# Transitive Signatures Based on Bilinear Maps

### Changshe Ma, Kefei Chen, Shengli Liu, Dong Zheng

#### Abstract

The notion of transitive signature, firstly introduced by Micali and Rivest, is a way to digitally sign the vertices and edges of a dynamically growing, transitively closed graph. All the previous proposed transitive signature schemes were constructed from discrete logarithm, factoring, or RSA assumption. In this paper, we introduce two alternative realizations of transitive signature based on bilinear maps. The proposed transitive signature schemes possess the following properties: (i) they are provably secure against adaptive chosen-message attacks in the random oracle model; (ii) there are no need for node certificates in our transitive signature schemes, so the signature algebra is compact; (iii) if using Weil pairing, our signature schemes are more efficient than all previous proposed schemes.

#### References

- D. Boneh and M. Franklin. Identity-based encryption from the Weil pairing. SIAM, J. Computing, 32(3), pp.583-615, 2003.
- D. Boneh, C. Gentry, B. Lynn, H. Shacham, Aggregate and verifiably encrypted signatures from bilinear maps. Advances in Cryptology-EUROCRYPT 2003, Lecture Notes in Computer. Science, Vol. 2656, pp.416-432, Springer, 2003.
- D. Boneh, B. Lymn and H. Shacham. Short signatures from the Weil pairing. Prodeedings of Asiacrypt 2001, Vol. 2248, Lecture Notes in Computer Science, pp.514-532, Springer, 2001.
- M. Bellare and G.. Neven. Transitive signatures based on factoring and RSA. Advances in Cryptology - ASIACRYPT'02, Lecture Noted in Computer Science Vol.2501, pp.391-414, Springer, 2002.
- M. Bellare and P. Rogaway. Random oracles are practical: A paradigm for designing efficient protocols. Proceeding s of the 1st Annual Conference on Computer and Communications Security, ACM. pp.62-73, 1993.
- J.-S. Coron, On the exact security of full domain hash. Advances in Cryptology-CRYPTO 2000, Lecture Notes in Computer Science, Vol.1880, pp.229-235, Springer, Berlin, 2000.
- S. Chari, T. Rabin and R. Rivest. An efficient signature scheme for route aggregation. http://theory.lcs.mit.edu/ rivest/publications.html, 2002.
- R. Housley, M. Ford, W. Polk, D.solo. Internet X.509 Public Key Infrastructure: Certificate and CRL Profile. http://www.ietf.org/rfc.html, January 1999.
- R. Johnson, D. Molnar, D. Song and D. Wagner. Homomorphic signature schemes. Topics in Cryptology - CT-RSA 7802, Lecture Notes in Computer Science Vol.2271, pp.244-262, Springer, 2002.
- A. Joux and K. Nguyen. Separating decision Diffie-Hellman form Diffie-Hellman in cryptographic groups. Cryptology ePrint Archive, Report 2001/003, 2001. http://eprint.iacr.org/.
- Changshe Ma and Kefei Chen, Publicly verifiable authenticated encryption. Electronics Letters, vol 39, pp.281-282, 2003.
- S. Micali and R. L. Rivest. Transitive signature schemes. Topics in Cryptology - CT-RSA 7802, Lecture Notes in Computer Science Vol.2271 , pp.236-243, Springer, 2002.
- R. Steinfeld, L. Bull and Y. Zheng. Content Extraction signatures. Information security and cryptology-ICI 2001, Lecture Notes in Computer SCience Vol.2288, pp.285-304, SpringVerlag, 2002.
- Fangguo Zhang, Rei Safavi-Naini, and Willy Susilo. An Efficient Signature Scheme from Bilinear Pairings and Its Application. Public Key Cryptography - PKC 2004, Lecture Notes in Computer Science, volume 2947, pages 277-290. Springer, 2004.
- H.Zhu and B. Feng, Robert H. Deng. Computing of Trust in Distributed Networks. http://www.iacr.org, eprint.

#### Paper Citation

#### in Harvard Style

Ma C., Chen K., Liu S. and Zheng D. (2005). **Transitive Signatures Based on Bilinear Maps** . In *Proceedings of the 3rd International Workshop on Security in Information Systems - Volume 1: WOSIS, (ICEIS 2005)* ISBN 972-8865-25-2, pages 48-56. DOI: 10.5220/0002542700480056

#### in Bibtex Style

@conference{wosis05,

author={Changshe Ma and Kefei Chen and Shengli Liu and Dong Zheng},

title={Transitive Signatures Based on Bilinear Maps},

booktitle={Proceedings of the 3rd International Workshop on Security in Information Systems - Volume 1: WOSIS, (ICEIS 2005)},

year={2005},

pages={48-56},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002542700480056},

isbn={972-8865-25-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Workshop on Security in Information Systems - Volume 1: WOSIS, (ICEIS 2005)

TI - Transitive Signatures Based on Bilinear Maps

SN - 972-8865-25-2

AU - Ma C.

AU - Chen K.

AU - Liu S.

AU - Zheng D.

PY - 2005

SP - 48

EP - 56

DO - 10.5220/0002542700480056