Abstract
We present a realization of the transitive signature scheme based on the algebraic properties of bilinear group pairs. The scheme is proven secure, i.e. transitively unforgeable under adaptive chosen message attack, assuming hardness of the computational co-Diffie-Hellman problem in bilinear group pairs and the security of the underlying standard signature scheme under known message attack. Our scheme mostly conforms to previously designed schemes of Micali-Rivest and Bellare-Neven in structure; yet there are two contributions: firstly, we take advantage of bilinear group pairs which were previously used by Boneh, Lynn, and Shacham to build short signature schemes. Secondly, we show that a slight modification in previous definitions of the transitive signature relaxes the security requirement for the underlying standard signature from being secure under chosen message attack to being secure under known message attack; thus shorter and more efficient signatures can be chosen for the underlying standard signature. These two facts eventually yield to short transitive signatures with respect to both node and edge signature size.
This research was supported in part by Iran Telecommunication Research Center (ITRC) grant #T/500/3649 through the School of Electrical Engineering, Sharif University of Technology.
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References
Barreto, P.: The Pairing-Based Crypto Lounge, Web Page, http://planeta.terra.com.br/informatica/paulobarreto/pblounge.html
Bellare, M., Neven, G.: Transitive Signatures Based on Factoring and RSA. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 397–414. Springer, Heidelberg (2002)
Bellare, M., Neven, G.: Transitive Signatures: New Schemes and Proofs. Cryptology ePrint Archive: Report 2004/215 (Full version of [2]), http://eprint.iacr.org/2004/215/ , http://www.cse.ucsd.edu/users/mihir/
Bellare, M., Rogaway, P.: Random Oracles Are Practical: A Paradigm for Designing Efficient Protocols. In: The First Annual Conference on Computer and Communications Security, ACM, New York (1993), http://www-cse.ucsd.edu/users/mihir
Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures – How to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996), Full Paper: http://www-cse.ucsd.edu/users/mihir
Boneh, D., Franklin, M.: Identity Based Encryption from the Weil Pairing. SIAM Journal of Computing 32(3), 586–615 (2001); Extended Abstract in Crypto 2001. Full Paper: http://crypto.stanford.edu/~dabo/pubs.html
Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, p. 514. Springer, Heidelberg (2001), Revised Full Paper: http://crypto.stanford.edu/~dabo/pubs.html
Boneh, D., Mironov, I., Shoup, V.: A Secure Signature Scheme from Bilinear Maps. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 98–110. Springer, Heidelberg (2003), Full Paper: http://crypto.stanford.edu/~dabo/pubs.html
Coron, J.S.: On the Exact Security of Full Domain Hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, p. 229. Springer, Heidelberg (2000), http://www.gemplus.com/smart/r_d/publications/pdf/Cor00fdh.pdf
Goldwasser, S., Micali, S., Rivest, R.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal of Computing 17(2), 281–308 (1988), http://theory.lcs.mit.edu/~rivest/publications.html
Hevia, A., Micciancio, D.: The Provable Security of Graph-Based One-Time Signatures and Extensions to Algebraic Signature Schemes. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 379–396. Springer, Heidelberg (2002), http://www.cs.ucsd.edu/~ahevia/publications/hm02.pdf
Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic Signature Schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, p. 244. Springer, Heidelberg (2002), http://citeseer.nj.nec.com/460118.html
Joux, A., Nguyen, K.: Separating Decision Diffie-Hellman from Computational Diffie-Hellman in Cryptographic Groups. Journal of Cryptology 16(4), 239–247 (2003); A previous version also available online: Separating Decision Diffie-Hellman from Diffie-Hellman in Cryptographic Protocols. Cryptology ePrint Archive. Report 2001/003, http://eprint.iacr.org/2001/003
Lipmaa, H.: Pairing-based Cryptography, Web Page on Cryptology Pointers, http://www.tcs.hut.fi/~helger/crypto/link/public/pairing/
Micali, S., Rivest, R.: Transitive Signature Schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, p. 236. Springer, Heidelberg (2002), http://citeseer.nj.nec.com/micali02transitive.html
Molnar, D.: Homomorphic Signature Schemes. BA Thesis, Computer Science Dept. Harvard College. Cambridge. Massachusetts. Michael Rabin adv (2003), http://www.cs.berkeley.edu/~dmolnar/papers/papers.html
Neven, G.: Provably secure identity-based identification schemes and transitive signatures. Ph.D. thesis. Katholieke Universiteit Leuven, Belgium (May 2004), http://www.cs.kuleuven.ac.be/~gregory/papers/phd.html
Rivest, R.: Two New Signature Schemes. Slides from Talk Given at Cambridge University (2000), http://www.cl.cam.ac.uk/Research/Security/seminars/2000/rivest-tss.pdf
Sujing, Z.: Transitive Signatures Based on Non-adaptive Standard Signatures. Cryptography ePrint Archive. Report 2004/044, http://eprint.iacr.org
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Shahandashti, S.F., Salmasizadeh, M., Mohajeri, J. (2005). A Provably Secure Short Transitive Signature Scheme from Bilinear Group Pairs. In: Blundo, C., Cimato, S. (eds) Security in Communication Networks. SCN 2004. Lecture Notes in Computer Science, vol 3352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30598-9_5
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