# VULNERABILITY OF A NON-MEMBERSHIP PROOF SCHEME

### Kun Peng, Feng Bao

#### Abstract

An accumulator system used for a special application of anonymous credential is extended by Li et al to a much wider range of applications: membership proof and non-membership proof. Given a committed secret integer and a public finite set of prime integers, two proof protocols, membership proof and non-membership proof are proposed in the extended scheme. The former proves that the integer is in the set when it is really in, while the latter proves that the integer is not in the set when it is really not in. Although the original accumulator technique works well in its appointed special application, the extension is insecure and vulnerable to attacks. Several attacks against membership proof and non-membership proof in the extended work is proposed in this paper to show its vulnerability in security. The attacks show that an attacker can employ various methods to give membership proof to an integer not in the set and non-membership proof to an integer in the set.

#### References

- Camenisch, J., Chaabouni, R., and Shelat, A. (2008). Efficient protocols for set membership and range proofs. In ASIACRYPT 7808, pages 234-252.
- Camenisch, J. and Lysyanskaya, A. (2002). Dynamic accumulators and application to efficient revocation of anonymous credentials. In CRYPTO 7802, pages 61- 76.
- Li, J., Li, N., and Xue, R. (2007). Universal accumulators with efficient nonmembership proofs. In ACNS 7807, pages 253-269.

#### Paper Citation

#### in Harvard Style

Peng K. and Bao F. (2010). **VULNERABILITY OF A NON-MEMBERSHIP PROOF SCHEME** . In *Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2010)* ISBN 978-989-8425-18-8, pages 419-422. DOI: 10.5220/0002912904190422

#### in Bibtex Style

@conference{secrypt10,

author={Kun Peng and Feng Bao},

title={VULNERABILITY OF A NON-MEMBERSHIP PROOF SCHEME},

booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2010)},

year={2010},

pages={419-422},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002912904190422},

isbn={978-989-8425-18-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2010)

TI - VULNERABILITY OF A NON-MEMBERSHIP PROOF SCHEME

SN - 978-989-8425-18-8

AU - Peng K.

AU - Bao F.

PY - 2010

SP - 419

EP - 422

DO - 10.5220/0002912904190422