# INFORMATION-THEORETICALLY SECURE STRONG VERIFIABLE SECRET SHARING

### Changlu Lin, Lein Harn, Dingfeng Ye

#### 2009

#### Abstract

In a (t,n) secret sharing scheme, a mutually trusted dealer divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. When there is no mutually trusted dealer, a (n, t,n) secret sharing scheme can be used to set up a (t,n) secret sharing because each shareholder also acts as a dealer to decide a master secret jointly and divide each selected secret for others. A verifiable secret sharing (VSS) allows each shareholder to verify that all shares are t-consistent (i.e. every subset of t of the n shares defines the same secret). In this paper, we show that (t,n)-VSS and (n, t,n)-VSS proposed by Pedersen can only ensure that all shares are t-consistent; but shares may not satisfy the security requirements of secret sharing scheme. Then, we introduce a new notion of strong VSS. A strong VSS scheme can ensure that (a) all shares are t-consistent, and (b) all shares satisfy the security requirements of secret sharing scheme. We propose two simple ways to convert Pedersen’s VSS schemes into strong VSS schemes, which are information-theoretically secure. We also prove that our proposed VSS schemes satisfy the strong verifiable property.

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#### Paper Citation

#### in Harvard Style

Lin C., Harn L. and Ye D. (2009). **INFORMATION-THEORETICALLY SECURE STRONG VERIFIABLE SECRET SHARING** . In *Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2009)* ISBN 978-989-674-005-4, pages 233-238. DOI: 10.5220/0002222402330238

#### in Bibtex Style

@conference{secrypt09,

author={Changlu Lin and Lein Harn and Dingfeng Ye},

title={INFORMATION-THEORETICALLY SECURE STRONG VERIFIABLE SECRET SHARING},

booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2009)},

year={2009},

pages={233-238},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002222402330238},

isbn={978-989-674-005-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2009)

TI - INFORMATION-THEORETICALLY SECURE STRONG VERIFIABLE SECRET SHARING

SN - 978-989-674-005-4

AU - Lin C.

AU - Harn L.

AU - Ye D.

PY - 2009

SP - 233

EP - 238

DO - 10.5220/0002222402330238