Special Subsets of Addresses for Blockchains Using the secp256k1 Curve

Antonio J. Di Scala, Andrea Gangemi, Giuliano Romeo and Gabriele Vernetti
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Antonio J. Di Scala: DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Andrea Gangemi: DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Giuliano Romeo: DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Gabriele Vernetti: DAUIN, Department of Control and Computer Engineering, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

Mathematics, 2022, vol. 10, issue 15, 1-11

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.

Keywords: cryptography; blockchain; Bitcoin; elliptic curves; subsets analysis; addresses; wallet (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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