A Probabilistic Analysis of the Nxt Forging Algorithm

Authors

  • Serguei Popov University of Campinas

DOI:

https://doi.org/10.5195/ledger.2016.46

Abstract

We discuss the forging algorithm of Nxt from a probabilistic point of view, and obtain explicit formulas and estimates for several important quantities, such as the probability that an account generates a block, the length of the longest sequence of consecutive blocks generated by one account, and the probability that one concurrent blockchain wins over an- other one. Also, we discuss some attack vectors related to splitting an account into many smaller ones. 

Author Biography

Serguei Popov, University of Campinas

Full professor at Department of Statistics, www.ime.unicamp.br

References

Andruiman. “Nxt forging algorithm: simulating approach.” (2014) https://scribd.com/doc/243341106/Nxt-forging-algorithm-simulating-approach

Andruiman. “PoS forging algorithms: formal approach and multibranch forging.” (2014) https://scribd.com/ doc/248208963/Multibranch-forging

Andruiman. “Multibranch forging algorithms: tails-switching effect and chain measures.” (2015) https://scribd.com/doc/256073121/Multibranch-forging-algorithms-tails-switching-effect-and-chain-measures

Andruiman. “PoS forging algorithms: multi-strategy forging and related security issues.” (2015) https://scribd.com/doc/256072839/PoS-forging-algorithms-multi-strategy-forging-and-related-security-issues

Athreya, K.B., Ney. P.E. Branching Processes. Berlin–Heidelberg–New York: Springer-Verlag (1972).

Gordon, L., Schilling, M.F., Waterman, M.S. “An extreme value theory for long head runs.” Probab. Theory Relat. Fields 72, 279–287 (1986).

MTHCL. “The math of Nxt forging.” (2014) www.docdroid.net/ecmz/forging0-5-2.pdf.html

Ross, S. M. A First Course in Probability, 8th ed. (2009).

Ross, S. M. Introduction to Probability Models. 10th ed. (2012).

Schilling, M. “The Longest Run of Heads.” The College Math J., 21 (3), 196–206 (1990).

Ledger: The Inaugural Issue

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Published

2016-12-21

How to Cite

Popov, S. (2016). A Probabilistic Analysis of the Nxt Forging Algorithm. Ledger, 1, 69–83. https://doi.org/10.5195/ledger.2016.46

Issue

Vol. 1 (2016)

Section

Research Articles

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