Secret sharing scheme realizing general access structure

@article{Ito1989SecretSS,
  title={Secret sharing scheme realizing general access structure},
  author={Mitsuru Ito and Akira Saito and Takao Nishizeki},
  journal={Electronics and Communications in Japan Part Iii-fundamental Electronic Science},
  year={1989},
  volume={72},
  pages={56-64}
}
As a method of sharing a secret, e.g., a secret key, Shamir's (k, n) threshold method is well known. However, Shamir's method has a problem in that general access structures cannot be realized. This paper shows that by providing the trustees with several information data concerning the distributed information of the (k, n) threshold method, any access structure can be realized. the update with the change of the secret trustees and the relation to the threshold graph are also discussed. 

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References

SHOWING 1-4 OF 4 REFERENCES

How to share a secret

  • A. Shamir
  • Computer Science, Mathematics
    CACM
  • 1979
TLDR
This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.

Cryptography and Data Security

TLDR
The goal of this book is to introduce the mathematical principles of data security and to show how these principles apply to operating systems, database systems, and computer networks.