Self-certified Signatures Based on Discrete Logarithms

  • Zuhua Shao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


In the trivial PKI, a digital signature provides the authenticity of a signed message with respect to a public key, while the authenticity of the public key with respect to a signer lies on a certificate provided by a certificate authority. To verify a signature, verifiers have to first verify the corresponding certificate. To avoid this burden, in this paper, we propose a self-certified signature scheme based on discrete logarithms to provide an implicit as well as mandatory verification of public keys. We show that this new scheme can achieve strong unforgeability in the random oracle model.


Discrete logarithm Self-certified public key signature strong unforgeability 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. IT-22, 644–654 (1976)MathSciNetGoogle Scholar
  2. 2.
    Kohnfelder, L.M.: A method for certificate, MIT Lab. For Computer Science, Cambridge, MA (1978)Google Scholar
  3. 3.
    IEEE P1363 Standard Specifications for Public Key Cryptography (2000)Google Scholar
  4. 4.
    Shamir, A.: Identity-based cryptosystem based on the discrete logarithm problem. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  5. 5.
    Girault, M.: Self-certified public keys. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 491–497. Springer, Heidelberg (1991)Google Scholar
  6. 6.
    Rivest, R.L., Shamir, A., Adelman, L.: A method for obtaining digital signatures and public-key cryptosystem. Commun. ACM 21(2), 120–126 (1978)zbMATHCrossRefGoogle Scholar
  7. 7.
    Gentry, C.: Certificated-based encryption and the certificate revocation problem. In: Biham, E. (ed.) Advances in Cryptology – EUROCRPYT 2003. LNCS, vol. 2656, pp. 272–293. Springer–Verlag, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Al-Riyami, S.S., Paterson, K.G.: Certificateless public key cryptography. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 452–473. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Shao, Z.: Self-certified signature scheme from pairings. Journal of System and Software 80(3), 388–395 (2007)CrossRefGoogle Scholar
  10. 10.
    Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Wail pairings. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Petersen, H., Hoster, P.: Self-certified keys-Concept and Applications. In: Petersen, H., Hoster, P. (eds.) Proc. Communication and Multimedia Security’97, pp. 102–116. Chapman & Hall, Sydney, Australia (1997)Google Scholar
  12. 12.
    Mambo, M., Usuda, K., Okamoto, E.: Proxy signatures: Delegation of the power to sign messages. IEICE Trans. Fundam. E79-A(9), 1338–1354 (1996)Google Scholar
  13. 13.
    Shao, Z.: Cryptographic systems using self-certified public key based on discrete logarithms. IEE Proc.-Comput. Digit. Tech. 148(6), 233–237 (2001)CrossRefGoogle Scholar
  14. 14.
    Lee, B., Kim, K.: Self-Certified Signatures. In: Menezes, A.J., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 199–214. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Wu, T.-S., Hsu, C.-L.: Threshold signature scheme using self-certified public keys. Journal of Systems and Software 67(2), 89–97 (2003)CrossRefGoogle Scholar
  16. 16.
    Bao, H., Cao, Z., Wang, S.: Remarks on Wu-Hsu’s threshold signature scheme using self-certified public keys. Journal of Systems and Software 78(1), 56–59 (2005)CrossRefGoogle Scholar
  17. 17.
    Schnorr, C.P.: Efficient signature generation by smart cards. Journal of Cryptology 3(3), 161–174 (1991)MathSciNetGoogle Scholar
  18. 18.
    An, J., Dodis, Y., Rabin, T.: On the security of joint signature and encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 83–107. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. Journal of Cryptology 13(3), 196–361 (2000)CrossRefGoogle Scholar
  20. 20.
    ElGamal, T.: A public-key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inform. Theory IT-31, 469–472 (1985)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Goldwasser, S., Micali, S., Rivest, R.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal on Computing 17(2), 281–308 (1988)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Zuhua Shao
    • 1
  1. 1.Department of Computer and Electronic Engineering, Zhejiang University of Science and Technology, No. 318, LiuHe Road, Hangzhou, Zhejiang, 310023P.R. of China

Personalised recommendations