*k*-root-*n*: An Efficient Algorithm for Avoiding Short Term Double-Spending Alongside Distributed Ledger Technologies Such as Blockchain

A peer-reviewed article of this Preprint also exists.

Schreiber, Z. *k*-Root-*n*: An Efficient Algorithm for Avoiding Short Term Double-Spending Alongside Distributed Ledger Technologies such as Blockchain. *Information* **2020**, *11*, 90.
Schreiber, Z. k-Root-n: An Efficient Algorithm for Avoiding Short Term Double-Spending Alongside Distributed Ledger Technologies such as Blockchain. Information 2020, 11, 90.

Journal reference: Information 2020, 11, 90

DOI: 10.3390/info11020090

## Abstract

*n*) messages; each node receiving money off-chain performs the due diligence of consulting

*k*√

*n*random nodes to check if any of them is aware of double-spending. Two nodes receiving double-spent money will in this way consult at least one common node with very high probability, due to the ‘birthday paradox’, and any common honest node consulted will detect the fraud. Since the velocity of money in the real world has coins circulating through at most a few wallets per day, the size of the due diligence communication is small in the short term. This `

*k*-root-

*n*’ algorithm is suitable for an environment with synchronous or asynchronous (but with fairly low latency) communication and with Byzantine faults. The presented

*k*-root-

*n*algorithm should be practical to avoid double-spending with arbitrarily high probability, while feasibly coping with the throughput of all world commerce. It is resistant to Sybil attacks even beyond 50% of nodes. In the long term, the

*k*-root-

*n*algorithm is less efficient. Therefore, it should preferably be used as a complement and not a replacement to a global distributed ledger technology.

## Subject Areas

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