# INFORMATION-THEORETICALLY SECURE STRONG VERIFIABLE SECRET SHARING

### Changlu Lin, Lein Harn, Dingfeng Ye

#### 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.

#### References

- Benaloh, J. C. (1986). Secret sharing homomorphisms: Keeping shares of a secret secret. In Proc. Crypto'86, volume 263 of LNCS, pages 251-260. SpringerVerlag.
- Blakley, G. R. (1979). Safeguarding cryptographic keys. In Proc. Nat. Computer Conf., volume 48, pages 313- 317. AFIPS Press.
- Cachin, C., Kursawe, K., Lysyanskaya, A., and Strobl, R. (2002). Asynchronous verifiable secret sharing and proactive cryptosystems. In Proc. 9th ACM Conf. Computer and Communications Security, pages 88- 97. ACM Press.
- Cachin, C., Kursawe, K., and Shoup, V. (2005). Random oracles in constantinople: practical asynchronous byzantine agreement using cryptography. J. Cryptology, 8(3):219-246.
- Chor, B., Goldwasser, S., Micali, S., and Awerbuch, B. (1985). Verifiable secret sharing and achieving simultaneously in the presence of faults. In Proc. 26th IEEE Symp. on Foundations of Computer Science, pages 383-395. IEEE Society.
- Cramer, R., Damga°rd, I., and Maurer, U. (2000). Verifiable secret sharing and achieving simultaneously in the presence of faults. In Proc. Eurocrypt'00, volume 1807 of LNCS, pages 316-334. Springer-Verlag.
- Dehkordi, M. H. and Mashhadi, S. (2008). New efficient and practical verifiable multi-secret sharing schemes. Information Sciences, 178(9):2262-2274.
- Feldman, P. (1987). A practical scheme for non-interactive verifiable secret sharing. In Proc. 28th IEEE Symp. on Foundations of Computer Science, pages 427-437. IEEE Society.
- Housley, R., Polk, W., Ford, W., and Solo, D. (2002). Internet x.509 public key infrastructure certificate and certificate revocation list (crl) profile. rfc3280, ietf. Available: http://www.ipa.go.jp/security/rfc/RFC3280- 00EN.html.
- Ingemarsson, I. and Simmons, G. J. (1991). A protocol to set up shared secret schemes without the assistance of a mutualy trusted party. In Proc. Eurocrypt'90, volume 472 of LNCS, pages 266-282. Springer-Verlag.
- Katz, J., Koo, C., and Kumaresan, R. (2008). Improved the round complexity of vss in point-to-point networks. In Proc. ICALP 2008, Part II, volume 5126 of LNCS, pages 499-510. Springer-Verlag.
- Ma, C. and Cheng, R. (2008). Key management based on hierarchical secret sharing in ad-hoc networks. In Proc. Inscrypt 2007, volume 4990 of LNCS, pages 182-191. Springer-Verlag.
- Pedersen, T. P. (1992). Non-interactive and informationtheoretic secure verfiable secret sharing. In Proc. Crypto'91, volume 576 of LNCS, pages 129-140. Springer-Verlag.
- Shamir, A. (1979). How to share a secret. Commun. ACM, 22(11):612-613.
- Zhou, L. and Haas, Z. J. (1999). Securing ad hoc networks. IEEE Networks Magazine, 13(6):24-30.

#### 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