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Rerandomizable Signatures Under Standard Assumption

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Progress in Cryptology – INDOCRYPT 2019 (INDOCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11898))

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Abstract

The Camenisch-Lysyanskaya rerandomizable signature (CL-RRS) scheme is an important tool in the construction of privacy preserving protocols. One of the limitations of CL-RRS is that the signature size is linear in the number of messages to be signed. In 2016, Pointcheval-Sanders introduced a variant of rerandomizable signature (PS-RRS) scheme which removes the above limitation. However, the security of PS-RRS scheme was proved under an interactive assumption. In 2018, Pointcheval-Sanders improved this to give a reduction under a parameterized assumption.

In 2012, Gerbush et al. introduced the dual-form signature technique to remove the dependency on interactive/parameterized assumption. They applied this technique on the CL-RRS scheme (for single message) and proved its unforgeability under static assumptions instead of the interactive assumption used in the original work but in the symmetric composite-order pairing setting.

In this work, we realize a fully rerandomizable signature scheme in the prime order setting without random oracle based on the SXDH assumption. The signature structure is derived from Ghadafi’s structure-preserving signature. We first apply the dual-form signature technique to obtain a composite-order variant, called RRSc. A signature in RRSc consists of only two group elements and is thus independent of the message block length. The security of the proposed scheme is based on subgroup hiding assumptions. Then we use the dual pairing vector space framework to obtain a prime-order variant called RRS and prove its security under the SXDH assumption.

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References

  1. Au, M.H., Susilo, W., Mu, Y.: Constant-size dynamic k-TAA. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 111–125. Springer, Heidelberg (2006). https://doi.org/10.1007/11832072_8

    Chapter  Google Scholar 

  2. 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). https://doi.org/10.1007/978-3-540-24676-3_14

    Chapter  Google Scholar 

  3. Bichsel, P., Camenisch, J., Neven, G., Smart, N.P., Warinschi, B.: Get shorty via group signatures without encryption. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 381–398. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15317-4_24

    Chapter  Google Scholar 

  4. Bernhard, D., Fuchsbauer, G., Ghadafi, E., Smart, N.P., Warinschi, B.: Anonymous attestation with user-controlled linkability. Int. J. Inf. Secur. 12(3), 219–249 (2013)

    Article  Google Scholar 

  5. Boldyreva, A., Gentry, C., O’Neill, A., Yum, D.H.: Ordered multisignatures and identity-based sequential aggregate signatures, with applications to secure routing. In: Ning, P., De Capitani di Vimercati, S., Syverson, P.F. (eds.) ACM CCS, pp. 276–285 (2007)

    Google Scholar 

  6. Chen, J., Gong, J., Kowalczyk, L., Wee, H.: Unbounded ABE via bilinear entropy expansion, revisited. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 503–534. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78381-9_19

    Chapter  Google Scholar 

  7. Cheon, J.H.: Security analysis of the strong Diffie-Hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_1

    Chapter  Google Scholar 

  8. Chatterjee, S., Kabaleeshwaran, R.: Towards static assumption based cryptosystem in pairing setting: further applications of DéjàQ and Dual-Form signature (Extended Abstract). In: Baek, J., Susilo, W., Kim, J. (eds.) ProvSec 2018. LNCS, vol. 11192, pp. 220–238. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01446-9_13

    Chapter  Google Scholar 

  9. Chatterjee, S., Kabaleeshwaran, R.: Rerandomizable Signatures under Standard Assumption. IACR Cryptology ePrint Archive, 2019:1144 (2019)

    Google Scholar 

  10. Camenisch, J., 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). https://doi.org/10.1007/978-3-540-28628-8_4

    Chapter  Google Scholar 

  11. Chen, J., Lim, H.W., Ling, S., Wang, H., Wee, H.: Shorter IBE and signatures via asymmetric pairings. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 122–140. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36334-4_8

    Chapter  Google Scholar 

  12. Chase, M., Meiklejohn, S.: Déjà Q: using dual systems to revisit q-type assumptions. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 622–639. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_34

    Chapter  Google Scholar 

  13. Chase, M., Maller, M., Meiklejohn, S.: Déjà Q all over again: tighter and broader reductions of q-type assumptions. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 655–681. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_22

    Chapter  Google Scholar 

  14. Canard, S., Pointcheval, D., Sanders, O., Traoré, J.: Divisible e-cash made practical. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 77–100. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_4

