How Bitcoin Prevents Double Spending Without a Central Authority

Table of Links Abstract and I. Introduction A. Quantum Bitcoin Mining B. Our Contribution C. Comparison with Related Works D. Conventions II. Background A. Bitcoin Basics B. Bitcoin Security C. Grover’s Search Algorithm D. Quantum Attacks III. Approach A. Algorithm B. Markov Chain C. Assumptions and Approximations IV. Results A. Probability of Success B. Performance Measures C. Example Application V. Discussion, Acknowledgments, and References B. Bitcoin Security The central problem all digital currencies must overcome is double spending attacks, in which currency is spent twice by the same entity. To overcome this problem, protocols can use a central authority that verifies, before every transaction, that the currency involved has not already been spent. The Bitcoin network has no such central authority and instead relies on the blockchain. The blockchain provides a public ledger which can be used to check against double spending. Authors: (1) Robert R. Nerem, Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada (riley.nerem@gmail.com); (2) Daya R. Gaur, Department of Mathematics and Computer Science, University of Lethbridge, Alberta T1K 3M4, Canada. This paper is available on arxiv under CC BY 4.0 DEED license. Table of Links Abstract and I. Introduction Abstract and I. Introduction Abstract and I. Introduction A. Quantum Bitcoin Mining A. Quantum Bitcoin Mining B. Our Contribution B. Our Contribution C. Comparison with Related Works C. Comparison with Related Works D. Conventions D. Conventions II. Background II. Background A. Bitcoin Basics A. Bitcoin Basics B. Bitcoin Security B. Bitcoin Security C. Grover’s Search Algorithm C. Grover’s Search Algorithm D. Quantum Attacks D. Quantum Attacks III. Approach III. Approach III. Approach A. Algorithm A. Algorithm B. Markov Chain B. Markov Chain C. Assumptions and Approximations C. Assumptions and Approximations IV. Results IV. Results A. Probability of Success A. Probability of Success B. Performance Measures B. Performance Measures C. Example Application C. Example Application V. Discussion, Acknowledgments, and References V. Discussion, Acknowledgments, and References V. Discussion, Acknowledgments, and References B. Bitcoin Security The central problem all digital currencies must overcome is double spending attacks, in which currency is spent twice by the same entity. To overcome this problem, protocols can use a central authority that verifies, before every transaction, that the currency involved has not already been spent. The Bitcoin network has no such central authority and instead relies on the blockchain. The blockchain provides a public ledger which can be used to check against double spending. Authors: (1) Robert R. Nerem, Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada (riley.nerem@gmail.com); (2) Daya R. Gaur, Department of Mathematics and Computer Science, University of Lethbridge, Alberta T1K 3M4, Canada. Authors: Authors: (1) Robert R. Nerem, Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada (riley.nerem@gmail.com); (2) Daya R. Gaur, Department of Mathematics and Computer Science, University of Lethbridge, Alberta T1K 3M4, Canada. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv