Skip to main content
SpringerLink
Log in

Homomorphic Witness Encryption from Indistinguishable Obfuscation

  • Conference paper
  • First Online:
Provable and Practical Security (ProvSec 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14217))

Included in the following conference series:

Abstract

Witness encryption (WE) is a new encryption paradigm that allows encrypting a message using the instance of a particular NP problem, and someone who knows a solution to this problem (i.e., a witness) can effectively decrypt the ciphertext. Traditional witness encryption is built from multi-linear encodings. In this work, we put forth the concept of homomorphic witness encryption (HWE), where one can evaluate functions over ciphertexts of the same instance without decrypting them, i.e., one can manipulate a set of ciphertexts with messages \((m_1,\cdots ,m_n)\) to obtain the evaluation of \(f(m_1,\cdots ,m_n)\), for any function f. We declare that such homomorphic witness encryption schemes can be generically constructed from indistinguishable obfuscation (\(i\mathcal {O}\)) for any classes of functions. Then we propose an instantiate of multiplicative homomorphic witness encryption (MHWE) using an \(i\mathcal {O}\), homomorphic encryption for NP problems such as Subset-Sum and a batch-processed GS-proof system, which enables us to evaluate multiplication operations over ciphertext. Furthermore, we give the security and efficiency of our candidate schemes.

M. Zhang—This work is partially supported by the National Natural Science Foundation of China under grants 62072134 and U2001205, the Key projects of Guangxi Natural Science Foundation under grant 2019JJD170020.

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 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 79.99
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

References

  1. Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing, pp. 467–476 (2013)

    Google Scholar 

  2. Arita, S., Handa, S.: Two applications of multilinear maps: group key exchange and witness encryption. In: Proceedings of the 2nd ACM Workshop on ASIA Public-Key Cryptography, pp. 13–22 (2014)

    Google Scholar 

  3. Liu, J., Garcia, F., Ryan, M.: Time-release protocol from bitcoin and witness encryption for sat. Korean Circ. J. 40(10), 530–535 (2015)

    Google Scholar 

  4. Liu, J., Jager, T., Kakvi, S.A., Warinschi, B.: How to build time-lock encryption. Des. Codes Cryptogr. 86(11), 2549–2586 (2018). https://doi.org/10.1007/s10623-018-0461-x

    Article  MathSciNet  MATH  Google Scholar 

  5. Uberti, G., Luo, K., Cheng, O., Goh, W.: Building usable witness encryption. arXiv preprint arXiv:2112.04581 (2021)

  6. Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_1

    Chapter  Google Scholar 

  7. Barak, B., et al.: On the (Im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_1

    Chapter  Google Scholar 

  8. Bartusek, J., Ishai, Y., Jain, A., Ma, F., Sahai, A., Zhandry, M.: Affine determinant programs: a framework for obfuscation and witness encryption. In: 11th Innovations in Theoretical Computer Science Conference (2020)

    Google Scholar 

  9. Derler, D., Slamanig, D.: Practical witness encryption for algebraic languages or how to encrypt under groth-sahai proofs. Des. Codes Cryptogr. 86(11), 2525–2547 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Campanelli, M., David, B., Khoshakhlagh, H., Konring, A., Nielsen, J.B.: Encryption to the future: a paradigm for sending secret messages to future (anonymous) committees. In: Advances in Cryptology-ASIACRYPT 2022: 28th International Conference on the Theory and Application of Cryptology and Information Security, Taipei, Taiwan, 5–9 December 2022, Proceedings, Part III, pp. 151–180. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-22969-5_6

  11. Döttling, N., Hanzlik, L., Magri, B., Wohnig, S.: Mcfly: verifiable encryption to the future made practical. Cryptology ePrint Archive (2022)

    Google Scholar 

  12. Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13

    Chapter  Google Scholar 

  13. Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27

    Chapter  Google Scholar 

  14. Garg, S., Gentry, C., Halevi, S., Zhandry, M.: Fully secure attribute based encryption from multilinear maps. Cryptology ePrint Archive (2014)

    Google Scholar 

  15. Benhamouda, F., Lin, H.: Mr NISC: multiparty reusable non-interactive secure computation. In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12551, pp. 349–378. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64378-2_13

    Chapter  Google Scholar 

  16. Campanelli, M., Fiore, D., Khoshakhlagh, H.: Witness encryption for succinct functional commitments and applications. Cryptology ePrint Archive (2022)

    Google Scholar 

  17. Badrinarayanan, S., Miles, E., Sahai, A., Zhandry, M.: Post-zeroizing obfuscation: new mathematical tools, and the case of evasive circuits. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 764–791. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_27

