Efficient Unlinkable Sanitizable Signatures from Signatures with Re-randomizable Keys

  • Nils Fleischhacker
  • Johannes Krupp
  • Giulio Malavolta
  • Jonas Schneider
  • Dominique Schröder
  • Mark Simkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9614)

Abstract

In a sanitizable signature scheme the signer allows a designated third party, called the sanitizer, to modify certain parts of the message and adapt the signature accordingly. Ateniese et al. (ESORICS 2005) introduced this primitive and proposed five security properties which were formalized by Brzuska et al. (PKC 2009). Subsequently, Brzuska et al. (PKC 2010) suggested an additional security notion, called unlinkability which says that one cannot link sanitized message-signature pairs of the same document. Moreover, the authors gave a generic construction based on group signatures that have a certain structure. However, the special structure required from the group signature scheme only allows for inefficient instantiations.

Here, we present the first efficient instantiation of unlinkable sanitizable signatures. Our construction is based on a novel type of signature schemes with re-randomizable keys. Intuitively, this property allows to re-randomize both the signing and the verification key separately but consistently. This allows us to sign the message with a re-randomized key and to prove in zero-knowledge that the derived key originates from either the signer or the sanitizer. We instantiate this generic idea with Schnorr signatures and efficient \(\varSigma \)-protocols, which we convert into non-interactive zero-knowledge proofs via the Fiat-Shamir transformation. Our construction is at least one order of magnitude faster than instantiating the generic scheme of Brzuska et al. with the most efficient group signature schemes.

References

  1. 1.
    Ateniese, G., Chou, D.H., de Medeiros, B., Tsudik, G.: Sanitizable signatures. In: di Vimercati, S.C., Syverson, P.F., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 159–177. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Attrapadung, N., Libert, B., Peters, T.: Efficient completely context-hiding quotable and linearly homomorphic signatures. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 386–404. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Fuchsbauer, G.: Policy-based signatures. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 520–537. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  4. 4.
    Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Boldyreva, A., Palacio, A., Warinschi, B.: Secure proxy signature schemes for delegation of signing rights. Cryptology ePrint Archive, Report 2003/096 (2003). http://eprint.iacr.org/2003/096
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Boneh, D., Boyen, X.: Short signatures without random oracles and the SDH assumption in bilinear groups. J. Crypt. 21(2), 149–177 (2008)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  10. 10.
    Brzuska, C., Busch, H., Dagdelen, O., Fischlin, M., Franz, M., Katzenbeisser, S., Manulis, M., Onete, C., Peter, A., Poettering, B., Schröder, D.: Redactable signatures for tree-structured data: definitions and constructions. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 87–104. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Brzuska, C., Fischlin, M., Freudenreich, T., Lehmann, A., Page, M., Schelbert, J., Schröder, D., Volk, F.: Security of sanitizable signatures revisited. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 317–336. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Brzuska, C., Fischlin, M., Lehmann, A., Schröder, D.: Unlinkability of sanitizable signatures. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 444–461. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Brzuska, C., Pöhls, H.C., Samelin, K.: Non-interactive public accountability for sanitizable signatures. In: De Capitani di Vimercati, S., Mitchell, C. (eds.) EuroPKI 2012. LNCS, vol. 7868, pp. 178–193. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Brzuska, C., Pöhls, H.C., Samelin, K.: Efficient and perfectly unlinkable sanitizable signatures without group signatures. In: Katsikas, S., Agudo, I. (eds.) EuroMPI 2013. LNCS, vol. 8341, pp. 12–30. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  15. 15.
    Camenisch, J.L., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  16. 16.
    Canard, S., Jambert, A.: On extended sanitizable signature schemes. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 179–194. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Canard, S., Jambert, A., Lescuyer, R.: Sanitizable signatures with several signers and sanitizers. In: Mitrokotsa, A., Vaudenay, S. (eds.) AFRICACRYPT 2012. LNCS, vol. 7374, pp. 35–52. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  18. 18.
    Catalano, D.: Homomorphic signatures and message authentication codes. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 514–519. Springer, Heidelberg (2014)Google Scholar
  19. 19.
    Chang, E.-C., Lim, C.L., Xu, J.: Short redactable signatures using random trees. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 133–147. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Chaum, D., Pedersen, T.P.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  21. 21.
    Cramer, R., Damgård, I.B., Schoenmakers, B.: Proof of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)Google Scholar
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Derler, D., Slamanig, D.: Rethinking privacy for extended sanitizable signatures and a black-box construction of strongly private schemes. In: Au, M.-H., Miyaji, A. (eds.) ProvSec 2015. LNCS, vol. 9451, pp. 455–474. Springer, Heidelberg (2015). doi:10.1007/978-3-319-26059-4_25 CrossRefGoogle Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    Fischlin, M., Fleischhacker, N.: Limitations of the meta-reduction technique: the case of Schnorr signatures. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 444–460. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  26. 26.
    Fleischhacker, N., Krupp, J., Malavolta, G., Schneider, J., Schröder, D., Simkin, M.: Efficient unlinkable sanitizable signatures from signatureswith rerandomizable keys. Cryptology ePrint Archive, Report 2015/395 (2015). http://eprint.iacr.org/2015/395
  27. 27.
    Franco, P.: Understanding Bitcoin: Cryptography: Engineering and Economics. Wiley, Chichester (2015)Google Scholar
  28. 28.
    Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    Furukawa, J., Yonezawa, S.: Group signatures with separate and distributed authorities. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 77–90. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  30. 30.
    Groth, J.: Fully anonymous group signatures without random oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  31. 31.
    Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 21–38. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  32. 32.
    Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. J. Crypt. 25(3), 484–527 (2012)CrossRefMathSciNetMATHGoogle Scholar
  33. 33.
    Johnson, R., Walsh, L., Lamb, M.: Homomorphic signatures for digital photographs. In: Danezis, G. (ed.) FC 2011. LNCS, vol. 7035, pp. 141–157. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  34. 34.
    Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  35. 35.
    Klonowski, M., Lauks, A.: Extended sanitizable signatures. In: Rhee, M.S., Lee, B. (eds.) ICISC 2006. LNCS, vol. 4296, pp. 343–355. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  36. 36.
    Mitsunari, S., Saka, R., Kasahara, M.: A new traitor tracing. IEICE Trans. E85–A(2), 481–484 (2002)Google Scholar
  37. 37.
    Pöhls, H.C., Samelin, K.: On updatable redactable signatures. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 457–475. Springer, Heidelberg (2014)Google Scholar
  38. 38.
    Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  39. 39.
    Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Crypt. 13(3), 361–396 (2000)CrossRefMATHGoogle Scholar
  40. 40.
    Schnorr, C.-P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)Google Scholar
  41. 41.
    Schnorr, C.-P.: Efficient signature generation by smart cards. J. Crypt. 4(3), 161–174 (1991)CrossRefMathSciNetMATHGoogle Scholar
  42. 42.
    Steinfeld, R., Bull, L., Zheng, Y.: Content extraction signatures. In: Kim, K. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 285–304. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Nils Fleischhacker
    • 1
  • Johannes Krupp
    • 1
  • Giulio Malavolta
    • 1
  • Jonas Schneider
    • 1
  • Dominique Schröder
    • 1
  • Mark Simkin
    • 1
  1. 1.CISPASaarland UniversitySaarbrückenGermany

Personalised recommendations