Skip to main content

Improving the Efficiency of Re-randomizable and Replayable CCA Secure Public Key Encryption

  • Conference paper
  • First Online:
Applied Cryptography and Network Security (ACNS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12146))

Included in the following conference series:

  • 1011 Accesses

Abstract

Public key encryption schemes that are simultaneously re-randomizable and replayable CCA (Rand-RCCA) secure offer a unique combination of malleability and non-malleability properties: ciphertexts can be re-randomized (and thus made unlinkable) while still retaining the important security guarantee that the message inside stays intact.

In this paper we show a new public-key encryption scheme that is Rand-RCCA secure in the random oracle model. Our scheme is more efficient than the state-of-art Rand-RCCA PKE scheme of Faonio et al. (ASIACRYPT’19) but it achieves a weaker re-randomization property. On the other hand, our scheme achieves a strictly stronger re-randomization property than the PKE scheme of Phan and Pointcheval (ASIACRYPT’04).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    The table does not include the schemes in [9, 22] and a second scheme from [16], which achieve the nice property that validity of ciphertexts can be checked publicly, but perform way worse than ours, e.g., a ciphertext contains about 33–60 group elements and decryption requires over 40 pairings computations.

  2. 2.

    The value are taken from the benchmarks of Miracl [1] on a single core of a 2.4 GHz Intel i5 520 processor.

  3. 3.

    Notice that perfect re-randomizability captures chosen-ciphertext attacks thanks to the knowledge of the secret material.

References

  1. Miracl cryptographic library user guide. https://github.com/miracl/MIRACL/blob/master/docs/miracl-explained/benchmarks.md

  2. Abe, M.: Universally verifiable mix-net with verification work independent of the number of mix-servers. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 437–447. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054144

    Chapter  Google Scholar 

  3. Barbulescu, R., Duquesne, S.: Updating key size estimations for pairings. J. Cryptol. 32(4), 1298–1336 (2018). https://doi.org/10.1007/s00145-018-9280-5

    Article  MathSciNet  MATH  Google Scholar 

  4. Barreto, P.S.L.M., Naehrig, M.: Pairing-friendly elliptic curves of prime order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319–331. Springer, Heidelberg (2006). https://doi.org/10.1007/11693383_22

    Chapter  Google Scholar 

  5. Bellare, M., Rogaway, P.: Optimal asymmetric encryption. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0053428

    Chapter  Google Scholar 

  6. Blazy, O., Fuchsbauer, G., Pointcheval, D., Vergnaud, D.: Signatures on randomizable ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 403–422. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_25

    Chapter  Google Scholar 

  7. Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS (2001)

    Google Scholar 

  8. Canetti, R., Krawczyk, H., Nielsen, J.B.: Relaxing chosen-ciphertext security. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 565–582. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_33

    Chapter  Google Scholar 

  9. Chase, M., Kohlweiss, M., Lysyanskaya, A., Meiklejohn, S.: Malleable proof systems and applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 281–300. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_18

    Chapter  Google Scholar 

  10. Chaum, D.L.: Untraceable electronic mail, return addresses, and digital pseudonyms. Commun. ACM 24(2), 84–90 (1981)

    Article  Google Scholar 

  11. 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). https://doi.org/10.1007/BFb0055717

    Chapter  Google Scholar 

  12. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4

    Chapter  Google Scholar 

  13. Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: 23rd ACM STOC (1991)

    Google Scholar 

  14. Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_8

    Chapter  Google Scholar 

  15. Faonio, A., Fiore, D.: Optimistic mixing, revisited. Cryptology ePrint Archive, Report 2018/864 (2018). https://eprint.iacr.org/2018/864

  16. Faonio, A., Fiore, D., Herranz, J., Ràfols, C.: Structure-preserving and re-randomizable RCCA-secure public key encryption and its applications. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 159–190. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_6

    Chapter  Google Scholar 

  17. Fujisaki, E., Okamoto, T., Pointcheval, D., Stern, J.: RSA-OAEP is secure under the RSA assumption. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 260–274. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_16

    Chapter  Google Scholar 

  18. Golle, P., Jakobsson, M., Juels, A., Syverson, P.: Universal re-encryption for mixnets. In: Okamoto, T. (ed.) CT-RSA 2004. LNCS, vol. 2964, pp. 163–178. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24660-2_14

    Chapter  Google Scholar 

  19. Groth, J.: Rerandomizable and replayable adaptive chosen ciphertext attack secure cryptosystems. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 152–170. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_9

    Chapter  Google Scholar 

  20. Kim, T., Barbulescu, R.: Extended tower number field sieve: a new complexity for the medium prime case. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 543–571. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_20

    Chapter  Google Scholar 

  21. Kurosawa, K., Desmedt, Y.: A new paradigm of hybrid encryption scheme. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 426–442. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_26

    Chapter  Google Scholar 

  22. Libert, B., Peters, T., Qian, C.: Structure-preserving chosen-ciphertext security with shorter verifiable ciphertexts. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10174, pp. 247–276. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54365-8_11

    Chapter  Google Scholar 

  23. Micali, S., Rackoff, C., Sloan, B.: The notion of security for probabilistic cryptosystems (extended abstract). In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 381–392. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_27

    Chapter  Google Scholar 

  24. Pereira, O., Rivest, R.L.: Marked mix-nets. In: Brenner, M., et al. (eds.) FC 2017. LNCS, vol. 10323, pp. 353–369. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70278-0_22

    Chapter  Google Scholar 

  25. Phan, D.H., Pointcheval, D.: OAEP 3-round: a generic and secure asymmetric encryption padding. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 63–77. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30539-2_5

    Chapter  Google Scholar 

  26. Prabhakaran, M., Rosulek, M.: Rerandomizable RCCA encryption. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 517–534. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_29

    Chapter  Google Scholar 

  27. Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004)

    Google Scholar 

Download references

Acknowledgements

Research leading to these results has been supported by the Spanish Government under projects SCUM (ref. RTI2018-102043-B-I00), CRYPTOEPIC (ref. EUR2019-103816), and SECURITAS (ref. RED2018-102321-T), by the Madrid Regional Government under project BLOQUES (ref. S2018/TCS-4339).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Antonio Faonio .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Faonio, A., Fiore, D. (2020). Improving the Efficiency of Re-randomizable and Replayable CCA Secure Public Key Encryption. In: Conti, M., Zhou, J., Casalicchio, E., Spognardi, A. (eds) Applied Cryptography and Network Security. ACNS 2020. Lecture Notes in Computer Science(), vol 12146. Springer, Cham. https://doi.org/10.1007/978-3-030-57808-4_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-57808-4_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-57807-7

  • Online ISBN: 978-3-030-57808-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics