Designs, Codes and Cryptography

, Volume 78, Issue 1, pp 87–102 | Cite as

Cryptocash, cryptocurrencies, and cryptocontracts

  • Neal Koblitz
  • Alfred J. MenezesEmail author


One of the central challenges for mathematical cryptography is to create a payment system that provides the advantages of cash in a digital world. In this expository article we describe two very different solutions to this problem. The first is an elliptic-curve-based version of a construction of Brands, and the second is Bitcoin. We also discuss a generalization of Bitcoin that supports peer-to-peer contracts.


Cryptography Public key Cryptocurrency Bitcoin Ethereum 

Mathematics Subject Classification

94A60 68P25 14G50 94-02 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

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