Skip to main content
SpringerLink
Log in

Improving Signature Schemes with Tight Security Reductions

  • Conference paper
  • First Online:
Information Security Practice and Experience (ISPEC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11879))

Abstract

In 2003, Katz and Wang proposed the claw-free trapdoor full domain hash (CFT-FDH) which achieves a tight security for FDH signature schemes using the bit selector technique. However, it is noted that the CFT-FDH is not backward compatible with its original FDH counterpart, since the selected bit is hashed with the message, modifying the structure of the original signature. In this paper, we take a step further to propose a general framework that is able to achieve backward compatibility while maintaining the tight reduction of FDH signatures using the properties of trapdoor samplable relations and also Katz-Wang’s bit selector technique.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It is worth mentioning that the co-CDH problem is a Type-3 Pairing counterpart to the CDH problem which is based on the Type-1 Pairing [11].

  2. 2.

    We denote this hard problem as the co-DBDH problem as the Type-3 Pairing version of the DBDH problem, to distinguish between the DBDH problem which is based on the Type-1 Pairing. It is noted that in a work by Vercauteren [41], the co-DBDH problem itself is denoted as the DBDH problem, which covers the specification of both Type-1 and Type-3 pairings.

  3. 3.

    The signer may enclose the bit r alongside \(\sigma \) to avoid confusion during verification where two different signatures for a message (i.e. \(r \in \{0,1\}\)) may exist at once, as stated in [31].

  4. 4.

    Different from Katz-Wang’s work in [31], \(\mathcal {A}\) is not able to query for the value of r considering it is not a portion of the hash input.

References

  1. Abdalla, M., An, J.H., Bellare, M., Namprempre, C.: From identification to signatures via the fiat-shamir transform: minimizing assumptions for security and forward-security. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 418–433. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_28

    Chapter  Google Scholar 

  2. Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_28

    Chapter  MATH  Google Scholar 

  3. An, J.H., 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). https://doi.org/10.1007/3-540-46035-7_6

    Chapter  Google Scholar 

  4. Bao, F., Deng, R.H., Zhu, H.F.: Variations of Diffie-Hellman problem. In: Qing, S., Gollmann, D., Zhou, J. (eds.) ICICS 2003. LNCS, vol. 2836, pp. 301–312. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-39927-8_28

    Chapter  Google Scholar 

  5. Bresson, E., Lakhnech, Y., Mazaré, L., Warinschi, B.: A generalization of DDH with applications to protocol analysis and computational soundness. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 482–499. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_27

    Chapter  Google Scholar 

  6. Beth, T.: Efficient zero-knowledge identification scheme for smart cards. In: Barstow, D., et al. (eds.) EUROCRYPT 1988. LNCS, vol. 330, pp. 77–84. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-45961-8_7

    Chapter  Google Scholar 

  7. Boneh, D., Franklin, M.B.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  8. Bellare, M., Fischlin, M., Goldwasser, S., Micali, S.: Identification protocols secure against reset attacks. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 495–511. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_30

    Chapter  Google Scholar 

  9. Boyen, X., Li, Q.: Towards Tightly Secure Short Signature and IBE. IACR Cryptology ePrint Archive – Report 2016/498, pp. 514–532 (2001)

    Google Scholar 

  10. 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). https://doi.org/10.1007/3-540-45682-1_30

    Chapter  Google Scholar 

  11. Bellare, M., Namprempre, C., Neven, G.: Unrestricted aggregate signatures. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 411–422. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73420-8_37

    Chapter  Google Scholar 

  12. Bellare, M., Namprempre, C., Neven, G.: Security proofs for identity-based identification and signature schemes. J. Cryptol. 22(1), 1–61 (2009)

    Article  MathSciNet  Google Scholar 

  13. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security – ACM CCS 1993, pp. 62–73. ACM (1993)

    Google Scholar 

  14. Bellare, M., Rogaway, P.: The exact security of digital signatures-how to sign with RSA and rabin. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_34

    Chapter  Google Scholar 

  15. Choon, J.C., Hee Cheon, J.: An identity-based signature from gap Diffie-Hellman groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36288-6_2

    Chapter  Google Scholar 

  16. Chaum, D.: Zero-knowledge undeniable signatures (extended abstract). In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 458–464. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46877-3_41

    Chapter  Google Scholar 

  17. Coron, J.-S.: On the exact security of full domain hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 229–235. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_14

    Chapter  Google Scholar 

  18. 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). https://doi.org/10.1007/3-540-46035-7_18

    Chapter  Google Scholar 

  19. Coron, J.S.: A variant of Boneh-Franklin IBE with a tight reduction in the random oracle model. Des. Codes Crypt. 50(1), 115–133 (2009)

    Article  MathSciNet  Google Scholar 

  20. Cramer, R., Shoup, V.: Signature schemes based on the strong RSA assumption. ACM Trans. Inf. Syst. Secur. (TISSEC) 3(3), 161–185 (2000)

    Article  Google Scholar 

  21. Kerry, C.F., Director, C.R.: FIPS PUB 186–4 federal information processing standards publication digital signature standard (DSS). FIPS Publication (2013)

    Google Scholar 

  22. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_2

    Chapter  Google Scholar 

  23. Guo, F., Chen, R., Susilo, W., Lai, J., Yang, G., Mu, Y.: Optimal security reductions for unique signatures: bypassing impossibilities with a counterexample. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 517–547. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_18

    Chapter  Google Scholar 

  24. Goh, E.-J., Jarecki, S.: A signature scheme as secure as the Diffie-Hellman problem. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 401–415. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_25

    Chapter  Google Scholar 

  25. Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)

    Article  MathSciNet  Google Scholar 

  26. Guillou, L.C., Quisquater, J.-J.: A practical zero-knowledge protocol fitted to security microprocessor minimizing both transmission and memory. In: Barstow, D., et al. (eds.) EUROCRYPT 1988. LNCS, vol. 330, pp. 123–128. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-45961-8_11

    Chapter  Google Scholar 

  27. Huang, J., Huang, Q., Pan, C.: A black-box construction of strongly unforgeable signature schemes in the bounded leakage model. In: Chen, L., Han, J. (eds.) ProvSec 2016. LNCS, vol. 10005, pp. 320–339. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47422-9_19

    Chapter  Google Scholar 

  28. Katz, J.: Full-domain hash (and related) signature schemes. In: Katz, J. (ed.) Digital Signatures, pp. 143–153. Springer, Boston (2010). https://doi.org/10.1007/978-0-387-27712-7_7

    Chapter  MATH  Google Scholar 

  29. Koblitz, N., Menezes, A.J.: The random oracle model: a twenty-year retrospective. Des. Codes Crypt. 77(2–3), 587–610 (2015)

    Article  MathSciNet  Google Scholar 

  30. Kiltz, E., Masny, D., Pan, J.: Optimal security proofs for signatures from identification schemes. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 33–61. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_2

    Chapter  Google Scholar 

  31. Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: ACM CCS 2003, pp. 155–164 (2003)

    Google Scholar 

  32. Lacharité, M.S.: Security of BLS and BGLS signatures in a multi-user setting. In: Advances in Cryptology 2016, vol. 2 – ARCTICCRYPT 2016, pp. 244–261 (2016)

    Google Scholar 

  33. Lynn, B.: On the implementation of pairing-based cryptosystems. Doctoral dissertation, Stanford University (2007)

    Google Scholar 

  34. Katz, J., Menezes, A., Van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)

    MATH  Google Scholar 

  35. Morita, H., Schuldt, J.C.N., Matsuda, T., Hanaoka, G., Iwata, T.: On the security of the schnorr signature scheme and DSA against related-key attacks. In: Kwon, S., Yun, A. (eds.) ICISC 2015. LNCS, vol. 9558, pp. 20–35. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30840-1_2

    Chapter  MATH  Google Scholar 

  36. Barker, E., Barker, W., Burr, W., Polk, W., Smid, M.: Recommendation for key management-part 1: general (revised). NIST Special Publication (2006)

    Google Scholar 

  37. Ng, T.-S., Tan, S.-Y., Chin, J.-J.: A variant of BLS signature scheme with tight security reduction. In: Hu, J., Khalil, I., Tari, Z., Wen, S. (eds.) MONAMI 2017. LNICST, vol. 235, pp. 150–163. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-90775-8_13

    Chapter  Google Scholar 

  38. Ogata, W., Kurosawa, K., Heng, S.-H.: The security of the FDH variant of chaum’s undeniable signature scheme. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 328–345. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30580-4_23

    Chapter  Google Scholar 

  39. Pereira, G.C., Simplício, M.A., Naehrig, M., Barreto, P.S.: A family of implementation-friendly BN elliptic curves. J. Syst. Softw. 84(8), 1319–1326 (2011)

    Article  Google Scholar 

  40. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    Article  MathSciNet  Google Scholar 

  41. Vercauteren, F.: Final report on main computational assumptions in cryptography. European Network of Excellence in Cryptography II (2013)

    Google Scholar 

Download references

Acknowledgement

The authors would like to thank Thomas Groß for the helpful comments on an earlier version of this paper. The authors would also like to acknowledge the Fundamental Research Grant Scheme (FRGS/1/2019/ICT04/MMU/02/5) by the Ministry of Education of Malaysia in providing financial support for this work.

Author information

Authors and Affiliations

  1. Multimedia University, Melaka, Malaysia

    Tiong-Sik Ng

  2. Newcastle University, Newcastle upon Tyne, UK

    Syh-Yuan Tan

  3. Multimedia University, Cyberjaya, Malaysia

    Ji-Jian Chin

Authors
  1. Tiong-Sik Ng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Syh-Yuan Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ji-Jian Chin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tiong-Sik Ng .

Editor information

Editors and Affiliations

  1. Multimedia University, Malacca, Malaysia

    Swee-Huay Heng

  2. University of Malaga, Malaga, Spain

    Javier Lopez

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ng, TS., Tan, SY., Chin, JJ. (2019). Improving Signature Schemes with Tight Security Reductions. In: Heng, SH., Lopez, J. (eds) Information Security Practice and Experience. ISPEC 2019. Lecture Notes in Computer Science(), vol 11879. Springer, Cham. https://doi.org/10.1007/978-3-030-34339-2_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34339-2_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34338-5

  • Online ISBN: 978-3-030-34339-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation