Abstract
In many applications, it is desirable to work with signatures that are short, and yet where many messages from different signers be verified very quickly. RSA signatures satisfy the latter condition, but are generally thousands of bits in length. Recent developments in pairing-based cryptography produced a number of “short” signatures which provide equivalent security in a fraction of the space. Unfortunately, verifying these signatures is computationally intensive due to the expensive pairing operation. Toward achieving “short and fast” signatures, Camenisch, Hohenberger and Pedersen (Eurocrypt 2007) showed how to batch verify two pairing-based schemes so that the total number of pairings was independent of the number of signatures to verify.
In this work, we present both theoretical and practical contributions. On the theoretical side, we introduce new batch verifiers for a wide variety of regular, identity-based, group, ring and aggregate signature schemes. These are the first constructions for batching group signatures, which answers an open problem of Camenisch et al. On the practical side, we implement each of these algorithms and compare each batching algorithm to doing individual verifications. Our goal is to test whether batching is practical; that is, whether the benefits of removing pairings significantly outweigh the cost of the additional operations required for batching, such as group membership testing, randomness generation, and additional modular exponentiations and multiplications. We experimentally verify that the theoretical results of Camenisch et al. and this work, indeed, provide an efficient, effective approach to verifying multiple signatures from (possibly) different signers.
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References
Car 2 Car: Communication consortium, http://car-to-car.org
SeVeCom: Security on the road, http://www.sevecom.org
Raya, M., Hubaux, J.-P.: Securing vehicular ad hoc networks. J. of Computer Security 15, 39–68 (2007)
Gennaro, R., Rohatgi, P.: How to sign digital streams. Inf. Comput. 165(1), 100–116 (2001)
Lysyanskaya, A., Tamassia, R., Triandopoulos, N.: Multicast authentication in fully adversarial networks. In: IEEE Security and Privacy, pp. 241–253 (2004)
Perrig, A., Canetti, R., Song, D.X., Tygar, J.D.: Efficient and secure source authentication for multicast. In: NDSS 2001, The Internet Society (2001)
Monnerat, J., Vaudenay, S.: Undeniable signatures based on characters: How to sign with one bit. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 69–85. Springer, Heidelberg (2004)
Monnerat, J., Vaudenay, S.: Short 2-move undeniable signatures. In: Nguyên, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 19–36. Springer, Heidelberg (2006)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)
Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Boneh, D., Shacham, H.: Group signatures with verifier-local revocation. In: CCS, pp. 168–177 (2004)
Chow, S.S.M., Yiu, S.-M., Hui, L.C.K.: Efficient identity based ring signature. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 499–512. Springer, Heidelberg (2005)
Boyen, X.: Mesh signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 210–227. Springer, Heidelberg (2007)
Camenisch, J.L., Hohenberger, S., Pedersen, M.Ø.: Batch verification of short signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 246–263. Springer, Heidelberg (2007), http://eprint.iacr.org/2007/172
Law, L., Matt, B.J.: Finding invalid signatures in pairing-based batches. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 34–53. Springer, Heidelberg (2007)
Ferrara, A.L., Green, M., Hohenberger, S., Pedersen, M.Ø.: Practical short signature batch verification, Cryptology ePrint Archive: Report 2008/015 (2008)
Chen, L., Cheng, Z., Smart, N.: Identity-based key agreement protocols from pairings, Cryptology ePrint Archive: Report 2006/199 (2006)
Bellare, M., Garay, J.A., Rabin, T.: Fast batch verification for modular exponentiation and digital signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)
Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)
Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)
Naccache, D.: Secure and practical identity-based encryption, Cryptology ePrint Archive: Report 2005/369 (2005)
Chatterjee, S., Sarkar, P.: Trading time for space: Towards an efficient IBE scheme with short(er) public parameters in the standard model. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 424–440. Springer, Heidelberg (2006)
Chatterjee, S., Sarkar, P.: HIBE with short public parameters without random oracle. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 145–160. Springer, Heidelberg (2006)
Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential aggregate signatures and multisignatures without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 465–485. Springer, Heidelberg (2006)
Pastuszak, J., Michatek, D., Pieprzyk, J., Seberry, J.: Identification of bad signatures in batches. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 28–45. Springer, Heidelberg (2000)
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. Journal of Cryptology 17(4), 297–319 (2004)
Cha, J.C., Cheon, J.H.: An identity-based signature from gap Diffie-Hellman groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2002)
Boyen, X., Waters, B.: Compact group signatures without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 427–444. Springer, Heidelberg (2006)
Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)
Shao, Z.: Enhanced aggregate signatures from pairings. In: Feng, D., Lin, D., Yung, M. (eds.) CISC 2005. LNCS, vol. 3822, pp. 140–149. Springer, Heidelberg (2005)
Scott, M.: Multiprecision Integer and Rational Arithmetic C/C++ Library (MIRACL). Published by Shamus Software Ltd. (October 2007), http://www.shamus.ie/
Page, D., Smart, N., Vercauteren, F.: A comparison of MNT curves and supersingular curves. Applicable Algebra in Eng. Com. and Comp. 17(5), 379–392 (2006)
Adida, B., Chau, D., Hohenberger, S., Rivest, R.L.: Lightweight email signatures (Extended abstract). In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 288–302. Springer, Heidelberg (2006)
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Ferrara, A.L., Green, M., Hohenberger, S., Pedersen, M.Ø. (2009). Practical Short Signature Batch Verification. In: Fischlin, M. (eds) Topics in Cryptology – CT-RSA 2009. CT-RSA 2009. Lecture Notes in Computer Science, vol 5473. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00862-7_21
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