Skip to main content

Probabilistic Micropayments with Transferability

  • 1974 Accesses

Part of the Lecture Notes in Computer Science book series (LNSC,volume 12972)


Micropayments are one of the challenges in cryptocurrencies. The problems in realizing micropayments in the blockchain are the low throughput and the high blockchain transaction fee. As a solution, decentralized probabilistic micropayment has been proposed. The winning amount is registered in the blockchain, and the tickets are issued to be won with probability p, which allows us to aggregate approximately transactions into one. Unfortunately, existing solutions do not allow for ticket transferability, and the smaller p, the more difficult it to use them in the real world. We propose a novel decentralized probabilistic micropayment Transferable Scheme. It allows tickets to be transferable among users. By allowing tickets to be transferable, we can make p smaller. We also propose a novel Proportional Fee Scheme. This is a scheme where each time a ticket is transferred, a portion of the blockchain transaction fee will be charged. With the proportional fee scheme, users will have the advantage of sending money with a smaller fee than they would generally send through the blockchain. For example, sending one dollar requires only ten cents.


  • Blockchain
  • Micropayment
  • Transferability
  • Tamper-proof wallet

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-88418-5_19
  • Chapter length: 17 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   89.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-88418-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   119.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.


  1. 1.

    The wallet does not check the validity of the escrow transaction \(\tau _0\) and \(\epsilon \). Payees will reject the ticket which is not transferred from \(\epsilon \).

  2. 2.

    Double-spending attacks can be perfectly detected, and the adversary’s address is discovered. See Sect. 6.

  3. 3.

    The compensated amount is the same as the return when received the ticket. See Sect. 5 for the value of a ticket when it is in transfer.

  4. 4.

    For practical purposes, we assume that the height of \(\tau \) can only be measured when all tickets in the sequence from \(\epsilon \) to \(\tau \) are given. Even if such sequence exists, the height of \(\tau \) is considered to be \(\infty \) unless the entire sequence is specifically presented.

  5. 5.

    In reality, the adversaries are biased, but we assume it can not be distinguishable from a legitimate user from outside.

  6. 6.

    In reality, the number of addresses each user has is considered more likely to follow exponential distribution. It is an unfavorable assumption that all user have the same number of addresses \(\alpha \).


  1. Bitcoin average cost per transaction (2020).

  2. Almashaqbeh, G., Bishop, A., Cappos, J.: MicroCash: practical concurrent processing of micropayments. In: Bonneau, J., Heninger, N. (eds.) FC 2020. LNCS, vol. 12059, pp. 227–244. Springer, Cham (2020).

    CrossRef  Google Scholar 

  3. 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).

    CrossRef  Google Scholar 

  4. Chiesa, A., Green, M., Liu, J., Miao, P., Miers, I., Mishra, P.: Decentralized anonymous micropayments. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 609–642. Springer, Cham (2017).

    CrossRef  Google Scholar 

  5. Garay, J., Kiayias, A., Leonardos, N.: The bitcoin backbone protocol: analysis and applications. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 281–310. Springer, Heidelberg (2015).

    CrossRef  Google Scholar 

  6. Gudgeon, L., Moreno-Sanchez, P., Roos, S., McCorry, P., Gervais, A.: SoK: layer-two blockchain protocols. In: Bonneau, J., Heninger, N. (eds.) FC 2020. LNCS, vol. 12059, pp. 201–226. Springer, Cham (2020).

    CrossRef  Google Scholar 

  7. Karame, G.O., Androulaki, E., Capkun, S.: Double-spending fast payments in bitcoin. In: Proceedings of the 2012 ACM conference on Computer and communications security, CCS 2012, pp. 906–917. Association for Computing Machinery (2012)

    Google Scholar 

  8. Miller, A., Bentov, I., Bakshi, S., Kumaresan, R., McCorry, P.: Sprites and state channels: payment networks that go faster than lightning. In: Goldberg, I., Moore, T. (eds.) FC 2019. LNCS, vol. 11598, pp. 508–526. Springer, Cham (2019).

    CrossRef  Google Scholar 

  9. Pass, R., shelat, a.: Micropayments for decentralized currencies. In: Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, CCS 2015, pp. 207–218. Association for Computing Machinery (2015)

    Google Scholar 

  10. Rivest, R.L.: Electronic lottery tickets as micropayments. In: Hirschfeld, R. (ed.) FC 1997. LNCS, vol. 1318, pp. 307–314. Springer, Heidelberg (1997).

    CrossRef  Google Scholar 

  11. Takahashi, T., Otsuka, A.: Short paper: secure offline payments in bitcoin. In: Bracciali, A., Clark, J., Pintore, F., Rønne, P.B., Sala, M. (eds.) FC 2019. LNCS, vol. 11599, pp. 12–20. Springer, Cham (2020).

    CrossRef  Google Scholar 

  12. Wheeler, D.: Transactions using bets. In: Lomas, M. (ed.) Security Protocols 1996. LNCS, vol. 1189, pp. 89–92. Springer, Heidelberg (1997).

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Taisei Takahashi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Takahashi, T., Otsuka, A. (2021). Probabilistic Micropayments with Transferability. In: Bertino, E., Shulman, H., Waidner, M. (eds) Computer Security – ESORICS 2021. ESORICS 2021. Lecture Notes in Computer Science(), vol 12972. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-88417-8

  • Online ISBN: 978-3-030-88418-5

  • eBook Packages: Computer ScienceComputer Science (R0)