Skip to main content
SpringerLink
Log in

Delay Encryption

  • Conference paper
  • First Online:
Advances in Cryptology – EUROCRYPT 2021 (EUROCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12696))

Abstract

We introduce a new primitive named Delay Encryption, and give an efficient instantiation based on isogenies of supersingular curves and pairings. Delay Encryption is related to Time-lock Puzzles and Verifiable Delay Functions, and can be roughly described as “time-lock identity based encryption”. It has several applications in distributed protocols, such as sealed bid Vickrey auctions and electronic voting.

We give an instantiation of Delay Encryption by modifying Boneh and Frankiln’s IBE scheme, where we replace the master secret key by a long chain of isogenies, as in the isogeny VDF of De Feo, Masson, Petit and Sanso. Similarly to the isogeny-based VDF, our Delay Encryption requires a trusted setup before parameters can be safely used; our trusted setup is identical to that of the VDF, thus the same parameters can be generated once and shared for many executions of both protocols, with possibly different delay parameters.

We also discuss several topics around delay protocols based on isogenies that were left untreated by De Feo et al., namely: distributed trusted setup, watermarking, and implementation issues.

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 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
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

Notes

  1. 1.

    Bitansky et al. require pre-processing to run in sequential time \(T\cdot {{\,\mathrm{poly}\,}}(\lambda )\), but parallel time only \({{\,\mathrm{poly}\,}}(\lambda ,\log T)\).

References

  1. Bernstein, D.J., Sorenson, J.: Modular exponentiation via the explicit Chinese remainder theorem. Math. Comput. 76, 443–454 (2007). https://doi.org/10.1090/S0025-5718-06-01849-7

    Article  MathSciNet  MATH  Google Scholar 

  2. Beullens, W., Kleinjung, T., Vercauteren, F.: CSI-FiSh: efficient isogeny based signatures through class group computations. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 227–247. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_9

    Chapter  Google Scholar 

  3. Bitansky, N., Goldwasser, S., Jain, A., Paneth, O., Vaikuntanathan, V., Waters, B.: Time-lock puzzles from randomized encodings. In: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, ITCS 2016, New York, NY, USA, pp. 345–356. Association for Computing Machinery (2016). https://doi.org/10.1145/2840728.2840745

  4. Boneh, D., Bonneau, J., Bünz, B., Fisch, B.: Verifiable delay functions. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 757–788. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_25

    Chapter  Google Scholar 

  5. Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 425–439. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052253

    Chapter  Google Scholar 

  6. Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003). https://doi.org/10.1137/S0097539701398521

    Article  MathSciNet  MATH  Google Scholar 

  7. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. J. Cryptol. 17(4), 297–319 (2004). https://doi.org/10.1007/s00145-004-0314-9

    Article  MathSciNet  MATH  Google Scholar 

  8. Bowe, S., Chiesa, A., Green, M., Miers, I., Mishra, P., Wu, H.: ZEXE: enabling decentralized private computation. In: 2020 IEEE Symposium on Security and Privacy (SP), pp. 947–964 (2020). https://doi.org/10.1109/SP40000.2020.00050

  9. Brakerski, Z., Döttling, N., Garg, S., Malavolta, G.: Leveraging linear decryption: rate-1 fully-homomorphic encryption and time-lock puzzles. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11892, pp. 407–437. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36033-7_16

    Chapter  Google Scholar 

  10. Castryck, W., Decru, T.: CSIDH on the surface. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 111–129. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_7

    Chapter  Google Scholar 

  11. Castryck, W., Lange, T., Martindale, C., Panny, L., Renes, J.: CSIDH: an efficient post-quantum commutative group action. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11274, pp. 395–427. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03332-3_15

    Chapter  Google Scholar 

  12. Castryck, W., Panny, L., Vercauteren, F.: Rational isogenies from irrational endomorphisms. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 523–548. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_18

    Chapter  Google Scholar 

  13. Costello, C., Longa, P., Naehrig, M.: Efficient algorithms for supersingular isogeny Diffie-Hellman. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 572–601. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_21

    Chapter  Google Scholar 

  14. De Feo, L., Galbraith, S.D.: SeaSign: compact isogeny signatures from class group actions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 759–789. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_26

    Chapter  Google Scholar 

  15. De Feo, L., Jao, D., Plût, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. J. Math. Cryptol. 8(3), 209–247 (2014). https://doi.org/10.1007/978-3-642-25405-5_2

    Article  MathSciNet  MATH  Google Scholar 

  16. De Feo, L., Kohel, D., Leroux, A., Petit, C., Wesolowski, B.: SQISign: compact post-quantum signatures from quaternions and isogenies. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020, Part I. LNCS, vol. 12491, pp. 64–93. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64837-4_3

    Chapter  Google Scholar 

  17. De Feo, L., Masson, S., Petit, C., Sanso, A.: Verifiable delay functions from supersingular isogenies and pairings. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 248–277. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_10

    Chapter  Google Scholar 

  18. Eisenträger, K., Hallgren, S., Lauter, K., Morrison, T., Petit, C.: Supersingular isogeny graphs and endomorphism rings: reductions and solutions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 329–368. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_11

    Chapter  Google Scholar 

  19. Gabizon, A., Williamson, Z.J.: plookup: a simplified polynomial protocol for lookup tables. Cryptology ePrint Archive, Report 2020/315 (2020). https://eprint.iacr.org/2020/315

  20. Galbraith, S.D., Vercauteren, F.: Computational problems in supersingular elliptic curve isogenies. Quantum Inf. Process. 17(10), 1–22 (2018). https://doi.org/10.1007/s11128-018-2023-6

    Article  MathSciNet  MATH  Google Scholar 

  21. Howard, M., Cohen, B.: Chia network announces 2nd VDF competition with \$100,000 in total prize money (2019). https://www.chia.net/2019/04/04/chia-network-announces-second-vdf-competition-with-in-total-prize-money.en.html

  22. Kohel, D.R., Lauter, K., Petit, C., Tignol, J.P.: On the quaternion-isogeny path problem. LMS J. Comput. Math. 17(A), 418–432 (2014)

    Google Scholar 

  23. Kutas, P., Martindale, C., Panny, L., Petit, C., Stange, K.E.: Weak instances of SIDH variants under improved torsion-point attacks. Cryptology ePrint Archive, Report 2020/633 (2020). https://eprint.iacr.org/2020/633

  24. Love, J., Boneh, D.: Supersingular curves with small noninteger endomorphisms. Open Book Series 4(1), 7–22 (2020)

    Article  Google Scholar 

  25. Malavolta, G., Thyagarajan, S.A.K.: Homomorphic time-lock puzzles and applications. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part I. LNCS, vol. 11692, pp. 620–649. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_22

    Chapter  Google Scholar 

  26. Petit, C.: Faster algorithms for isogeny problems using torsion point images. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 330–353. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_12

    Chapter  Google Scholar 

  27. Pietrzak, K.: Simple verifiable delay functions. In: Blum, A. (ed.) 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), vol. 124, pp. 60:1–60:15. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2018). https://doi.org/10.4230/LIPIcs.ITCS.2019.60

  28. Renes, J.: Computing isogenies between montgomery curves using the action of (0, 0). In: Lange, T., Steinwandt, R. (eds.) PQCrypto 2018. LNCS, vol. 10786, pp. 229–247. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-79063-3_11

    Chapter  Google Scholar 

  29. Rivest, R.L., Shamir, A., Wagner, D.A.: Time-lock puzzles and timed-release crypto. Technical report, Cambridge, MA, USA (1996). https://people.csail.mit.edu/rivest/pubs/RSW96.pdf

  30. Delpech de Saint Guilhem, C., Kutas, P., Petit, C., Silva, J.: SÉTA: supersingular encryption from torsion attacks. Cryptology ePrint Archive, Report 2019/1291 (2019). https://eprint.iacr.org/2019/1291

  31. Shlomovits, O.: Diogenes Octopus: Playing red team for Eth2.0 VDF, June 2020. https://medium.com/zengo/dac3f2e3cc7b

  32. Shlomovits, O.: DogByte attack: playing red team for Eth2.0 VDF, August 2020. https://medium.com/zengo/ea2b9b2152af

  33. VDF Alliance: VDF FPGA competition (2019). https://supranational.atlassian.net/wiki/spaces/VA/pages/36569208/FPGA+Competition

  34. Wesolowski, B.: Efficient verifiable delay functions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part III. LNCS, vol. 11478, pp. 379–407. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_13

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Web 3 Foundation, Zug, Switzerland

    Jeffrey Burdges

  2. IBM Research Europe, Zürich, Switzerland

    Luca De Feo

Authors
  1. Jeffrey Burdges
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luca De Feo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeffrey Burdges .

Editor information

Editors and Affiliations

  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

Rights and permissions

Reprints and permissions

Copyright information

© 2021 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Burdges, J., De Feo, L. (2021). Delay Encryption. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12696. Springer, Cham. https://doi.org/10.1007/978-3-030-77870-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-77870-5_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-77869-9

  • Online ISBN: 978-3-030-77870-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation