Security Analysis of Three Cryptographic Schemes from Other Cryptographic Schemes

  • Sherman S. M. Chow
  • Zhengjun Cao
  • Joseph K. Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3822)


Relations between various cryptographic schemes make it possible to build a new cryptographic scheme from (some components of) other kinds of cryptographic schemes. Recently, three new schemes are proposed by exploiting these relationships: a group signature scheme from identity-based signature, another group signature scheme from proxy signature and a signcryption scheme from secret sharing. Unfortunately, we show that these schemes are insecure. These group signature schemes cannot satisfy at least half of the standard security requirements while the signcryption scheme does not even satisfy the basic requirement of a secure signcryption scheme. We hope this work can exhibit the precautions one should take when making schemes with a similar approach.


Group signature signcryption identity-based signature proxy signature secret sharing bilinear pairings 


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  1. 1.
    Abdalla, M., Warinschi, B.: On the minimal assumptions of group signature schemes. In: López, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 1–13. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Al-Ibrahim, M.: A signcryption scheme based on secret sharing technique. In: Gorodetsky, V., Popyack, L.J., Skormin, V.A. (eds.) MMM-ACNS 2003. LNCS, vol. 2776, pp. 279–288. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)Google Scholar
  7. 7.
    Chow, S.S.M., Yiu, S.M., Hui, L.C.K., Chow, K.P.: Efficient Forward and Provably Secure ID-Based Signcryption Scheme with Public Verifiability and Public Ciphertext Authenticity. In: Lim, J.I., Lee, D.H. (eds.) Information Security and Cryptology - ICISC 2006. 6th International Conference Seoul, Korea, November 27-28, 2003. LNCS, vol. 2971, pp. 352–369. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Deng, D., Zhao, Y.: An Efficient Group Signature from Gap Diffe-Hellman Groups. In: ChinaCrypt 2004, pp. 186–194 (2004) (in English)Google Scholar
  9. 9.
    Fu, C., Xu, C.: A New Group Signature Scheme with Unlimited Group Size. In: Chen, K. (ed.) Progress on Cryptography, 25 Years of Cryptography in China, pp. 89–96. Kluwer Academic Publishers, Dordrecht (2004)Google Scholar
  10. 10.
    Goldwasser, S., Micali, S.: Probabilistic Encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Horster, P., Michels, M., Petersen, H.: Authenticated Encryption Schemes with Low Communication Costs. Electronics Letters 30(15), 1212–1213 (1994)CrossRefGoogle Scholar
  12. 12.
    Lee, W.-B., Chang, C.-C.: Authenticated Encryption Schemes Without Using a One Way Function. Electronics Letters 31(19), 1656–1657 (1995)CrossRefGoogle Scholar
  13. 13.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Rompel, J.: One-Way Functions are Necessary and Sufficient for Secure Signatures. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing (STOC 1990), pp. 387–394. ACM Press, New York (1990)CrossRefGoogle Scholar
  15. 15.
    Shamir, A.: How to Share A Secret. Communications of the ACM 22(11), 612–613 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sui, A.f., Chow, S.S.M., Hui, L.C.K., Yiu, S.M., Chow, K.P., Tsang, W.W., Chong, C.F., Pun, K.H., Chan, H.W.: Separable and Anonymous Identity-Based Key Issuing. In: 1st International Workshop on Security in Networks and Distributed Systems (SNDS 2005), in conjunction with 11th International Conference on Parallel and Distributed Systems (ICPADS 2005), Fukuoka, Japan, July 20-22 (2005); Full version available at Cryptology ePrint Archive, Report 2004/322.Google Scholar
  17. 17.
    Wang, G., Bao, F., Zhou, J., Deng, R.H.: Security Analysis of Some Proxy Signatures. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, Springer, Heidelberg (2004)Google Scholar
  18. 18.
    Zheng, Y.: Digital signcryption or how to achieve cost (Signature & encryption) < < cost(Signature) + cost(Encryption). In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 165–179. Springer, Heidelberg (1997)Google Scholar
  19. 19.
    Zheng, Y.: Signcryption and Its Applications in Efficient Public Key Solutions. In: Okamoto, E., Davida, G.I., Mambo, M. (eds.) ISW 1997. LNCS, vol. 1396, pp. 291–312. Springer, Heidelberg (1998); Invited LectureCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sherman S. M. Chow
    • 1
  • Zhengjun Cao
    • 2
  • Joseph K. Liu
    • 3
  1. 1.Department of Computer Science, Courant Institute of Mathematical SciencesNew York UniversityUSA
  2. 2.Key Lab of Mathematics MechanizationAcademy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingP.R. China
  3. 3.Department of Computer ScienceUniversity of BristolBristolUK

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