    Chapter  Google Scholar 

  15. Chen, J., Wee, H.: Semi-adaptive attribute-based encryption and improved delegation for boolean formula. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 277–297. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10879-7_16

    Chapter  MATH  Google Scholar 

  16. Freeman, D.M.: Converting pairing-based cryptosystems from composite-order groups to prime-order groups. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 44–61. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_3

    Chapter  Google Scholar 

  17. Ghadafi, E.: More efficient structure-preserving signatures - or: bypassing the type-III lower bounds. In: Foley, S.N., Gollmann, D., Snekkenes, E. (eds.) ESORICS 2017. LNCS, vol. 10493, pp. 43–61. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66399-9_3

    Chapter  Google Scholar 

  18. Gerbush, M., Lewko, A., O’Neill, A., Waters, B.: Dual form signatures: an approach for proving security from static assumptions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 25–42. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_4

    Chapter  Google Scholar 

  19. Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113–3121 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Guillevic, A.: Arithmetic of Pairings on Algebraic Curves for Cryptography. École Normale Supérieure, Paris (2013). PhD thesis

    Google Scholar 

  21. Lewko, A.: Tools for simulating features of composite order bilinear groups in the prime order setting. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 318–335. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_20

    Chapter  MATH  Google Scholar 

  22. Libert, B., Joye, M., Yung, M., Peters, T.: Concise multi-challenge CCA-secure encryption and signatures with almost tight security. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 1–21. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8_1

    Chapter  Google Scholar 

  23. Lee, K., Lee, D.H., Yung, M.: Aggregating CL-signatures revisited: extended functionality and better efficiency. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 171–188. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39884-1_14

    Chapter  Google Scholar 

  24. Libert, B., Mouhartem, F., Peters, T., Yung, M.: Practical “Signatures with efficient protocols” from simple assumptions. In: Chen, X., Wang, X., Huang, X. (eds.) AsiaCCS, pp. 511–522. ACM (2016)

    Google Scholar 

  25. Libert, B., Peters, T., Yung, M.: Short group signatures via structure-preserving signatures: standard model security from simple assumptions. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 296–316. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_15

    Chapter  Google Scholar 

  26. Lewko, A., Waters, B.: New techniques for dual system encryption and fully secure hibe with short ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_27

    Chapter  Google Scholar 

  27. Okamoto, T., Takashima, K.: Homomorphic encryption and signatures from vector decomposition. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 57–74. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85538-5_4

    Chapter  Google Scholar 

  28. Okamoto, T., Takashima, K.: Fully secure functional encryption with general relations from the decisional linear assumption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 191–208. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_11

    Chapter  Google Scholar 

  29. Pointcheval, D., Sanders, O.: Short randomizable signatures. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 111–126. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29485-8_7

    Chapter  Google Scholar 

  30. Pointcheval, D., Sanders, O.: Reassessing security of randomizable signatures. In: Smart, N.P. (ed.) CT-RSA 2018. LNCS, vol. 10808, pp. 319–338. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76953-0_17

    Chapter  Google Scholar 

  31. Waters, B.: Dual system encryption: Realizing fully secure IBE and HIBE under simple assumptions. IACR Cryptology ePrint Archive, 2009:385 (2009)

    Google Scholar 

  32. Yuen, T.H., Chow, S.S.M., Zhang, C., Yiu, S.-M.: Exponent-inversion Signatures and IBE under Static Assumptions. IACR Cryptology ePrint Archive, 2014:311 (2014)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India

    Sanjit Chatterjee & R. Kabaleeshwaran

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  1. Sanjit Chatterjee
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  2. R. Kabaleeshwaran
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Correspondence to R. Kabaleeshwaran .

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Editors and Affiliations

  1. University of Warwick, Warwick, UK

    Feng Hao

  2. CSIRO Data61, Marsfield, NSW, Australia

    Sushmita Ruj

  3. Nanyang Technological University, Singapore, Singapore

    Sourav Sen Gupta

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Chatterjee, S., Kabaleeshwaran, R. (2019). Rerandomizable Signatures Under Standard Assumption. In: Hao, F., Ruj, S., Sen Gupta, S. (eds) Progress in Cryptology – INDOCRYPT 2019. INDOCRYPT 2019. Lecture Notes in Computer Science(), vol 11898. Springer, Cham. https://doi.org/10.1007/978-3-030-35423-7_3

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  • DOI: https://doi.org/10.1007/978-3-030-35423-7_3

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