Secret sharing schemes with detection of cheaters for a general access structure

  • Sergio Cabello
  • Carles Padró
  • Germán Sáez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)


In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefits. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.


Cryptography Secret sharing schemes Detection of cheaters Robust and secure schemes 


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  1. 1.
    G.R. Blakley. Safeguarding cryptographic keys. AFIPS Conference Proceedings 48 (1979) 313–317.Google Scholar
  2. 2.
    C. Blundo and A. De Santis. Lower Bounds for Robust Secret Sharing Schemes. Information Processing Letters 63 (1997) 317–321.CrossRefMathSciNetGoogle Scholar
  3. 3.
    C. Blundo, A. De Santis, L. Gargano and U. Vaccaro. Tight Bounds on the Information Rate of Secret Sharing Schemes. Designs, Codes and Cryptography 11 (1997) 107–122.zbMATHCrossRefGoogle Scholar
  4. 4.
    C. Blundo, A. De Santis, D.R. Stinson and U. Vaccaro. Graph Decompositions and Secret Sharing Schemes. J. Cryptology 8 (1995) 39–64.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105–113.MathSciNetGoogle Scholar
  6. 6.
    E. F. Brickell and D. M. Davenport. On the Classification of Ideal Secret Sharing Schemes. J. Cryptology, 4 (1991) 123–134.zbMATHGoogle Scholar
  7. 7.
    M. Carpentieri, A. De Santis and U. Vaccaro. Size of shares and probability of cheating in threshold schemes. Advances in Cryptology, EUROCRYPT 93, Lectures Notes in Computer Science 765, Springer-Verlag (1994) 118–125.Google Scholar
  8. 8.
    W. Ogata and K. Kurosawa. Optimum Secret Sharing Scheme Secure against Cheating. Advances in Cryptology, EUROCRYPT 96, Lecture Notes in Computer Science 1070 (1996) 200–211.Google Scholar
  9. 9.
    C. Padró. Robust vector space secret sharing schemes. Information Processing Letters 68(1998) 107–111.CrossRefMathSciNetGoogle Scholar
  10. 10.
    C. Padró and G. Sáez. Secret sharing schemes with bipartite access structure. Advances in Cryptology, EUROCRYPT’98, Lecture Notes in Computer Science 1403 (1998) 500–511.CrossRefGoogle Scholar
  11. 11.
    C. Padró, G. Sáez and J.L. Villar. Detection of cheaters in vector space secret sharing schemes. Designs, Codes and Cryptography 16 (1999) 75–85.zbMATHCrossRefGoogle Scholar
  12. 12.
    J. Rifà-Coma. How to avoid cheaters succeeding in the key sharing scheme. Designs, Codes and Cryptography 3 (1993) 221–228.zbMATHCrossRefGoogle Scholar
  13. 13.
    A. Shamir. How to share a secret. Commun. of the ACM 22 (1979) 612–613.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    G.J. Simmons. An Introduction to Shared Secret and/or Shared Control Schemes and Their Application. Contemporary Cryptology. The Science of Information Integrity. IEEE Press (1991) 441–497.Google Scholar
  15. 15.
    G.J. Simmons, W. Jackson and K. Martin. The geometry of secret sharing schemes. Bulletin of the ICA 1 (1991) 71–88.zbMATHMathSciNetGoogle Scholar
  16. 16.
    D.R. Stinson. An explication of secret sharing schemes. Designs, Codes and Cryptography 2 (1992) 357–390.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    D.R. Stinson. Decomposition Constructions for Secret-Sharing Schemes. IEEE Trans. on Information Theory 40 (1994) 118–125.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    D.R. Stinson. Cryptography: Theory and Practice. CRC Press Inc., Boca Raton (1995).zbMATHGoogle Scholar
  19. 19.
    M. Tompa and H. Woll. How to share a secret with cheaters. J. Cryptology 1 (1988) 133–139.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Sergio Cabello
    • 1
  • Carles Padró
    • 1
  • Germán Sáez
    • 1
  1. 1.Dep. Matemática Aplicada i TelemáticaUniversitat Politècnica de CatalunyaBarcelonaSpain

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