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International Conference on Financial Cryptography and Data Security

FC 2016: Financial Cryptography and Data Security pp 61–78Cite as

Proofs of Proofs of Work with Sublinear Complexity

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9604))

Abstract

In the setting of blockchain based transaction ledgers we study the problem of “simplified payment verification” (SPV) which refers to the setting of a transaction verifier that wishes to examine the last k blocks of the blockchain (e.g., for the purpose of verification of a certain transaction) using as only advice the genesis block (or some “checkpoint” block that is known to it).

The straightforward solution to this task requires the delivery of the blockchain, the verification of the proof of work it contains, and subsequently the examination of the last k blocks. It follows that the communication required to complete this task is linear in the length of the chain.

At first thought the above seems the best one can hope: a sublinear in the length of the chain solution to the problem will be susceptible to an attacker that, using precomputation, can fool the verifier.

Contrary to this intuition, we show that with a suitable modification to the current Bitcoin blockchain protocol (that incurs a single hash expansion in each block and gives rise to the notion of an interconnected blockchain) we can produce proofs of proof of work with sublinear complexity in the length of the chain hence enabling SPV to be performed much more efficiently.

This research was supported by ERC project CODAMODA, # 259152.

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Notes

  1. 1.

    Or a checkpoint block, if the verifier is in possession of such a block.

  2. 2.

    We thank the anonymous reviewers of the 3rd Workshop on Bitcoin and Blockchain Research for providing pointers to the relevant forum posts.

  3. 3.

    We note that there is no provision for authenticated channels in the Bitcoin setting; hence when we refer to a request for information from a certain player this is not performed in an authenticated fashion.

  4. 4.

    Here we use the following variant: \(\mathrm {Pr}(X \le k ) \le \exp (- (np-k)^2/ 2np) \), where \(k\le np\).

  5. 5.

    Roughly because \(\gamma = \alpha - \alpha ^2\) and thus this condition approximates the “honest majority” condition only if \(\alpha ^2\) is close to 0. See [6] for more details.

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Acknowledgement

The authors wish to thank Giorgos Panagiotakos for helpful discussions as well as the anonymous referees of the 3rd Workshop on Bitcoin and Blockchain Research for their valuable comments.

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Authors and Affiliations

  1. National and Kapodistrian University of Athens, Athens, Greece

    Aggelos Kiayias, Nikolaos Lamprou & Aikaterini-Panagiota Stouka

Authors
  1. Aggelos Kiayias
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  2. Nikolaos Lamprou
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  3. Aikaterini-Panagiota Stouka
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Corresponding author

Correspondence to Nikolaos Lamprou .

Editor information

Editors and Affiliations

  1. Concordia University, Montreal, Québec, Canada

    Jeremy Clark

  2. University College London, London, United Kingdom

    Sarah Meiklejohn

  3. Université du Luxembourg, Luxembourg, Luxembourg

    Peter Y.A. Ryan

  4. Rice University, Houston, Texas, USA

    Dan Wallach

  5. Leibniz Universität Hannover, Hannover, Germany

    Michael Brenner

  6. New Jersey Institute of Technology, Newark, New Jersey, USA

    Kurt Rohloff

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© 2016 International Financial Cryptography Association

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Kiayias, A., Lamprou, N., Stouka, AP. (2016). Proofs of Proofs of Work with Sublinear Complexity. In: Clark, J., Meiklejohn, S., Ryan, P., Wallach, D., Brenner, M., Rohloff, K. (eds) Financial Cryptography and Data Security. FC 2016. Lecture Notes in Computer Science(), vol 9604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53357-4_5

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  • DOI: https://doi.org/10.1007/978-3-662-53357-4_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53356-7

  • Online ISBN: 978-3-662-53357-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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