Skip to main content

Range Proofs with Constant Size and Trustless Setup

  • 562 Accesses

Part of the Lecture Notes in Networks and Systems book series (LNNS,volume 655)

Abstract

Range proofs are widely adopted in practice in many privacy-preserving cryptographic protocols in the public blockchain. The performances known in the literature for range proofs are logarithmic-sized proofs and linear verification time. In contexts where the proof verification is left to the ledger maintainers and proofs are stored in blocks, one might expect higher transaction fees and blockchain space when the size of the relation over the proof grows. With this paper, we improve Bulletproofs, a zero-knowledge argument of knowledge for range proofs, by modifying its Inner Product Argument (IPA) subroutine. In particular, we adopt a new relation from the polynomial commitment scheme of Halo, based on standard groups and assumptions (DLOG and RO) with a trustless setup. We design a two-step reduction algorithm and we obtain a constant number of two rounds in the IPA and a constant-sized proof composed of 5 \(\mathbb {G}_1\) points and 2 \(\mathbb {Z}_p\) scalars.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   279.99
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

Learn about institutional subscriptions

References

  1. Alonso, K.M., et al.: Zero to Monero (2020)

    Google Scholar 

  2. arkworks rs. arkworks

    Google Scholar 

  3. Bootle, J., Cerulli, A., Chaidos, P., Groth, J., Petit, C.: Efficient zero-knowledge arguments for arithmetic circuits in the discrete log setting. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 327–357. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_12

    Chapter  MATH  Google Scholar 

  4. 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. IEEE (2020)

    Google Scholar 

  5. Bowe, S., Grigg, J., Hopwood, D.: Recursive proof composition without a trusted setup. Cryptology ePrint Archive (2019)

    Google Scholar 

  6. Bünz, B., Agrawal, S., Zamani, M., Boneh, D.: Zether: towards privacy in a smart contract world. In: Bonneau, J., Heninger, N. (eds.) FC 2020. LNCS, vol. 12059, pp. 423–443. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51280-4_23

    Chapter  Google Scholar 

  7. Bünz, B., Bootle, J., Boneh, D., Poelstra, A., Wuille, P., Maxwell. G.: Bulletproofs: short proofs for confidential transactions and more. In: 2018 IEEE Symposium on Security and Privacy (SP), pp. 315–334. IEEE (2018)

    Google Scholar 

  8. Bünz, B., Chiesa, A., Mishra, P., Spooner, N.: Proof-carrying data from accumulation schemes. Cryptology ePrint Archive (2020)

    Google Scholar 

  9. Bünz, B., Maller, M., Mishra, P., Tyagi, N., Vesely, P.: Proofs for inner pairing products and applications. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13092, pp. 65–97. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92078-4_3

    Chapter  Google Scholar 

  10. Corradini, F., Mostarda, L., Scala, E.: ZeroMT: multi-transfer protocol for enabling privacy in off-chain payments. In: Barolli, L., Hussain, F., Enokido, T. (eds.) AINA 2022. LNNS, vol. 450, pp. 611–623. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-99587-4_52

    Chapter  Google Scholar 

  11. Daza, V., Ràfols, C., Zacharakis, A.: Updateable inner product argument with logarithmic verifier and applications. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12110, pp. 527–557. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_18

    Chapter  Google Scholar 

  12. EmanueleSc. Zeromt

    Google Scholar 

  13. Fauzi, P., Meiklejohn, S., Mercer, R., Orlandi, C.: Quisquis: a new design for anonymous cryptocurrencies. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11921, pp. 649–678. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34578-5_23

    Chapter  Google Scholar 

  14. Jivanyan, A.: Lelantus: towards confidentiality and anonymity of blockchain transactions from standard assumptions. IACR Cryptol. ePrint Arch. 2019, 373 (2019)

    Google Scholar 

  15. Lee, J.: Dory: efficient, transparent arguments for generalised inner products and polynomial commitments. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13043, pp. 1–34. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90453-1_1

    Chapter  Google Scholar 

  16. Mehmood, N.Q., Culmone, R., Mostarda, L.: Modeling temporal aspects of sensor data for MongoDB NoSQL database. J. Big Data 4(1), (2017)

    Google Scholar 

  17. Russello, G., Mostarda, L., Dulay, N.: A policy-based publish/subscribe middleware for sense-and-react applications. J. Syst. Softw. 84(4), 638–654 (2011)

    Article  Google Scholar 

  18. Vannucch, C., et al.: Symbolic verification of event–condition–action rules in intelligent environments. J. Reliable Intell. Environ. 3(2), 117–130 (2017)

    Article  Google Scholar 

  19. Xiong, A.I., Chen, B., Zhang, Bünz, B., Fisch, B., Krell, F., Camacho. P.: Veri-zexe: decentralized private computation with universal setup. Cryptology ePrint Archive (2022)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Emanuele Scala .

Editor information

Editors and Affiliations

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

Scala, E., Mostarda, L. (2023). Range Proofs with Constant Size and Trustless Setup. In: Barolli, L. (eds) Advanced Information Networking and Applications. AINA 2023. Lecture Notes in Networks and Systems, vol 655. Springer, Cham. https://doi.org/10.1007/978-3-031-28694-0_28

Download citation

Publish with us

Policies and ethics