Efficient discrete logarithm based multi-signature scheme in the plain public key model
Article
First Online:
- 190 Downloads
- 10 Citations
Abstract
In this paper, we provide a new multi-signature scheme that is proven secure in the plain public key model. Our scheme is practical and efficient according to computational costs, signature size and security assumptions. At first, our scheme matches the single ordinary discrete logarithm based signature scheme in terms of signing time, verification time and signature size. Secondly, our scheme requires only two rounds of interactions and each signer needs nothing more than a certified public key to produce the signature, meaning that our scheme is compatible with existing PKIs. Thirdly, our scheme has been proven secure in the random oracle model under standard discrete logarithm (DL) assumption. It outperforms a newly proposed multi-signature scheme by Bagherzandi, Cheon and Jarecki (BCJ scheme) in terms of both computational costs and signature size.
Keywords
Cryptography Digital signature Multi-signature Provable security Plain public key modelMathematics Subject Classifications (2000)
11T71 94A60Preview
Unable to display preview. Download preview PDF.
References
- 1.Avanzi R.: On multi-exponentiation in cryptography. Cryptology ePrint Archive: Report 2002/154 (2002).Google Scholar
- 2.Bagherzandi A., Cheon J.H., Jarecki S.: Multisignatures secure under the discrete logarithm assumption and a generalized forking lemma. In: The 15th ACM Conference on Computer and Communication Security (2008).Google Scholar
- 3.Bellare M., Neven G.: Multi-signature in the plain public-key model and a genral forking lemma. In: The 13th ACM Conference on Computer and Communication Security (2006).Google Scholar
- 4.Bellare M., Rogaway P.: Random oracles are practical: a paradigm for designing efficient protocols. In: The 1st ACM Conference on Computer and Communications Security (1993).Google Scholar
- 5.Boldyreva A.: Efficient threshold signature, multisignature and blind signature schemes based on the gap-Difiie-Hellman-group signature schemes. In: Public Key Cryptography 2003. Lecture Notes in Computer Science, vol. 1567 (2003).Google Scholar
- 6.Boneh D., Lynn B., Shacham H.: Short signatures from the Weil pairing. In: Advances in Cryptology-ASIACRYPT 2001. Lecture Notes in Computer Science, vol. 2248 (2001).Google Scholar
- 7.Feige U., Shamir A.: Witness indistinguishable and witness hiding protocols. In: The 22nd Annual ACM Symposium on Theory of Computing (1990).Google Scholar
- 8.Fiat A., Shamir A.: How to prove yourself: practical solutions to identification and signature problems. In: Advances in Cryptology-CRYPTO 1986. Lecture Notes in Computer Science, vol. 263 (1986).Google Scholar
- 9.Goldwasser S., Micali S., Rivest R.: A digital signature scheme secure against adaptive chosen message attacks. SIAM J. Comput. 17(2), 281–308 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
- 10.Harn L.: Group-oriented (t, n) threshold digital signature scheme and digital multisignature. IEE Proc. Comput. Digit. Tech. 141(5), 307–313 (1994)zbMATHCrossRefGoogle Scholar
- 11.Housley R., Ford M., Polk W., Solo D.: Internet X.509 Public Key Infrastructure: certificate and CRL profile, http://www.ietf.org/rfc/rfc2459.txt. Accessed January 1999.
- 12.Horster P., Michels M., Petersen H.: Meta-multisignatures schemes based on the discrete logarithm problem. In: IFIP/SEC, Chapman & Hall (1995).Google Scholar
- 13.Itakura K., Nakamura K.: A public-key cryptosystem suitable for digital multisignatures. NEC Res. Dev. 71, 1–8 (1983)Google Scholar
- 14.Katz J., Wang N.: Efficiency improvements for signature schemes with tight security reductions. In: The 10th ACM Conference on Computer and Communications Security (2003).Google Scholar
- 15.Langford S.K.: Weakness in some threshold cryptosystems. In: Advances in Cryptology-CRYPTO 1996. Lecture Notes in Computer Science, vol. 1109 (1996).Google Scholar
- 16.Li C.-M., Hwang T., Lee N.-Y.: Threshold-multisignature schemes where suspected forgery implies traceability of adversarial shareholders. In: Advances in Cryptology-EUROCRYPT 1994. Lecture Notes in Computer Science, vol. 950 (1994).Google Scholar
- 17.Lu S., Ostrovsky R., Sahai A., Shacham H., Waters B.: Sequential aggregate signatures and multisignatures without random oracles. In: Advances in Cryptology-EUROCRYPT 2006. Lecture Notes in Computer Science, vol. 4004 (2006).Google Scholar
- 18.Micali S., Ohta K., Reyzin L.: Accountable-subgroup multisignatures. In: The 8th ACM Conference on Computer and Communications Security (2001).Google Scholar
- 19.Michels M., Horster P.: On the risk of disruption in several multiparty signature schemes. In: Advances in Cryptology-ASIACRYPT 1996. Lecture Notes in Computer Science, vol. 1163 (1996).Google Scholar
- 20.Moller B.: Algorithms for multi-exponentiation. In: Selected Areas in Cryptography - SAC 2001. Lecture Notes in Computer Science, vol. 2259 (2001).Google Scholar
- 21.Ohta K., Okamoto T.: A digital multisignature scheme based on the Fiat-Shamir scheme. In: Advances in Cryptology-ASIACRYPT 1991. Lecture Notes in Computer Science, vol. 739 (1991).Google Scholar
- 22.Ohta K., Okamoto T.: Multi-signature schemes secure against active insider attacks. IEICE Trans. Fundam. Electr. Commun. Comput. Sci. E82-A(1), 21–31 (1999)Google Scholar
- 23.Okamoto T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Advances in Cryptology-CRYPTO 1992. Lecture Notes in Computer Science, vol. 740 (1992).Google Scholar
- 24.Ong H., Schnorr C.-P.: Fast signature generation with a Fiat Shamir-like scheme. In: Advances in Cryptology-EUROCRYPT 1990. Lecture Notes in Computer Science, vol. 473 (1990).Google Scholar
- 25.Pointcheval D., Stern J.: Security arguments for digital signatures and blind signatures. J. Cryptol. 13(3), 361–396 (2000)zbMATHCrossRefGoogle Scholar
- 26.Ristenpart T., Yilek S.: The power of proofs of possession: Securing multiparty signatures against rogue-key attacks. In: Advances in Cryptology-EUROCRYPT 2007. Lecture Notes in Computer Science, vol. 4515 (2007).Google Scholar
- 27.Schaad J.: Internet X.509 Public Key Infrastructure Certificate Request Message Format. Internet Engineering Task Force RFC 4211 (2005).Google Scholar
- 28.Schnorr C.-P.: Efficient signature generation by smart cards. J. Cryptol. 4(3), 161–174 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
Copyright information
© Springer Science+Business Media, LLC 2009