Advertisement

All-But-Many Encryption

A New Framework for Fully-Equipped UC Commitments
  • Eiichiro Fujisaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8874)

Abstract

We present a general framework for constructing non- interactive universally composable (UC) commitment schemes that are secure against adaptive adversaries in the non-erasure model under a re-usable common reference string. Previously, such “fully-equipped” UC commitment schemes have been known only in [5,6], with strict expansion factor O(κ); meaning that to commit λ bits, communication strictly requires O(λκ) bits, where κ denotes the security parameter. Efficient construction of a fully-equipped UC commitment scheme is a long-standing open problem. We introduce new abstraction, called all-but-many encryption (ABME), and prove that it captures a fully-equipped UC commitment scheme. We propose the first fully-equipped UC commitment scheme with optimal expansion factor Ω(1) from our ABME scheme related to the DCR assumption. We also provide an all-but-many lossy trapdoor function (ABM-LTF) [18] from our DCR-based ABME scheme, with a better lossy rate than [18].

Keywords

Commitment Scheme Oblivious Transfer Honest Party Random Coin Cryptology ePrint Archive 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Bellare, M., Hofheinz, D., Yilek, S.: Possibility and impossibility results for encryption and commitment secure under selective opening. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 1–35. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Micali, S., Ostrovsky, R.: Perfect zero-knowledge in constant rounds. In: STOC 1990, pp. 482–493. ACM (1990)Google Scholar
  3. 3.
    Camenisch, J., Shoup, V.: Practical verifiable encryption and decryption of discrete logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2001), pp. 136–145. IEEE Computer Society (2001), The full version available at at Cryptology ePrint Archive, http://eprint.iacr.org/2000/067
  5. 5.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC 2002, pp. 494–503. ACM, New York (2002), The full version is available at http://eprint.iacr.org/2002/140
  7. 7.
    Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt (ed.) [11], pp. 174–187.Google Scholar
  8. 8.
    Damgård, I., Groth, J.: Non-interactive and reusable non-malleable commitment schemes. In: STOC 2003, pp. 426–437. ACM (2003)Google Scholar
  9. 9.
    Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 125–140. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Damgård, I., Nielsen, J.B.: Perfect hiding and perfect binding universally composable commitment schemes with constant expansion factor. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 581–596. Springer, Heidelberg (2002), The full version is available at http://www.brics.dk/RS/01/41/ CrossRefGoogle Scholar
  11. 11.
    Desmedt, Y.G. (ed.): CRYPTO 1994. LNCS, vol. 839. Springer, Heidelberg (1994)zbMATHGoogle Scholar
  12. 12.
    Fehr, S., Hofheinz, D., Kiltz, E., Wee, H.: Encryption schemes secure against chosen-ciphertext selective opening attacks. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 381–402. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Fischlin, M., Libert, B., Manulis, M.: Non-interactive and re-usable universally composable string commitments with adaptive security. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 468–485. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Fujisaki, E.: All-but-many encryption: A framework for efficient fully-equipped UC commitments. IACR Cryptology ePrint Archive, 2012:379 (2012)Google Scholar
  15. 15.
    Fujisaki, E.: New constructions of efficient simulation-sound commitments using encryption and their applications. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 136–155. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Garay, J.A., Mackenzie, P.P., Yang, K.: Strengthening zero-knowledge protocols using signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 177–194. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Gennaro, R.: Multi-trapdoor commitments and their applications to proofs of knowledge secure under concurrent man-in-the-middle attacks. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 220–236. Springer, Heidelberg (2004), The full version available at at Cryptology ePrint Archive, http://eprint.iacr.org/2003/214 CrossRefGoogle Scholar
  18. 18.
    Hofheinz, D.: All-but-many lossy trapdoor functions. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 209–227. Springer, Heidelberg (2012), http://eprint.iacr.org/2011/230 (last revised March 18, 2013)CrossRefGoogle Scholar
  19. 19.
    Itoh, T., Ohta, Y., Shizuya, H.: Language dependent secure bit commitment. In: Desmedt (ed.) [11], pp. 188–201Google Scholar
  20. 20.
    Lindell, Y.: Highly-efficient universally-composable commitments based on the DDH assumption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 446–466. Springer, Heidelberg (2011), The full version available at Cryptology ePrint Archive, http://eprint.iacr.org/2011/180 CrossRefGoogle Scholar
  21. 21.
    MacKenzie, P., Yang, K.: On simulation-sound trapdoor commitments. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 382–400. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Nishimaki, R., Fujisaki, E., Tanaka, K.: An efficient non-interactive universally composable string-commitment scheme. IEICE Transactions 95-A(1), 167–175 (2012)CrossRefGoogle Scholar
  23. 23.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  24. 24.
    Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  25. 25.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Ladner, R.E., Dwork, C. (eds.) STOC 2008, pp. 187–196. ACM (2008)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Eiichiro Fujisaki
    • 1
  1. 1.NTT Secure Platform LaboratoriesTokyoJapan

Personalised recommendations