Advertisement

International Journal of Information Security

, Volume 17, Issue 2, pp 193–220 | Cite as

Accumulable optimistic fair exchange from verifiably encrypted homomorphic signatures

  • Jae Hong Seo
  • Keita Emura
  • Keita Xagawa
  • Kazuki Yoneyama
Regular Contribution

Abstract

Let us consider a situation where a client (Alice) frequently buys a certain kind of product from a shop (Bob) (e.g., an online music service sells individual songs at the same price, and a client buys songs multiple times in a month). In this situation, Alice and Bob would like to aggregate the total transactions and pay once per month because individual payments are troublesome. Though optimistic fair exchange (OFE) has been considered in order to swap electronic items simultaneously, known OFE protocols cannot provide such aggregate function efficiently because various costs are bounded by the number of transactions in the period. In order to run this aggregation procedure efficiently, we introduce a new kind of OFE called accumulable OFE (AOFE) that allows clients to efficiently accumulate payments in each period. In AOFE, any memory costs, computational costs, and communication complexity of the payment round must be constant in terms of the number of transactions. Since a client usually has just a low power and poor memory device, these efficiencies are desirable in practice. Currently, known approaches (e.g., based on verifiably encrypted signature scheme) are not very successful for constructing AOFE. Thus, we consider a new approach based on a new cryptographic primitive called verifiably encrypted homomorphic signature scheme (VEHS). In this paper, we propose a generic construction of AOFE from VEHS and also present a concrete VEHS scheme over a composite-order bilinear group by using the dual-form signature techniques. This VEHS scheme is also of independent interest. Since we can prove the security of VEHS without random oracles, our AOFE protocol is also secure without random oracles. Finally, we implemented our AOFE protocol, and it is efficient enough for practical use.

Keywords

Optimistic fair exchange Homomorphic signatures Verifiably encrypted signatures 

Notes

Acknowledgements

This work is supported in part by JSPS KAKENHI Grant No. 15H06063.

