On the information rate of secret sharing schemes

Theoretical Computer Science

Volumn 154, Issue 2, 1996, Pages 283-306

  Blundo, Carlo ^a   De Santis, Alfredo ^a   Gargano, Luisa ^a   Vaccaro, Ugo ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; GRAPH THEORY; OPTIMAL SYSTEMS; SECURITY OF DATA; SET THEORY; THEOREM PROVING;

ACCESS STRUCTURES; INFORMATION RATE; OPTIMAL AVERAGE INFORMATION RATE; OPTIMAL INFORMATION; SECRET SHARING METHOD;

INFORMATION THEORY;

EID: 0030569864     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00065-8     Document Type: Article

References (47)

1. J.C. Benaloh and J. Leichter, Generalized Secret Sharing and Monotone Functions, in: S. Goldwasser, ed., Advances in Cryptology - CRYPTO 88, Lecture Notes in Computer Science, Vol. 403 (Springer, Berlin, 1985) 27-35.
2. A. Beutelspacher, How to say 'no', in: Quisquater and Vandewalle eds., Advances in Cryptology -EUROCRYPT 89, Lecture Notes in Computer Science, Vol. 434 (Springer, Berlin, 1990) 491-496.
3. G.R. Blakley, Safeguarding cryptographic keys, in: Proc. AFIPS 1979 National Computer Conf., (June 1979) 313-317.
4. B. Blakley, G.R. Blakley, A.H. Chan, and J.L. Massey, Threshold schemes with disenrollment, in: E. Brickell, ed., Advances in Cryptology - CRYPTO '92, Lecture Notes in Computer Science, Vol. 740 (Springer, Berlin, 1993) 546-554.
5. C. Blundo, Secret sharing schemes for access structures based on graphs, Tesi di Laurea, University of Salemo, Italy, 1991 (in Italian).
6. C. Blundo, A. Cresti, A. De Santis, and U. Vaccaro, Fully Dynamic Secret Sharing Schemes, in: D.R. Stinson, ed., Advances in Cryptology - CRYPTO 93, Lecture Notes in Computer Science, Vol. 773 (Springer, Berlin, 1994) 126-135.
7. C. Blundo, A. De Santis, G. Di Crescenzo, A. Giorgio Gaggia, and U. Vaccaro, Multi-Secret Sharing Schemes, in: Y. Desmedt, ed., Advances in Cryptology - CRYPTO 94, Lecture Notes in Computer Science, Vol. 839 (Springer, Berlin, 1994) 150-163.
8. C. Blundo, A. De Santis, L. Gargano and U. Vaccaro, Secret Sharing Schemes with Veto Capabilities, in: C. Cohen, S. Litsyn, A. Lobstein and G. Zemor, eds., Proceedings of the French-Israeli Workshop in Algebraic Coding, Lecture Notes in Computer Science, Vol. 781 (Springer, Berlin, 1994) 82-89.
9. C. Blundo, A. De Santis, A. Giorgio Gaggia and U. Vaccaro, New bounds on the information rate of secret sharing schemes, IEEE Trans. Inform. Theory 41 (1995) 549-554.
10. C. Blundo, A. De Santis, D.R. Stinson and U. Vaccaro, Graph decomposition and secret sharing schemes, J. Cryptology 8 (1995) 39-64; preliminary version in: R. Rueppel, ed., Advances in Cryptology - EUROCRYPT '92, Lecture Notes in Computer Science, Vol. 658 (Springer, Berlin, 1993) 1-24.
11. C. Blundo, A. De Santis, D.R. Stinson and U. Vaccaro, Graph decomposition and secret sharing schemes, J. Cryptology 8 (1995) 39-64; preliminary version in: R. Rueppel, ed., Advances in Cryptology - EUROCRYPT '92, Lecture Notes in Computer Science, Vol. 658 (Springer, Berlin, 1993) 1-24.
12. C. Blundo, A. De Santis and U. Vaccaro, Efficient sharing of many secrets, in: P. Enjalbert, A. Finkel and K.W. Wagner, eds., Proc. STACS '93 (10th Symp. on Theoretical Aspects of Computer Science), Lecture Notes in Computer Science, Vol. 665 (Springer, Berlin, 1993) 692-703.
13. C. Blundo, A. De Santis and U. Vaccaro, On secret sharing schemes, Technical Report, Univ. of Salerno, 1995.
14. C. Blundo, A. De Santis, and U. Vaccaro, Randomness in distribution protocols, in: S. Abiteboul and E. Shamir, eds., Proc. 21st Internat. Colloq. on Automata, Languages and Programming (ICALP '94), Lecture Notes in Computer Science, Vol. 820 (Springer, Berlin, 1994) 568-579.
15. E.F. Brickell and D.M. Davenport, On the classification of ideal secret sharing schemes, J. Cryptology 4 (1991) 123-124.
16. E.F. Brickell and D.R. Stinson, The detection of cheaters in threshold schemes, SIAM J. Discrete Math. 4 (1991) 502-510.
17. E.F. Brickell and D.R. Stinson, Some improved bounds on the information rate of perfect secret sharing schemes, J. Cryptology 5 (1992) 153-166.
18. R.M. Capocelli, A. De Santis, L. Gargano and U. Vaccaro, On the size of shares for secret sharing schemes, J. Cryptology 6 (1993) 157-168.
