Skip to main content
SpringerLink
Log in

Compact E-Cash and Simulatable VRFs Revisited

  • Conference paper
Pairing-Based Cryptography – Pairing 2009 (Pairing 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5671))

Included in the following conference series:

Abstract

Efficient non-interactive zero-knowledge proofs are a powerful tool for solving many cryptographic problems. We apply the recent Groth-Sahai (GS) proof system for pairing product equations (Eurocrypt 2008) to two related cryptographic problems: compact e-cash (Eurocrypt 2005) and simulatable verifiable random functions (CRYPTO 2007). We present the first efficient compact e-cash scheme that does not rely on a random oracle. To this end we construct efficient GS proofs for signature possession, pseudo randomness and set membership. The GS proofs for pseudorandom functions give rise to a much cleaner and substantially faster construction of simulatable verifiable random functions (sVRF) under a weaker number theoretic assumption. We obtain the first efficient fully simulatable sVRF with a polynomial sized output domain (in the security parameter).

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Boneh, D., Boyen, X.: Efficient selective id secure identity based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Belenkiy, M., Camenisch, J., Chase, M., Kohlweiss, M., Lysyanskaya, A., Shacham, H.: Delegatable anonymous credentials. In: Halevi, S. (ed.) CRYPTO 2009. LNCS. Springer, Heidelberg (2009)

    Google Scholar 

  4. Belenkiy, M., Chase, M., Kohlweiss, M., Lysyanskaya, A.: P-signatures and noninteractive anonymous credentials. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 356–374. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications (extended abstract). In: STOC 1988, Chicago, Illinois, May 2-4, pp. 103–112 (1988)

    Google Scholar 

  6. Bellare, M., Goldwasser, S.: New paradigms for digital signatures and message authentication based on non-interative zero knowledge. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 194–211. Springer, Heidelberg (1990)

    Google Scholar 

  7. Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-dnf formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Boudot, F.: Efficient proofs that a committed number lies in an interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  9. Brands, S.: An efficient off-line electronic cash system based on the representation problem. Technical Report CS-R9323, CWI (April 1993)

    Google Scholar 

  10. Boyen, X., Waters, B.: Full-domain subgroup hiding and constant-size group signatures. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 1–15. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Camenisch, J., Chaabouni, R., Shelat, A.: Efficient protocols for set membership and range proofs. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 234–252. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Chaum, D., Fiat, A., Naor, M.: Untraceable electronic cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  13. Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) CRYPTO 1982, pp. 199–203. Plenum Press, New York (1999)

    Google Scholar 

  14. Camenisch, J., Hohenberger, S., Kohlweiss, M., Lysyanskaya, A., Meyerovich, M.: How to win the clonewars: efficient periodic n-times anonymous authentication. In: CCS 2006, pp. 201–210. ACM Press, New York (2006)

    Google Scholar 

  15. Camenisch, J., Hohenberger, S., Lysyanskaya, A.: Compact E-cash. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 302–321. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Camenisch, J., Koprowski, M., Warinschi, B.: Efficient blind signatures without random oracles. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 134–148. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Chase, M., Lysyanskaya, A.: Simulatable vrfs with applications to multi-theorem nizk. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 303–322. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Camenisch, J., Lysyanskaya, A., Meyerovich, M.: Endorsed e-cash. In: IEEE Symposium on Security and Privacy, pp. 101–115 (2007)

    Google Scholar 

  19. Cook, S.A.: The complexity of theorem-proving procedures. In: STOC 1971, pp. 151–158. ACM, New York (1971)

    Google Scholar 

  20. Chaum, D., Pedersen, T.P.: Transferred cash grows in size. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 390–407. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  21. Camenisch, J., Stadler, M.: Efficient group signature schemes for large groups. In: Kaliski, B. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 410–424. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  22. Camenisch, J., Stadler, M.: Proof systems for general statements about discrete logarithms. Technical Report TR 260, Institute for Theoretical Computer Science, ETH Zürich (March 1997)

    Google Scholar 

  23. Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  24. Damgård, I.: Efficient concurrent zero-knowledge in the auxiliary string model. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  25. Damgård, I.: On Σ-protocols (2002), http://www.daimi.au.dk/~ivan/Sigma.ps

  26. Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: STOC 1991, pp. 542–552 (1991)

    Google Scholar 

  27. Dodis, Y., Yampolskiy, A.: A verifiable random function with short proofs and keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  28. Fiat, A., Shamir, A.: How to prove yourself: Practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  29. Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. Cryptology ePrint Archive, Report 2006/372 (2006), http://eprint.iacr.org/

  30. Frankel, Y., Tsiounis, Y., Yung, M.: Indirect discourse proofs: Achieving efficient fair off-line E-cash. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 286–300. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  31. Franklin, M., Yung, M.: Towards provably secure efficient electronic cash. Technical Report TR CUSC-018-92, Columbia University, Dept. of Computer Science (April 1992); Also in: Lingas, A., Carlsson, S., Karlsson, R. (eds.): ICALP 1993. LNCS, vol. 700. Springer, Heidelberg (1993)

    Google Scholar 

  32. Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: FOCS 2003, pp. 102–115. IEEE Computer Society Press, Los Alamitos (2003)

    Google Scholar 

  33. Goldwasser, S., Ostrovsky, R.: Invariant signatures and non-interactive zero-knowledge proofs are equivalent. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 228–245. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  34. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups (2007), http://eprint.iacr.org/2007/155

  35. Juels, A., Luby, M., Ostrovsky, R.: Security of blind digital signatures (extended abstract). In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 150–164. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  36. Jarecki, S., Shmatikov, V.: Efficient two-party secure computation on committed inputs. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 97–114. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  37. Micali, S., Rabin, M., Vadhan, S.: Verifiable random functions. In: FOCS 1999, pp. 120–130. IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  38. Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991, vol. 576, pp. 433–444. Springer, Heidelberg (1992)

    Google Scholar 

  39. Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: FOCS 1999, pp. 543–553. IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  40. Stadler, M., Piveteau, J.-M., Camenisch, J.: Fair blind signatures. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 209–219. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  41. Sander, T., Ta-Shma, A.: Auditable, anonymous electronic cash extended abstract. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 555–572. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  42. Trolin, M.: A universally composable scheme for electronic cash. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 347–360. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  43. Teranishi, I., Sako, K.: k-times anonymous authentication with a constant proving cost. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 525–542. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  44. Tsiounis, Y.S.: Efficient Electonic Cash: New Notions and Techniques. Ph.D thesis, Northeastern University, Boston, Massachusetts (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Microsoft Research, USA

    Mira Belenkiy & Melissa Chase

  2. KU Leuven, ESAT-COSIC / IBBT, Belgium

    Markulf Kohlweiss

  3. Brown University, USA

    Anna Lysyanskaya

Authors
  1. Mira Belenkiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Melissa Chase
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Markulf Kohlweiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anna Lysyanskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of California, San Diego, 9500 Gilman Drive, MC 0404, 92093-0404, La Jolla, CA, USA

    Hovav Shacham

  2. University of Texas at Austin Department of Computer Science, 1 University Station C0500 Taylor Hall 2.124, 78712-1188, Austin, TX, USA

    Brent Waters

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Belenkiy, M., Chase, M., Kohlweiss, M., Lysyanskaya, A. (2009). Compact E-Cash and Simulatable VRFs Revisited. In: Shacham, H., Waters, B. (eds) Pairing-Based Cryptography – Pairing 2009. Pairing 2009. Lecture Notes in Computer Science, vol 5671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03298-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03298-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03297-4

  • Online ISBN: 978-3-642-03298-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation