Abstract
A multisignature scheme enables multiple signers to cooperate to generate one signature for some message. The aim of the multisignatures is to decrease the total length of the signature and/or the signing (verification) costs. This paper first discusses a formal security model of multisignatures following that of the group signatures [1,4]. This model allows an attacker against multisignatures to access five oracles adaptively. With this model, we can ensure more general security result than that with the existence model [14,11,12]. Second, we propose a multisignature scheme using a claw-free permutation. The proposed scheme can decrease the signature length compared to those of existence multisignature schemes using a trapdoor one-way permutation (TWOP) [11,12], because its signing does not require the random string. We also prove that the proposed scheme is tightly secure with the formal security model, in the random oracle model. Third, we discuss the security of the multisignature schemes [11,12] using a TOWP with the formal security model to confirm that these schemes can be proven to be tightly secure.
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References
Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: Formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Proc. of the First ACM Conference on Computer and Communications Security, pp. 62–73. ACM Press, New York (1993)
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)
Bellare, M., Shi, H., Zhang, C.: Foundations of group signatures: The case of dynamic groups. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 136–153. Springer, Heidelberg (2005)
Boldyreva, A.: Threshold signatures, multisignatures and blind signatures based on the gap-diffie-hellman-group signature scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2002)
Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiability encrypted signature form biliner maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, Springer, Heidelberg (2003)
Coron, J.-S.: Optimal security proofs for PSS and other signature schemes. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 272–287. Springer, Heidelberg (2002)
Itakura, K., Nakamura, K.: A public-key cryptosystem suitable for digital multisignatures. NEC Research & Development (71), 1–8 (1983)
Katz, J., Wang, N.: Eficiency improvements for signature schemes with tight security reductions. In: CCS 2003, 10th ACM Conference on Computer and Communications Security (2003)
Kawauchi, K., Tada, M.: On the exact security of multisignature schemes based on RSA. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 336–349. Springer, Heidelberg (2003)
Kawauchi, K., Tada, M.: On the security and the efficiency of multi-signature schemes based on a trapdoor one-way permutation. IEICE Transactions Fundamentals of Electronics, Communications and Computer Sciences E88–A(5), 1274–1282 (2005)
Komano, Y., Ohta, K., Shimbo, A., Kawamura, S.-i.: On the Security of Probabilistic Multisignature Schemes and Their Optimality. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol. 3715, pp. 132–150. Springer, Heidelberg (2005)
Lysyanskaya, A., Micali, S., Reyzin, L., Shacham, H.: Sequential aggregate signatures from trapdoor permutations. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 74–90. Springer, Heidelberg (2004)
Micali, S., Ohta, K., Reyzin, L.: Accountable-subgroup multisignatures. In: CCS 2001, Eighth ACM Conference on Computer and Communications Security (2001)
Mitomi, S., Miyaji, A.: A general model of multisignature schemes with message flexibility, order flexibility, and order verifiability. IEICE Transaction of fundamentals E-84-A, 2488–2499 (2001)
Ohta, K., Okamoto, T.: A digital multisignature scheme based on the fiat-shamir scheme. In: Matsumoto, T., Imai, H., Rivest, R.L. (eds.) ASIACRYPT 1991. LNCS, vol. 739, pp. 139–148. Springer, Heidelberg (1993)
Ohta, K., Okamoto, T.: Multi-signature schemes secure against active insider attacks. IEICE Transactions Fundamentals of Electronics, Communications and Computer Sciences E82–A(1), 21–31 (1999)
Okamoto, T.: A digital multisignature scheme using bijective public-key cryptosystems. ACM Transactions on Comp. Systems 6(8), 432–441 (1988)
Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)
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Komano, Y., Ohta, K., Shimbo, A., Kawamura, S. (2006). Formal Security Model of Multisignatures. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds) Information Security. ISC 2006. Lecture Notes in Computer Science, vol 4176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11836810_11
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DOI: https://doi.org/10.1007/11836810_11
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