347
[35] Herranz J, Sáez G. New results on multipartite access structures. IEE Proc Inf Secur, 2006, 153: 153-162
[36] Ng S L. Ideal secret sharing schemes with multipartite access structures. IEE Proc Commun, 2006, 153: 165-168 · Zbl 1273.94366
[37] Tassa T. Hierarchical threshold secret sharing. J Cryptol, 2007, 20: 237-264 · Zbl 1113.68048
[38] Beutelspacher A, Wettl F. On 2-level secret sharing. Des Codes Cryptogr, 1993, 3: 127-134 · Zbl 0770.94004
[39] Giuletti M, Vincenti R. Three-level secret sharing schemes from the twisted cubic. Discrete Math, 2010, 310: 3236-3240 · Zbl 1228.05103
[40] Farràs O, Mart´i-Farrré J, Padró C. Ideal multipartite secret sharing schemes. J Cryptol, 2012, 25: 434-463 · Zbl 1272.94078
[41] Herzog J, Hibi T. Discrete polymatroids. J Algebr Comb, 2002, 16: 239-268 · Zbl 1012.05046
[42] Brickell E F, Davenport D M. On the classification of ideal secret sharing schemes. J Cryptol, 1991, 4: 123-134 · Zbl 0747.94010
[43] Martí-Farré J, Padró C. Ideal secret sharing schemes whose minimal qualified subsets have at most three participants. Des Codes Cryptogr, 2009, 52: 1-14 · Zbl 1237.94114
[44] Oxley J G. Matroid Theory. New York: Oxford University Press,
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