### Abstract

Recently, Bitcoin is becoming one of the most popular decentralized cryptographic currency technologies, and Bitcoin mining is a process of adding transaction records to Bitcoin’s public ledger of past transactions or blockchain. To obtain a bitcoin, the mining process involves compiling recent transactions into blocks and trying to solve a computationally difficult puzzle, e.g., proof of work puzzle. A proof of work allows miners the ability to quantify how much work a given proof contains. Basically, the required time for mining is decided in advance, but problems will occur if the value is large for dispersion. In this paper, we first accept that the required time between consecutive blocks follows the exponential distribution. That is, the variance is stable as long as the expected time is fixed. Then, we focus on the graph clique mining technique proposed by the literature, like Tromp (BITCOIN 2015) and Bag-Ruj-Sakurai (Inscrypt 2015), which is based on a computational difficulty problem of searching cliques of undirected graphs, where a clique is a subset of vertices. In particular, when the clique size is two, graph clique mining can be used to gain Bitcoins. The previous work also claimed that if the clique size is parameterized and increased, even if the expected time is fixed, the variance would not be stable. However, no qualitative or quantitative results were given to support their claim. Motivated by this issue, in this work, we propose a simple search algorithm for graph cliques mining, and perform a small scale evaluation on Bitcoin and Graph cliques’s solo mining to investigate the variance issue.

Original language | English |
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Title of host publication | Information Security and Cryptology - 14th International Conference, Inscrypt 2018, Revised Selected Papers |

Editors | Moti Yung, Xinyi Huang, Fuchun Guo |

Publisher | Springer Verlag |

Pages | 101-114 |

Number of pages | 14 |

ISBN (Print) | 9783030142339 |

DOIs | |

Publication status | Published - Jan 1 2019 |

Event | 14th International Conference on Information Security and Cryptology, Inscrypt 2018 - Fuzhou, China Duration: Dec 14 2018 → Dec 17 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11449 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th International Conference on Information Security and Cryptology, Inscrypt 2018 |
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Country | China |

City | Fuzhou |

Period | 12/14/18 → 12/17/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Information Security and Cryptology - 14th International Conference, Inscrypt 2018, Revised Selected Papers*(pp. 101-114). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11449 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-14234-6_6

**Analysis of variance of graph-clique mining for scalable proof of work.** / Anada, Hiroaki; Matsushima, Tomohiro; Su, Chunhua; Meng, Weizhi; Kawamoto, Junpei; Bag, Samiran; Sakurai, Kouichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Information Security and Cryptology - 14th International Conference, Inscrypt 2018, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11449 LNCS, Springer Verlag, pp. 101-114, 14th International Conference on Information Security and Cryptology, Inscrypt 2018, Fuzhou, China, 12/14/18. https://doi.org/10.1007/978-3-030-14234-6_6

}

TY - GEN

T1 - Analysis of variance of graph-clique mining for scalable proof of work

AU - Anada, Hiroaki

AU - Matsushima, Tomohiro

AU - Su, Chunhua

AU - Meng, Weizhi

AU - Kawamoto, Junpei

AU - Bag, Samiran

AU - Sakurai, Kouichi

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Recently, Bitcoin is becoming one of the most popular decentralized cryptographic currency technologies, and Bitcoin mining is a process of adding transaction records to Bitcoin’s public ledger of past transactions or blockchain. To obtain a bitcoin, the mining process involves compiling recent transactions into blocks and trying to solve a computationally difficult puzzle, e.g., proof of work puzzle. A proof of work allows miners the ability to quantify how much work a given proof contains. Basically, the required time for mining is decided in advance, but problems will occur if the value is large for dispersion. In this paper, we first accept that the required time between consecutive blocks follows the exponential distribution. That is, the variance is stable as long as the expected time is fixed. Then, we focus on the graph clique mining technique proposed by the literature, like Tromp (BITCOIN 2015) and Bag-Ruj-Sakurai (Inscrypt 2015), which is based on a computational difficulty problem of searching cliques of undirected graphs, where a clique is a subset of vertices. In particular, when the clique size is two, graph clique mining can be used to gain Bitcoins. The previous work also claimed that if the clique size is parameterized and increased, even if the expected time is fixed, the variance would not be stable. However, no qualitative or quantitative results were given to support their claim. Motivated by this issue, in this work, we propose a simple search algorithm for graph cliques mining, and perform a small scale evaluation on Bitcoin and Graph cliques’s solo mining to investigate the variance issue.

AB - Recently, Bitcoin is becoming one of the most popular decentralized cryptographic currency technologies, and Bitcoin mining is a process of adding transaction records to Bitcoin’s public ledger of past transactions or blockchain. To obtain a bitcoin, the mining process involves compiling recent transactions into blocks and trying to solve a computationally difficult puzzle, e.g., proof of work puzzle. A proof of work allows miners the ability to quantify how much work a given proof contains. Basically, the required time for mining is decided in advance, but problems will occur if the value is large for dispersion. In this paper, we first accept that the required time between consecutive blocks follows the exponential distribution. That is, the variance is stable as long as the expected time is fixed. Then, we focus on the graph clique mining technique proposed by the literature, like Tromp (BITCOIN 2015) and Bag-Ruj-Sakurai (Inscrypt 2015), which is based on a computational difficulty problem of searching cliques of undirected graphs, where a clique is a subset of vertices. In particular, when the clique size is two, graph clique mining can be used to gain Bitcoins. The previous work also claimed that if the clique size is parameterized and increased, even if the expected time is fixed, the variance would not be stable. However, no qualitative or quantitative results were given to support their claim. Motivated by this issue, in this work, we propose a simple search algorithm for graph cliques mining, and perform a small scale evaluation on Bitcoin and Graph cliques’s solo mining to investigate the variance issue.

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U2 - 10.1007/978-3-030-14234-6_6

DO - 10.1007/978-3-030-14234-6_6

M3 - Conference contribution

SN - 9783030142339

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 101

EP - 114

BT - Information Security and Cryptology - 14th International Conference, Inscrypt 2018, Revised Selected Papers

A2 - Yung, Moti

A2 - Huang, Xinyi

A2 - Guo, Fuchun

PB - Springer Verlag

ER -