Abstract
Spontaneous anonymous group (SAG) cryptography is a fundamental alternative to achieve thresholding without group secret or setup. It has gained wide interests in applications to ad hoc groups. We present a general construction of blind SAG 1-out-of-n and t-out-of-n signature schemes from essentially any major blind signature. In the case when our scheme is built from blind Schnorr (resp. Okamoto-Schnorr) signature, the parallel one-more unforgeability is reduced to Schnorr’s ROS Problem in the random oracle model plus the generic group model. In the process of our derivations, we obtain a generalization of Schnorr’s result [17] from single public key to multiple public keys.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abe, M., Ohkubo, M., Suzuki, K.: 1-out-of-n signatures from a variety of keys. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 415–432. Springer, Heidelberg (2002)
Bellare, M., Micciancio, D.: A new paradigm for collision-free hasing: incrementality at reduced cost. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 163–192. Springer, Heidelberg (1997)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Proc. 1st ACM Conference on Computer and Communications Security, pp. 62–73. ACM Press, New York (1993)
Blakley, G.R.: Safeguarding cryptographic keys. In: Proc. AFIPS National Computer Conference, vol. 48, pp. 313–317 (1979)
Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)
Bresson, E., Stern, J., Szydlo, M.: Threshold ring signatures and applications to ad-hoc groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 465–480. Springer, Heidelberg (2002)
Camenisch, J., Lysyanskaya, A.: An efficient system for non-transferable anonymous credentials with optional anonymity revocation. In: EUROCRYPT 2001. LNCS, vol. 1294, pp. 93–118. Springer, Heidelberg (2001)
Chaum, D.: Blind signatures for untraceable payments. In: Proc. CRYPTO 1982, pp. 199–203. Plenum Press, New York (1982)
Chaum, D.: Security without identification: Transaction systems to make big brother obsolete. CACM 29(10), 1030–1044 (1985)
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)
Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Proc. First International Workshop on Information Security, ISW 1997. LNCS, vol. 1196, pp. 158–173. Springer, Heidelberg (1997)
Liu, J.K., Wei, V.K., Wong, D.S.: Cryptanalyzing Bresson, et al.’s spontaneous anonymous group threshold signature for ad hoc groups and patching via updating Cramer, et al.’s threshold proof-of-knowledge. eprint, 2004(042) (2004)
Liu, J.K., Wei, V.K., Wong, D.S.: Linkable and culpable ring signatures. eprint, 2004(027) (2004)
Nechaev, V.I.: Complexity of a determinate algorithm for the discrete logarithm. Mathematical Notes 55, 165–172 (1994)
Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31–53. Springer, Heidelberg (1993)
Rivest, R., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001)
Schnorr, C.-P.: Security of blind discrete log signatures against interactive attacks. In: Qing, S., Okamoto, T., Zhou, J. (eds.) ICICS 2001. LNCS, vol. 2229, p. 1. Springer, Heidelberg (2001)
Schnorr, C.P.: Efficient identication and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)
Shamir, A.: How to share a secret. Communications of the ACM 22(2), 612–613 (1979)
Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)
Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–303. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chan, T.K., Fung, K., Liu, J.K., Wei, V.K. (2005). Blind Spontaneous Anonymous Group Signatures for Ad Hoc Groups. In: Castelluccia, C., Hartenstein, H., Paar, C., Westhoff, D. (eds) Security in Ad-hoc and Sensor Networks. ESAS 2004. Lecture Notes in Computer Science, vol 3313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30496-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-30496-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24396-0
Online ISBN: 978-3-540-30496-8
eBook Packages: Computer ScienceComputer Science (R0)