Call for Paper - March 2023 Edition
IJCA solicits original research papers for the March 2023 Edition. Last date of manuscript submission is February 20, 2023. Read More

Efficient Multi Secret Sharing with Generalized Access Structures

International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 90 - Number 12
Year of Publication: 2014
Binu V P
Sreekumar A

Binu V P and Sreekumar A. Article: Efficient Multi Secret Sharing with Generalized Access Structures. International Journal of Computer Applications 90(12):1-6, March 2014. Full text available. BibTeX

	author = {Binu V P and Sreekumar A},
	title = {Article: Efficient Multi Secret Sharing with Generalized Access Structures},
	journal = {International Journal of Computer Applications},
	year = {2014},
	volume = {90},
	number = {12},
	pages = {1-6},
	month = {March},
	note = {Full text available}


Multi secret sharing is an extension of secret sharing technique where several secrets are shared between the participants, each according to a specified access structure. The secrets can be reconstructed according to the access structure by participants using their private shares. Each participant has to hold a single share, additional information are made available in a public bulletin board. The scheme is computationally efficient and also each participant can verify the shares of the other participants and also the reconstructed secret. The scheme doesn't need any secure channel also.


  • Charles Asmuth and John Bloom. A modular approach to key safeguarding. Information Theory, IEEE Transactions on, 29(2):208–210, 1983.
  • Amos Beimel. Secret-sharing schemes: a survey. In Coding and Cryptology, pages 11–46. Springer, 2011.
  • Michael Ben-Or, Shafi Goldwasser, and Avi Wigderson. Completeness theorems for non-cryptographic fault-tolerant distributed computation. In Proceedings of the twentieth annual ACM symposium on Theory of computing, pages 1–10. ACM, 1988.
  • Josh Benaloh and Jerry Leichter. Generalized secret sharing and monotone functions. In Advances in Cryptology- CRYPTO88, pages 27–35. Springer, 1990.
  • John Bethencourt, Amit Sahai, and Brent Waters. Ciphertextpolicy attribute-based encryption. In Security and Privacy, 2007. SP'07. IEEE Symposium on, pages 321–334. IEEE, 2007.
  • George Robert Blakley et al. Safeguarding cryptographic keys. In Proceedings of the national computer conference, volume 48, pages 313–317, 1979.
  • Carlo Blundo, Alfredo De Santis, and Ugo Vaccaro. Efficient sharing of many secrets. In STACS 93, pages 692–703. Springer, 1993.
  • Ernest F Brickell. Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing, 9(2):105–113, 1989.
  • Ernest F Brickell and Daniel M Davenport. On the classification of ideal secret sharing schemes. Journal of Cryptology, 4(2):123–134, 1991.
  • Christian Cachin. On-line secret sharing. In Cryptography and coding, pages 190–198. Springer, 1995.
  • David Chaum, Claude Cr´epeau, and Ivan Damgard. Multiparty unconditionally secure protocols. In Proceedings of the twentieth annual ACM symposium on Theory of computing, pages 11–19. ACM, 1988.
  • Ronald Cramer, Ivan Damg°ard, and Ueli Maurer. General secure multi-party computation from any linear secret-sharing scheme. In Advances in CryptologyEUROCRYPT 2000, pages 316–334. Springer, 2000.
  • Angsuman Das and Avishek Adhikari. An efficient multi-use multi-secret sharing scheme based on hash function. Applied mathematics letters, 23(9):993–996, 2010.
  • Yvo Desmedt and Yair Frankel. Shared generation of authenticators and signatures. In Advances in Cryptology- CRYPTO91, pages 457–469. Springer, 1992.
  • Matthew Franklin and Moti Yung. Communication complexity of secure computation. In Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pages 699– 710. ACM, 1992.
  • H Ghodosi, J Pieprzyk, GR Chaudhry, and J Seberry. How to prevent cheating in pinch's scheme. Electronics Letters, 33(17):1453–1454, 1997.
  • Hossein Ghodosi, Josef Pieprzyk, Rei Safavi-Naini, and Huaxiong Wang. On construction of cumulative secret sharing schemes. In Information Security and Privacy, pages 379– 390. Springer, 1998.
  • Oded Goldreich, Silvio Micali, and Avi Wigderson. How to play any mental game. In Proceedings of the nineteenth annual ACM symposium on Theory of computing, pages 218– 229. ACM, 1987.