    Chapter  Google Scholar 

  18. Badrinarayanan, S., Garg, S., Ishai, Y., Sahai, A., Wadia, A.: Two-message witness indistinguishability and secure computation in the plain model from new assumptions. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10626, pp. 275–303. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_10

    Chapter  MATH  Google Scholar 

  19. Faonio, A., Nielsen, J.B., Venturi, D.: Predictable arguments of knowledge. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10174, pp. 121–150. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54365-8_6

    Chapter  Google Scholar 

  20. Bellare, M., Hoang, V.T.: Adaptive witness encryption and asymmetric password-based cryptography. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 308–331. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_14

    Chapter  Google Scholar 

  21. Chen, Y., Vaikuntanathan, V., Wee, H.: GGH15 beyond permutation branching programs: proofs, attacks, and candidates. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 577–607. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_20

    Chapter  Google Scholar 

  22. Pal, T., Dutta, R.: Semi-adaptively secure offline witness encryption from puncturable witness PRF. In: Nguyen, K., Wu, W., Lam, K.Y., Wang, H. (eds.) ProvSec 2020. LNCS, vol. 12505, pp. 169–189. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-62576-4_9

    Chapter  Google Scholar 

  23. Goyal, R., Vusirikala, S., Waters, B.: Collusion resistant broadcast and trace from positional witness encryption. In: Lin, D., Sako, K. (eds.) PKC 2019. LNCS, vol. 11443, pp. 3–33. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_1

    Chapter  Google Scholar 

  24. Chvojka, P., Jager, T., Kakvi, S.A.: Offline witness encryption with semi-adaptive security. In: Conti, M., Zhou, J., Casalicchio, E., Spognardi, A. (eds.) ACNS 2020. LNCS, vol. 12146, pp. 231–250. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57808-4_12

    Chapter  MATH  Google Scholar 

  25. Albrecht, M.R., Farshim, P., Han, S., Hofheinz, D., Larraia, E., Paterson, K.G.: Multilinear maps from obfuscation. J. Cryptol. 33(3), 1080–1113 (2020)

    Google Scholar 

  26. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 40–49 (2013)

    Google Scholar 

  27. Abusalah, H., Fuchsbauer, G., Pietrzak, K.: Offline witness encryption. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 285–303. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_16

    Chapter  Google Scholar 

  28. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24

    Chapter  Google Scholar 

  29. Blazy, O., Fuchsbauer, G., Izabachène, M., Jambert, A., Sibert, H., Vergnaud, D.: Batch Groth–Sahai. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 218–235. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13708-2_14

    Chapter  Google Scholar 

  30. Ferrara, A.L., Green, M., Hohenberger, S., Pedersen, M.Ø.: Practical short signature batch verification. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 309–324. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00862-7_21

    Chapter  Google Scholar 

  31. Zhandry, M.: How to avoid obfuscation using witness PRFs. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 421–448. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49099-0_16

    Chapter  Google Scholar 

  32. Pal, T., Dutta, R.: Offline witness encryption from witness PRF and randomized encoding in CRS model. In: Jang-Jaccard, J., Guo, F. (eds.) ACISP 2019. LNCS, vol. 11547, pp. 78–96. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-21548-4_5

    Chapter  MATH  Google Scholar 

  33. Feige, U., Lapidot, D., Shamir, A.: Multiple noninteractive zero knowledge proofs under general assumptions. SIAM J. Comput. 29(1), 1–28 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  34. Camenisch, J., Hohenberger, S., Pedersen, M.Ø.: Batch verification of short signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 246–263. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_14

    Chapter  Google Scholar 

  35. Jutla, C.S., Roy, A.: Switching lemma for bilinear tests and constant-size NIZK proofs for linear subspaces. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8617, pp. 295–312. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44381-1_17

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin, 541004, China

    Yuzhu Wang, Xingbo Wang & Mingwu Zhang

  2. School of Computer Science, Hubei University of Technology, Wuhan, 430068, China

    Mingwu Zhang

Authors
  1. Yuzhu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingbo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingwu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mingwu Zhang .

Editor information

Editors and Affiliations

  1. Hubei University of Technology, Wuhan, China

    Mingwu Zhang

  2. Hong Kong Polytechnic University, Kowloon, Hong Kong

    Man Ho Au

  3. University of Wollongong, Wollongong, NSW, Australia

    Yudi Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Wang, Y., Wang, X., Zhang, M. (2023). Homomorphic Witness Encryption from Indistinguishable Obfuscation. In: Zhang, M., Au, M.H., Zhang, Y. (eds) Provable and Practical Security. ProvSec 2023. Lecture Notes in Computer Science, vol 14217. Springer, Cham. https://doi.org/10.1007/978-3-031-45513-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-45513-1_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-45512-4

  • Online ISBN: 978-3-031-45513-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation