A Simple and Efficient Secret Sharing Scheme Secure against Cheating

Toshinori ARAKI; Wakaha OGATA

doi:10.1587/transfun.E94.A.1338

A Simple and Efficient Secret Sharing Scheme Secure against Cheating

Toshinori ARAKI, Wakaha OGATA

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In (k,n) threshold scheme, Tompa and Woll considered a problem of cheaters who try to make another participant reconstruct an invalid secret. Later, some models of such cheating were formalized and lower bounds of the size of share were shown in the situation of fixing the maximum successful cheating probability to ε. Some efficient schemes in which size of share is equal to the lower bound were also proposed. Let |S| be the field size of the secret. Under the assumption that cheaters do not know the distributed secret, these sizes of share of previous schemes which can work for ε > 1/|S| are somewhat larger than the bound. In this paper, we show the bound for this case is really tight by constructing a new scheme. When distributing uniform secret, the bit length of share in the proposed scheme is only 1 bit longer than the known bound. Further, we show a tighter bound of the size of share in case of ε < 1/|S|.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.6 pp.1338-1345

Publication Date: 2011/06/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E94.A.1338

Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

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Toshinori ARAKI, Wakaha OGATA, "A Simple and Efficient Secret Sharing Scheme Secure against Cheating" in IEICE TRANSACTIONS on Fundamentals, vol. E94-A, no. 6, pp. 1338-1345, June 2011, doi: 10.1587/transfun.E94.A.1338.
Abstract: In (k,n) threshold scheme, Tompa and Woll considered a problem of cheaters who try to make another participant reconstruct an invalid secret. Later, some models of such cheating were formalized and lower bounds of the size of share were shown in the situation of fixing the maximum successful cheating probability to ε. Some efficient schemes in which size of share is equal to the lower bound were also proposed. Let |S| be the field size of the secret. Under the assumption that cheaters do not know the distributed secret, these sizes of share of previous schemes which can work for ε > 1/|S| are somewhat larger than the bound. In this paper, we show the bound for this case is really tight by constructing a new scheme. When distributing uniform secret, the bit length of share in the proposed scheme is only 1 bit longer than the known bound. Further, we show a tighter bound of the size of share in case of ε < 1/|S|.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1338/_p

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@ARTICLE{e94-a_6_1338,
author={Toshinori ARAKI, Wakaha OGATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Simple and Efficient Secret Sharing Scheme Secure against Cheating},
year={2011},
volume={E94-A},
number={6},
pages={1338-1345},
abstract={In (k,n) threshold scheme, Tompa and Woll considered a problem of cheaters who try to make another participant reconstruct an invalid secret. Later, some models of such cheating were formalized and lower bounds of the size of share were shown in the situation of fixing the maximum successful cheating probability to ε. Some efficient schemes in which size of share is equal to the lower bound were also proposed. Let |S| be the field size of the secret. Under the assumption that cheaters do not know the distributed secret, these sizes of share of previous schemes which can work for ε > 1/|S| are somewhat larger than the bound. In this paper, we show the bound for this case is really tight by constructing a new scheme. When distributing uniform secret, the bit length of share in the proposed scheme is only 1 bit longer than the known bound. Further, we show a tighter bound of the size of share in case of ε < 1/|S|.},
keywords={},
doi={10.1587/transfun.E94.A.1338},
ISSN={1745-1337},
month={June},}

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TY - JOUR
TI - A Simple and Efficient Secret Sharing Scheme Secure against Cheating
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1338
EP - 1345
AU - Toshinori ARAKI
AU - Wakaha OGATA
PY - 2011
DO - 10.1587/transfun.E94.A.1338
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2011
AB - In (k,n) threshold scheme, Tompa and Woll considered a problem of cheaters who try to make another participant reconstruct an invalid secret. Later, some models of such cheating were formalized and lower bounds of the size of share were shown in the situation of fixing the maximum successful cheating probability to ε. Some efficient schemes in which size of share is equal to the lower bound were also proposed. Let |S| be the field size of the secret. Under the assumption that cheaters do not know the distributed secret, these sizes of share of previous schemes which can work for ε > 1/|S| are somewhat larger than the bound. In this paper, we show the bound for this case is really tight by constructing a new scheme. When distributing uniform secret, the bit length of share in the proposed scheme is only 1 bit longer than the known bound. Further, we show a tighter bound of the size of share in case of ε < 1/|S|.
ER -