Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve
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 pape...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/15/2746 |
| _version_ | 1797413082973077504 |
|---|---|
| author | Antonio J. Di Scala Andrea Gangemi Giuliano Romeo Gabriele Vernetti |
| author_facet | Antonio J. Di Scala Andrea Gangemi Giuliano Romeo Gabriele Vernetti |
| author_sort | Antonio J. Di Scala |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T05:12:26Z |
| format | Article |
| id | doaj.art-e23f1d9a566148a79520872d1e7f9de2 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:12:26Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e23f1d9a566148a79520872d1e7f9de22023-12-03T12:48:20ZengMDPI AGMathematics2227-73902022-08-011015274610.3390/math10152746Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> CurveAntonio J. Di Scala0Andrea Gangemi1Giuliano Romeo2Gabriele Vernetti3DISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, ItalyDISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, ItalyDISMA, Department of Mathematical Sciences, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, ItalyDAUIN, Department of Control and Computer Engineering, Politecnico of Turin, Corso Duca degli Abruzzi, 24, 10129 Torino, ItalyIn 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.https://www.mdpi.com/2227-7390/10/15/2746cryptographyblockchainBitcoinelliptic curvessubsets analysisaddresses |
| spellingShingle | Antonio J. Di Scala Andrea Gangemi Giuliano Romeo Gabriele Vernetti Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve Mathematics cryptography blockchain Bitcoin elliptic curves subsets analysis addresses |
| title | Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve |
| title_full | Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve |
| title_fullStr | Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve |
| title_full_unstemmed | Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve |
| title_short | Special Subsets of Addresses for Blockchains Using the <i>secp256k1</i> Curve |
| title_sort | special subsets of addresses for blockchains using the i secp256k1 i curve |
| topic | cryptography blockchain Bitcoin elliptic curves subsets analysis addresses |
| url | https://www.mdpi.com/2227-7390/10/15/2746 |
| work_keys_str_mv | AT antoniojdiscala specialsubsetsofaddressesforblockchainsusingtheisecp256k1icurve AT andreagangemi specialsubsetsofaddressesforblockchainsusingtheisecp256k1icurve AT giulianoromeo specialsubsetsofaddressesforblockchainsusingtheisecp256k1icurve AT gabrielevernetti specialsubsetsofaddressesforblockchainsusingtheisecp256k1icurve |