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Special Subsets of Addresses for Blockchains Using the secp256k1 Curve

Author

Listed:
  • Antonio J. Di Scala

    (DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
    These authors contributed equally to this work.
    Antonio J. Di Scala, Andrea Gangemi and Giuliano Romeo are members of CrypTO, GNSAGA of INdAM and of DISMA Dipartimento di Eccellenza MIUR 2018–2022.)

  • Andrea Gangemi

    (DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
    These authors contributed equally to this work.
    Antonio J. Di Scala, Andrea Gangemi and Giuliano Romeo are members of CrypTO, GNSAGA of INdAM and of DISMA Dipartimento di Eccellenza MIUR 2018–2022.)

  • Giuliano Romeo

    (DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
    These authors contributed equally to this work.
    Antonio J. Di Scala, Andrea Gangemi and Giuliano Romeo are members of CrypTO, GNSAGA of INdAM and of DISMA Dipartimento di Eccellenza MIUR 2018–2022.)

  • Gabriele Vernetti

    (DAUIN, Department of Control and Computer Engineering, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
    These authors contributed equally to this work.
    Gabriele Vernetti is member of CrypTO.)

Abstract

In 2020, Sala, Sogiorno and Taufer were able to find the private keys of some Bitcoin addresses, thus being able to spend the cryptocurrency linked to them. This was unexpected since the recovery of non-trivial private keys for blockchain addresses is deemed to be an infeasible problem. In this paper, we widen this analysis by mounting a similar attack on other small subsets of the set of private keys. We then apply it to other blockchains as well, examining Ethereum, Dogecoin, Litecoin, Dash, Zcash and Bitcoin Cash. In addition to the results, we also explain the techniques we have used to perform this exhaustive search for all the addresses that have ever appeared in these blockchains, and we give an estimate of the time needed to perform all the computations. Finally, we also examine the possibility of mounting a similar attack on other elliptic curves used in blockchains, i.e., Curve25519 and NIST P-256.

Suggested Citation

  • Antonio J. Di Scala & Andrea Gangemi & Giuliano Romeo & Gabriele Vernetti, 2022. "Special Subsets of Addresses for Blockchains Using the secp256k1 Curve," Mathematics, MDPI, vol. 10(15), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2746-:d:879237
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    References listed on IDEAS

    as
    1. Pilkington Marc, 2016. "Blockchain Technology: Principles and Applications," Post-Print halshs-01231205, HAL.
    2. Massimiliano Sala & Domenica Sogiorno & Daniele Taufer, 2020. "A Small Subgroup Attack on Bitcoin Address Generation," Mathematics, MDPI, vol. 8(10), pages 1-8, September.
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