American Institute of Mathematical Sciences

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February  2013, 7(1): 39-56. doi: 10.3934/amc.2013.7.39

On dealer-free dynamic threshold schemes

Mehrdad Nojoumian 1, and  Douglas R. Stinson 2,

1. 

Department of Computer Science, Southern Illinois University, Carbondale, IL 62901, United States
2. 

David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Received  April 2012 Published  January 2013

In a threshold scheme, the sensitivity of the secret as well as the number of players may fluctuate due to various reasons, e.g., mutual trust may vary or the structure of the players' organization might be changed. A possible solution to this problem is to modify the threshold and/or change the secret. Moreover, a common problem with almost all secret sharing schemes is that they are "one-time", meaning that the secret and shares are known to everyone after a public secret recovery process. This problem could be resolved if the dealer shares various secrets at the beginning, but a better solution is to dynamically generate new secrets in the absence of the dealer. These issues are our main motivation to revisit dynamic threshold schemes.
    Therefore, we first provide the first comprehensive study of threshold modification techniques in both the passive and active adversary models. We first review an existing method for threshold modification based on resharing shares of a secret; this method is secure in the setting of a passive adversarial coalition. We then discuss two methods, termed public evaluation (for threshold reduction) and zero addition (for threshold increase) that can be used in both the passive and active adversarial setting. In the case of an active adversary, the techniques make use of verifiable secret sharing schemes, whereas the schemes considered in the passive adversary model are all based on the Shamir scheme. As an application, we discuss how the threshold and the secret can be changed multiple times to arbitrary values after the scheme's initialization.
Keywords: unconditional security, threshold and secret changeability., Secret sharing.
Mathematics Subject Classification: Primary: 94A6.
Citation: Mehrdad Nojoumian, Douglas R. Stinson. On dealer-free dynamic threshold schemes. Advances in Mathematics of Communications, 2013, 7 (1) : 39-56. doi: 10.3934/amc.2013.7.39
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show all references

References:
[1]

IEEE Trans. Inform. Theory, 51 (2005), 620-633. doi: 10.1109/TIT.2004.840857.  Google Scholar

[2]

in "9th Annual International Cryptology Conference, CRYPTO,'' Springer, (1989), 560-572. Google Scholar

[3]

in "20th Annual ACM Symposium on Theory of Computing, STOC,'' (1988), 1-10. Google Scholar

[4]

in "CRYPTO,'' (1992), 540-548.  Google Scholar

[5]

in "National Computer Conference,'' AFIPS Press, (1979), 313-317. Google Scholar

[6]

Theoret. Comp. Sci., 165 (1996), 407-440.  Google Scholar

[7]

in "26th Annual IEEE Symposium on Foundations of Computer Science, FOCS,'' (1985), 383-395. Google Scholar

[8]

in "8th Int. Conf. on the Theory and Application of Cryptology and Info. Security, ASIACRYPT,'' Springer, (2002), 346-363.  Google Scholar

[9]

in "Technical Report ISSE TR-97-01,'' George Mason Univ., 1997. Google Scholar

[10]

in "33th Annual ACM Symposium on Theory of Computing, STOC,'' (2001), 580-589.  Google Scholar

[11]

in "17th annual ACM symposium on Principles of Distributed Computing, PODC,'' (1998), 101-111. Google Scholar

[12]

in "15th Annual International Cryptology Conference, CRYPTO,'' Springer, (1995), 339-352. Google Scholar

[13]

in "EUROCRYPT'' (I. Damgård), Springer, (1990), 266-282.  Google Scholar

[14]

J. Cryptology, 10 (1997), 261-289. doi: 10.1007/s001459900031.  Google Scholar

[15]

in "6th Australasian Conference Information Security and Privacy, ACISP,'' Springer, (2001), 403-416. Google Scholar

[16]

in "Proceedings of IEEE Information Theory Workshop (ITW 2005),'' IEEE, (2005), 61-66. Google Scholar

[17]

in "4th Australasian Conference Information Security and Privacy, ACISP,'' Springer, (1999), 177-191. Google Scholar

[18]

Computer J., 42 (1999), 638-649. Google Scholar

[19]

in "11th International Workshop on Selected Areas in Cryptography, SAC,'' Springer, (2004), 308-325.  Google Scholar

[20]

IET Inform. Secur., 4 (2010), 202-211. doi: 10.1049/iet-ifs.2009.0098.  Google Scholar

[21]

in "21st Annual ACM Symposium on Theory of Computing, STOC,'' (1989), 73-85. Google Scholar

[22]

Commun. ACM, 22 (1979), 612-613. doi: 10.1145/359168.359176.  Google Scholar

[23]

in "10th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT,'' Springer, (2004), 170-186.  Google Scholar

[24]

in "6th Annual Int. Workshop on Selected Areas in Cryptography, SAC,'' Springer, (1999), 200-214.  Google Scholar

[25]

in "2nd SKLOIS Conference on Information Security and Cryptology, Inscrypt,'' Springer, (2006), 103-117. doi: 10.1007/11937807_9.  Google Scholar

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