Advertisement

Chain of Antichains: An Efficient and Secure Distributed Ledger

Chapter
Part of the Blockchain Technologies book series (BT)

Abstract

Since the inception of blockchain and Bitcoin (Nakamoto, Bitcoin: A peer-to-peer electronic cash system (2008) [18]), a decentralized-distributed ledger system and its associated cryptocurrency, respectively, the world has witnessed a slew of newer adaptations and applications. Although the original distributed ledger technology of blockchain is deemed secure and decentralized, the confirmation of transactions is inefficient by design. Recently adopted, some distributed ledgers based on a directed acyclic graph validate transactions efficiently without the physically and environmentally costly building process of blocks (Lerner, Dagcoin: a crytocurrency without blocks (2015) [17]). However, centrally-controlled confirmation against the odds of multiple validation disqualifies that newer system as a decentralized-distributed ledger. In this regard, we introduce an innovative distributed ledger system by reconstructing a chain of antichains based on a given partially ordered pool of transactions. Each antichain contains distinct nodes whose approved transactions are recursively validated by subsequently augmenting nodes. The boxer node closes the box and keeps the hash of all transactions confirmed by the box-genesis node. Designation of boxers and box-geneses is conditionally randomized for decentralization. The boxes are serially concatenated with recursive confirmation without incurring the cost of box generation. Rewards are paid to the contributing nodes of the ecosystem whose trust is built on the doubly-secure protocol of confirmation. A value-preserving medium of payment is among numerous practical applications discussed herein.

Keywords

Blockchain Distributed ledger technology Decentralization Antichain Partially ordered set Consensus protocol Stablecoin Cryptocurrency 

Notes

Acknowledgements

The first and corresponding authors appreciate research support from the LeBow College of Business, Drexel University, and the College of Business, Ewha Womans University, respectively.

References

  1. 1.
    Baird L (2016) Hashgraph consensus: fair, fast, byzantine fault tolerance. Swirlds tech report TR-2016-01Google Scholar
  2. 2.
    Bowers NL Jr, Gerber HU, Hickman JC, Jones DA, Nesbitt CJ (1997) Actuarial Mathematics. The society of Actuaries, Schaumburg, IllinoiszbMATHGoogle Scholar
  3. 3.
    Churyumov A (2017) Byteball: a decentralized system for storage and transfer of value. http://byteball.org
  4. 4.
    Dickson DCM (1995) A review of Panjer’s recursion formula and its applications. Brit Act J 1(1):107–124CrossRefGoogle Scholar
  5. 5.
    Dilworth RP (1950) A decomposition theorem for partially ordered sets. Ann Math 51(1):161–166MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dilworth RP (1960) Some combinatorial problems on partially ordered sets. Proc AMS Sympos Appl Math 10:85–90MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fulkerson DR (1956) A note on Dilworth’s theorem for partially ordered sets. Proc Amer Math Soc 7:701MathSciNetzbMATHGoogle Scholar
  8. 8.
    Goodhart CAE (1989) Money, information and uncertainty, 2nd edn. Macmillan, LondonCrossRefGoogle Scholar
  9. 9.
    Greene C, Kleitman D (1976) The structure of Sperner \(k\)-family. J Comb Theory Ser A 20:80–88CrossRefGoogle Scholar
  10. 10.
    Greenwood M, Yule GU (1920) An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. J R Stat Soc 83(2):255–279CrossRefGoogle Scholar
  11. 11.
    Iota (2016) A crytocurrency for internet-of-things. http://www.iotatoken.com
  12. 12.
    Kataoka S (1963) A stochastic programming model. Econometrica 31:181–196MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kindleberger CP (2015) A financial history of Western Europe. RoutledgeGoogle Scholar
  14. 14.
    Lee J (2017) Computing the probability of union in the \(n\)-dimensional Euclidean space for application of the multivariate quantile: \(p\)-level efficient points. Oper Res Lett 45:242–247MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lee J, Kim J, Prékopa A (2017) Extreme value estimation for a function of a random sample using binomial moment scheme and Boolean functions of events. Discrete Appl Math 219(11):210–218MathSciNetCrossRefGoogle Scholar
  16. 16.
    Lee J, Prékopa A (2017) On the probability of union in the n-space. Oper Res Lett 45:19–24MathSciNetCrossRefGoogle Scholar
  17. 17.
    Lerner SD (2015) Dagcoin: a crytocurrency without blocks. http://bitslog.wordpress.com/2015/09/11/dagcoin
  18. 18.
    Nakamoto S (2008) Bitcoin: a peer-to-peer electronic cash system. http://www.bitocin.org
  19. 19.
    NXTFORUM.ORG, PEOPLE ON (2014) Dag, a generalized blockchain. http://nxtforum.org/proof-of-stake-algorithm/dag-a-generalized-blockchain/
  20. 20.
    Panjer H (1981) Recursive evaluation of a family of compound distributions. AST IN Bulletin 12:21–26MathSciNetGoogle Scholar
  21. 21.
    Panjer H, Lutek B (1983) Practical aspects of stop-loss calculations. Insur Math Econ 1:159–177zbMATHGoogle Scholar
  22. 22.
    Panjer H, Willmot GE (1986) Computational aspects of recursive evaluation of compound distributions. Insur Math Econ 5 113–116Google Scholar
  23. 23.
    Pflug GCH (2000) Some remarks on the value-at-risk and conditional value at risk. Prob Constrained Optim 272–281Google Scholar
  24. 24.
    Pflug GCH (1996) Optimization of stochastic models—the interface between simulation and optimization. Kluwer Academic PublishersGoogle Scholar
  25. 25.
    Popov S (2017) The tangle. http://www.iotatoken.com
  26. 26.
    Prékopa A (1995) Stochastic programming. Kluwer Academic PublishersGoogle Scholar
  27. 27.
    Prékopa A (2003) Probabilistic programming. In: Ruszczyński A, Shapiro A (eds) Hand books in operations research and management science, vol 10, pp 267–351Google Scholar
  28. 28.
    Prékopa A, Lee J (2018) Risk tomography. Eur J Oper Res 265(1):149–168MathSciNetCrossRefGoogle Scholar
  29. 29.
    Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on stochastic programming: modeling and theory. SIAM and MPS, PhiladelphiaCrossRefGoogle Scholar
  30. 30.
    Smith A (1776) An inquiry into the wealth of nations. W. Strahan and T. Cadell, LondonGoogle Scholar
  31. 31.
    Uryasev S, Rockafellar RT (2000) Optimization of conditional value at risk. J Risk 2:21–41CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.LeBow College of BusinessDrexel UniversityPhiladelphiaUSA
  2. 2.College of Business Administration, Ewha Womans UniversitySeoulRepublic of Korea

Personalised recommendations