  • Vipul Goyal, Omkant Pandey, Amit Sahai, and Brent Waters. Attribute-based encryption for fine-grained access control of encrypted data. In Proceedings of the 13th ACM conference on Computer and communications security, pages 89– 98. ACM, 2006.
  • Lein Harn. Efficient sharing (broadcasting) of multiple secrets. IEE Proceedings-Computers and Digital Techniques, 142(3):237–240, 1995.
  • Jingrui He and Ed Dawson. Multisecret-sharing scheme based on one-way function. Electronics Letters, 31(2):93–95, 1995.
  • Ren-Junn Hwang and Chin-Chen Chang. An on-line secret sharing scheme for multi-secrets. Computer Communications, 21(13):1170–1176, 1998.
  • Mitsuru Ito, Akira Saito, and Takao Nishizeki. Secret sharing scheme realizing general access structure. Electronics and Communications in Japan (Part III: Fundamental Electronic Science), 72(9):56–64, 1989.
  • Wen-Ai Jackson and Keith M Martin. Cumulative arrays and geometric secret sharing schemes. In Advances in CryptologyAUSCRYPT' 92, pages 48–55. Springer, 1993.
  • Wen-Ai Jackson, Keith M Martin, and Christine M OKeefe. Multisecret threshold schemes. In Advances in Cryptology- CRYPTO93, pages 126–135. Springer, 1994.
  • Mauricio Karchmer and Avi Wigderson. On span programs. In Structure in Complexity Theory Conference, 1993. , Proceedings of the Eighth Annual, pages 102–111. IEEE, 1993.
  • Ehud Karnin, Jonathan Greene, and Martin Hellman. On secret sharing systems. Information Theory, IEEE Transactions on, 29(1):35–41, 1983.
  • SC Kothari. Generalized linear threshold scheme. In Advances in Cryptology, pages 231–241. Springer, 1985.
  • Shoulun Long, Josef Pieprzyk, Huaxiong Wang, and Duncan S Wong. Generalised cumulative arrays in secret sharing. Designs, Codes and Cryptography, 40(2):191–209, 2006.
  • James L Massey. Minimal codewords and secret sharing. In Proceedings of the 6th Joint Swedish-Russian International Workshop on Information Theory, pages 276–279. Citeseer, 1993.
  • Robert J. McEliece and Dilip V. Sarwate. On sharing secrets and reed-solomon codes. Communications of the ACM, 24(9):583–584, 1981.
  • Maurice Mignotte. How to share a secret. In Cryptography, pages 371–375. Springer, 1983.
  • Moni Naor and Adi Shamir. Visual cryptography. In Advances in CryptologyEUROCRYPT'94, pages 1–12. Springer, 1995.
  • Moni Naor and Avishai Wool. Access control and signatures via quorum secret sharing. Parallel and Distributed Systems, IEEE Transactions on, 9(9):909–922, 1998.
  • Liao-Jun Pang, Hui-Xian Li, and Yu-Min Wang. An efficient and secure multi-secret sharing scheme with general access structures. Wuhan University Journal of Natural Sciences, 11(6):1649–1652, 2006.
  • Liao-Jun Pang, Hui-Xian Li, and Yu-MinWang. A secure and efficient secret sharing scheme with general access structures. In Fuzzy Systems and Knowledge Discovery, pages 646–649. Springer, 2006.
  • RGE Pinch. On-line multiple secret sharing. Electronics Letters, 32(12):1087–1088, 1996.
  • Irving S Reed and Gustave Solomon. Polynomial codes over certain finite fields. Journal of the Society for Industrial & Applied Mathematics, 8(2):300–304, 1960.
  • Adi Shamir. How to share a secret. Communications of the ACM, 22(11):612–613, 1979.
  • Bhavani Shankar, Kannan Srinathan, and C Pandu Rangan. Alternative protocols for generalized oblivious transfer. In Distributed Computing and Networking, pages 304–309. Springer, 2008.
  • Gustavus J Simmons. An introduction to shared secret and/or shared control schemes and their application. Contemporary Cryptology: The Science of Information Integrity, pages 441– 497, 1992.
  • A Sreekumar. Secret sharing schemes using visual cryptography. PhD thesis, Cochin University of Science and Technology, 2009.
  • Douglas R. Stinson. An explication of secret sharing schemes. Designs, Codes and Cryptography, 2(4):357–390, 1992.
  • Hung-Min Sun. On-line multiple secret sharing based on a one-way function. Computer communications, 22(8):745– 748, 1999.
  • Tamir Tassa. Generalized oblivious transfer by secret sharing. Designs, Codes and Cryptography, 58(1):11–21, 2011.
  • Chan Yeob Yeun and Chris J Mitchell. How to identify all cheaters in pinchs scheme. Proceedings of JWIS98, Singapore, pages 129–133, 1998.