Efficient threshold secret sharing schemes secure against rushing cheaters

Avishek Adhikari, Kirill Morozov, Satoshi Obana, Partha Sarathi Roy, Kouichi Sakurai, Rui Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

In this paper, we consider two very important issues namely detection and identification of k-out-of-n secret sharing schemes against rushing cheaters who are allowed to submit (possibly forged) shares after observing shares of the honest users in the reconstruction phase. Towards this, we present four different schemes. Among these, first we present two k-out-of-n secret sharing schemes, the first one being capable of detecting (k − 1)/3 cheaters such that |Vi| = |S|/∊3 and the second one being capable of detecting n − 1 cheaters such that |Vi| = |S|/∊k+1, where S denotes the set of all possible secrets, ∊ denotes the successful cheating probability of cheaters and Vi denotes set all possible shares. Next we present two k-out-of-n secret sharing schemes, the first one being capable of identifying (k−1)/3 rushing cheaters with share size |Vi| that satisfies |Vi| = |S|/∊k. This is the first scheme, whose size of shares does not grow linearly with n but only with k, where n is the number of participants. For the second one, in the setting of public cheater identification, we present an efficient optimal cheater resilient k-out-of-n secret sharing scheme against rushing cheaters having the share size |Vi| = (n−t)n+2t|S|/∊n+2t. The proposed scheme achieves flexibility in the sense that the security level (i.e., the cheater(s) success probability) is independent of the secret size. Each of the four proposed schemes has the smallest share size among the existing schemes having the mentioned properties in the respective models.

Original languageEnglish
Title of host publicationInformation Theoretic Security - 9th International Conference, ICITS 2016, Revised Selected Papers
EditorsPaulo Barreto, Anderson C.A. Nascimento
PublisherSpringer Verlag
Pages3-23
Number of pages21
ISBN (Print)9783319491745
DOIs
Publication statusPublished - Jan 1 2016
Event9th International Conference on Information-Theoretic Security, ICITS 2016 - Tacoma, United States
Duration: Aug 9 2016Aug 12 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10015 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th International Conference on Information-Theoretic Security, ICITS 2016
CountryUnited States
CityTacoma
Period8/9/168/12/16

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Adhikari, A., Morozov, K., Obana, S., Roy, P. S., Sakurai, K., & Xu, R. (2016). Efficient threshold secret sharing schemes secure against rushing cheaters. In P. Barreto, & A. C. A. Nascimento (Eds.), Information Theoretic Security - 9th International Conference, ICITS 2016, Revised Selected Papers (pp. 3-23). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10015 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-49175-2_1