References

  1. 1.
    Agrawal, S., Boneh, D.: Homomorphic MACs: MAC-based integrity for network coding. In: ACNS 2009, pp. 292–305 (2009)Google Scholar
  2. 2.
    Agrawal, S., Boneh, D., Boyen, X., Freeman, D.M.: Preventing pollution attacks in multi-source network coding. In: PKC 2010, pp. 161–176 (2010)Google Scholar
  3. 3.
    Asokan, N., Schunter, M., Waidner, M.: Optimistic protocols for fair exchange. In: ACM CCS 1997, pp. 7–17 (1997)Google Scholar
  4. 4.
    Asokan, N., Shoup, V., Waidner, M.: Asynchronous Protocols for Optimistic Fair Exchange. In: IEEE Symposium on S&P 1998, pp. 86–99 (1998)Google Scholar
  5. 5.
    Asokan, N., Shoup, V., Waidner, M.: Optimistic fair exchange of digital signatures (extended abstract). In: EUROCRYPT 1998, pp. 591–606 (1998)Google Scholar
  6. 6.
    Attrapadung, N., Libert, B.: Homomorphic network coding signatures in the standard model. In: PKC 2011, pp. 17–34 (2011)Google Scholar
  7. 7.
    Attrapadung, N., Libert, B., Peters, T.: Computing on authenticated data: New privacy definitions and constructions. In: ASIACRYPT 2012, pp. 367–385 (2012). http://hal.inria.fr/hal-00730665
  8. 8.
    Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: PKC 2013, pp. 386–404 (2013)Google Scholar
  9. 9.
    Bahreman, A., Tygar, J.D.: Certified electronic mail. In: NDSS 1994, pp. 3–19 (1994)Google Scholar
  10. 10.
    Bao, F., Deng, R.H., Nguyen, K.Q., Varadharajan, V.: Multi-party fair exchange with an off-line trusted neutral party. In: DEXA Workshop 1999, pp. 858–863 (1999)Google Scholar
  11. 11.
    Belenkiy, M., Chase, M., Erway, C.C., Jannotti, J., Küpçü, A., Lysyanskaya, A., Rachlin, E.: Making p2p accountable without losing privacy. In: WPES 2007, pp. 31–40 (2007)Google Scholar
  12. 12.
    Bellare, M., Namprempre, C., Neven, G.: Unrestricted aggregate signatures. In: ICALP 2007, pp. 411–422 (2007)Google Scholar
  13. 13.
    Ben-Or, M., Goldreich, O., Micali, S., Rivest, R.L.: A fair protocol for signing contracts. IEEE Trans. IT 36(1), 40–46 (1990)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: EUROCRYPT 2004, pp. 223–238 (2004)Google Scholar
  15. 15.
    Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: EUROCRYPT 2011, pp. 149–168 (2011)Google Scholar
  16. 16.
    Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: PKC 2011, pp. 1–16 (2011)Google Scholar
  17. 17.
    Boneh, D., Freeman, D.M., Katz, J., Waters, B.: Signing a linear subspace: signature schemes for network coding. In: PKC 2009, pp. 68–87 (2009)Google Scholar
  18. 18.
    Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: EUROCRYPT 2003, pp. 416–432 (2003)Google Scholar
  19. 19.
    Boneh, D., Naor, M.: Timed commitments. In: CRYPTO 2000, pp. 236–254 (2000)Google Scholar
  20. 20.
    Brands, S.A.: An efficient off-line electronic cash system based on the representation problem. Tech. Rep. CS-R9323, CWI, Amsterdam (1993). http://persistent-identifier.org/?identifier=urn:nbn:nl:ui:18-5303
  21. 21.
    Calderon, T., Meiklejohn, S., Shacham, H., Waters, B.: Rethinking verifiably encrypted signatures: a gap in functionality and potential solutions. In: CT-RSA 2014, pp. 349–366 (2014)Google Scholar
  22. 22.
    Camenisch, J., Damgård, I.: Verifiable encryption, group encryption, and their applications to separable group signatures and signature sharing schemes. In: ASIACRYPT 2000, pp. 331–345 (2000)Google Scholar
  23. 23.
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Catalano, D., Fiore, D., Warinschi, B.: Adaptive pseudo-free groups and applications. In: EUROCRYPT 2011, pp. 207–223 (2011)Google Scholar
  25. 25.
    Catalano, D., Fiore, D., Warinschi, B.: Efficient network coding signatures in the standard model. In: PKC 2012, pp. 680–696 (2012)Google Scholar
  26. 26.
    Coffey, T., Saidha, P.: Non-repudiation with mandatory proof of receipt. ACM SIGCOMM Comput. Commun. Rev. 26(1), 6–17 (1996)CrossRefGoogle Scholar
  27. 27.
    Cox, B., Tygar, J.D., Sirbu, M.: NetBill security and transaction protocol. In: USENIX Workshop Electronic Commerce 1995, pp. 77–88 (1995)Google Scholar
  28. 28.
    Deng, R.H., Gong, L., Lazar, A.A., Wang, W.: Practical protocols for certified electronic mail. J. Netw. Syst. Manag. 4(3), 279–297 (1996)CrossRefGoogle Scholar
  29. 29.
    Desmedt, Y.: Computer security by redefining what a computer is. NSPW 1993, pp. 160–166 (1993)Google Scholar
  30. 30.
    Dodis, Y., Lee, P.J., Yum, D.H.: Optimistic fair exchange in a multi-user setting. In: PKC 2007, pp. 118–133 (2007)Google Scholar