19. M. Carpentieri, A. De Santis and U. Vaccaro, Size of shares and probability of cheating in threshold schemes, in: T. Helleseth, ed., Advances in Cryptology - EUROCRYPT '93, Lecture Notes in Computer Science, Vol. 765 (Springer, Berlin, 1994) 118-125.
20. L. Csirmaz, The size of a share must be large, to appear in: A. De Santis, ed., Advances in Cryptology - EUROCRYPT '94, Lecture Notes in Computer Science, Vol. 950 (Springer, Berlin, 1995).
21. I. Csiszár and J. Körner, Information Theory. Coding Theorems for Discrete Memoryless Systems (Academic Press, 1981).
22. M. van Dijk, On the information rate of perfect secret sharing schemes, preprint, 1994.
23. P. Erdos and L. Pyber, unpublished.
24. T. Feder and R. Motwani, Clique partition, graph compression and speeding-up algorithms, in: Proc. 23rd Annual ACM Symp. on Theory of Computing (New Orleans, 1991) 123-133.
25. R.G. Gallager, Information Theory and Reliable Communications (John Wiley, New York, 1968).
26. M. Garey and D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness (W.H. Freeman, New York, 1979).
27. I. Ingemarsson and G.J. Simmons, A protocol to set up shared secret schemes without the assistance of a mutually trusted party, in: Advances in Cryptology - CRYPTO 90, Menezes and Vanstone eds., Lecture Notes in Computer Science, Vol. 473 (Springer, Berlin, 1991) 266-282.
28. M. Ito, A. Saito and T. Nishizeki, Secret sharing scheme realizing general access structure, in: Proc. IEEE Global Telecommunications Conf, Globecom 87, (Tokyo, Japan, 1987).
29. W.-A. Jackson, K.M. Martin, and C.M. O'Keefe, Multisecret threshold schemes, in: D.R. Stinson, ed., Advances in Cryptology -CRYPTO '93, Lecture Notes in Computer Science, Vol. 773 (Springer, Berlin, 1994) 126-135.
30. E.D. Karnin, J.W. Greene and M.E. Hellman, On secret sharing systems, IEEE Trans. Inform. Theory, IT-29, (1) (1983) 35-41.
31. D.E. Knuth and A.C. Yao, The complexity of nonuniform random number generation, in: J.F. Traub, ed., Algorithms and Complexity (Academic Press, New york, 1976) 357-428.
32. S.C. Kothari, Generalized linear threshold schemes, in: G.R. Blakley and D. Chaum, eds., Advances in Cryptology - CRYPTO 84, Lecture Notes in Computer Science, Vol 196 (Springer Berlin, 1985) 231-241.
33. R.J. McEliece and D.V. Sarwate, On sharing secrets and Reed-Solomon codes, Comm. ACM 24 (1981) 583-584.
34. K.M. Martin, Discrete structures in the theory of secret sharing, Ph.D. Thesis, University of London, 1991.
35. K.M. Martin, New secret sharing schemes from old, J. Combin. Math. Combin. Comput., 14 (1993) 65-67.
36. M. Naor and A. Shamir, Visual cryptography, to appear in: A. De Santis, ed., Advances in Cryptology - Eurocrypt '94, Lecture Notes in Computer Science, Vol. 950 (Springer, Berlin).
37. L. Pyber, Covering the edges of a graph by..., in: L. Lovász, D. Miklós and T. Szönyi, eds., Sets, Graphs and Numbers, Colloquia Mathematica Soc., János Bolyai (North-Holland, Amsterdam, 1992) 583-610
38. T. Rabin and M. Ben-Or, Verifiable secret sharing and multiparty protocols with honest majority, in: Proc. 21st ACM Symp. on Theory of Computing (1989) 73-85.
39. A. Shamir, How to share a secret, Comm. ACM 22 (11) (1979) 612-613.
40. G.J. Simmons, Robust shared secret schemes or 'how to be sure you have the right answer even though you don't know the question', Congr. Numer. 68 (1989) 215-248.
41. G.J. Simmons, Prepositioned shared secret and/or shared control schemes, in: Proc. Advances in Cryptology - CRYPTO '89, Lecture Notes in Computer Science, Vol. 434 (Springer, Berlin, 1990) 436-467.
42. G.J. Simmons, An Introduction to Shared Secret and/or Shared Control Schemes and Their Application, Contemp. Cryptology (IEEE Press, 1991) 441-497.
43. D.R. Stinson, An explication of secret sharing schemes, Designs, Codes and Cryptography 2 (1992) 357-390.
44. D.R. Stinson, New general lower bounds on the information rate of secret sharing schemes, in: E. Brickell, ed., Proc. Advances in Cryptology - CRYPTO '92, Lecture Notes in Computer Science, Vol. 740, (Springer Berlin, 1993) 170-184.
45. D.R. Stinson, Decomposition constructions for secret sharing schemes, IEEE Trans. Inform. Theory 40 (1994) 118-125.
46. M. Tompa and H. Woll, How to share a secret with cheaters, J. Cryptology 1 (1988) 133-138.
47. Z. Tuza, Covering of graphs by complete bipartite subgraphs; complexity of 0-1 matrices, Combinatorica 4 (1) (1984) 111-116.