  31. 31.
    Dodis, Y., Reyzin, L.: Breaking and repairing optimistic fair exchange from PODC 2003. In: Digital Rights Management Workshop 2003, pp. 47–54 (2003)Google Scholar
  32. 32.
    ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theory 31(4), 469–472 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Fischlin, M., Lehmann, A., Schröder, D.: History-free sequential aggregate signatures. In: SCN 2012, pp. 113–130 (2012)Google Scholar
  35. 35.
    Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: PKC 2012, pp. 697–714 (2012)Google Scholar
  36. 36.
    Garay, J.A., Jakobsson, M., MacKenzie, P.D.: Abuse-Free Optimistic Contract Signing. In: CRYPTO 1999, pp. 449–466 (1999)Google Scholar
  37. 37.
    Gennaro, R., Katz, J., Krawczyk, H., Rabin, T.: Secure network coding over the integers. In: PKC 2010, pp. 142–160 (2010)Google Scholar
  38. 38.
    Gerbush, M., Lewko, A.B., O’Neill, A., Waters, B.: Dual form signatures: an approach for proving security from static assumptions. In: ASIACRYPT 2012, pp. 25–42 (2012)Google Scholar
  39. 39.
    Hohenberger, S., Sahai, A., Waters, B.: Replacing a Random Oracle: Full Domain Hash From Indistinguishability Obfuscation. In: Eurocrypt, 2014 (2014)Google Scholar
  40. 40.
    Huang, Q., Yang, G., Wong, D.S., Susilo, W.: Ambiguous Optimistic Fair Exchange. In: ASIACRYPT 2008, pp. 74–89 (2008)Google Scholar
  41. 41.
    Huang, X., Mu, Y., Susilo, W., Wu, W., Xiang, Y.: Further observations on optimistic fair exchange protocols in the multi-user setting. In: PKC 2010, pp. 124–141 (2010)Google Scholar
  42. 42.
    Johnson, R., Molnar, D., Song, D.X., Wagner, D.: Homomorphic signature schemes. In: CT-RSA, 2002, pp. 244–262 (2002)Google Scholar
  43. 43.
    Kilinç, H., Küpçü, A.: Optimally efficient multi-party fair exchange and fair secure multi-party computation. In: CT-RSA 2015, pp. 330–349 (2015)Google Scholar
  44. 44.
    Küpçü, A., Lysyanskaya, A.: Usable optimistic fair exchange. Comput. Netw. 56(1), 50–63 (2012)CrossRefGoogle Scholar
  45. 45.
    Lee, K., Lee, D.H., Yung, M.: Aggregating CL-signatures revisited: extended functionality and better efficiency. In: FC 2013, (2013)Google Scholar
  46. 46.
    Lee, K., Lee, D.H., Yung, M.: Sequential aggregate signatures with short public Keys: design, analysis and implementation studies. In: PKC 2013, pp. 423–442 (2013)Google Scholar
  47. 47.
    Lewko, A.B., Waters, B.: New techniques for dual system encryption and fully secure hibe with short ciphertexts. In: TCC 2010, pp. 455–479 (2010). http://eprint.iacr.org/2009/482
  48. 48.
    Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential aggregate signatures and multisignatures without random oracles. In: EUROCRYPT 2006, pp. 465–485 (2006)Google Scholar
  49. 49.
    Micali, S.: Simple and fast optimistic protocols for fair electronic exchange. In: PODC, pp. 12–19 (2003)Google Scholar
  50. 50.
    Nishimaki, R., Xagawa, K.: Verifiably encrypted signatures with short keys based on the decisional linear problem and obfuscation for encrypted VES. In: PKC 2013, pp. 405–422 (2013)Google Scholar
  51. 51.
    PBC: The PBC (pairing-based cryptography) library (2013). http://crypto.stanford.edu/pbc/
  52. 52.
    Rückert, M., Schröder, D.: Security of verifiably encrypted signatures and a construction without random oracles. In: Pairing 2009, pp. 17–34 (2009). http://eprint.iacr.org/2009/027
  53. 53.
    Seo, J.H., Emura, K., Xagawa, K., Yoneyama, K.: Accumulable optimistic fair exchange from verifiably encrypted homomorphic signatures. In: ACNS 2015, pp. 192–214 (2015)Google Scholar
  54. 54.
    Waters, B.: Efficient identity-based encryption without random oracles. In: EUROCRYPT 2005, pp. 114–127 (2005)Google Scholar
  55. 55.
    Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: CRYPTO 2009, pp. 619–636 (2009)Google Scholar
  56. 56.
    Zhou, J., Gollmann, D.: A Fair Non-repudiation Protocol. In: IEEE Symposium on S & P 1996, pp. 55–61 (1996)Google Scholar
  57. 57.
    Zhu, H., Bao, F.: Stand-alone and setup-free verifiably committed signatures. CT-RSA 2006, 159–173 (2006)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Jae Hong Seo
    • 1
  • Keita Emura
    • 2
  • Keita Xagawa
    • 3
  • Kazuki Yoneyama
    • 4
  1. 1.Myongji UniversityYonginRepublic of Korea
  2. 2.National Institute of Information and Communications TechnologyTokyoJapan
  3. 3.NTT Secure Platform LaboratoriesTokyoJapan
  4. 4.Ibaraki UniversityIbarakiJapan

Personalised recommendations