Attempts to accurately measure the monetary velocity or related properties of Bitcoin have often attempted to either directly apply definitions from traditional macroeconomic theory or to use specialized metrics relative to the properties of the Blockchain such as bitcoin-days destroyed. In this paper, it is demonstrated that beyond being a useful metric, bitcoin-days destroyed has mathematical properties that allow one to calculate the average dormancy (time since last use in a transaction) of the bitcoins used in transactions over a given time period. In addition, transaction volume and average dormancy are shown to have unexpected significance in helping estimate the average size of the pool of traded bitcoins by virtue of the expression Little's Law, though only under limited conditions.

The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk is cryptocurrencies, a market currently worth over 100 billion USD. We investigate the risk posed to Bitcoin, and other cryptocurrencies, by attacks using quantum computers. We find that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers. On the other hand, the elliptic curve signature scheme used by Bitcoin is much more at risk, and could be completely broken by a quantum computer as early as 2027, by the most optimistic estimates. We analyze an alternative proof-of-work called Momentum, based on finding collisions in a hash function, that is even more resistant to speedup by a quantum computer. We also review the available post-quantum signature schemes to see which one would best meet the security and efficiency requirements of blockchain applications.

Proof-of-work is a central concept in modern cryptocurrencies and denial-ofservice protection tools, but the requirement for fast verification so far has made it an easy prey for GPU-, ASIC-, and botnet-equipped users. The attempts to rely on memory-intensive computations in order to remedy the disparity between architectures have resulted in slow or broken schemes. In this paper we solve this open problem and show how to construct an asymmetric proof-of-work (PoW) based on a computationally-hard problem, which requires a great deal of memory to generate a proof (called a ”memory-hardness” feature) but is instant to verify. Our primary proposal, Equihash, is a PoW based on the generalized birthday problem and enhanced Wagner’s algorithm for it. We introduce the new technique of algorithm binding to prevent cost amortization and demonstrate that possible parallel implementations are constrained by memory bandwidth. Our scheme has tunable and steep time-space tradeoffs, which impose large computational penalties if less memory is used. Our solution is practical and ready to deploy: a reference implementation of a proof-of-work requiring 700 MB of RAM runs in 15 seconds on a 2.1 GHz CPU, increases the computations by a factor of 1000 if memory is halved, and presents a proof of just 120 bytes long.

With the widespread use of Internet, Web, and mobile technologies, a new category of applications and transactions that requires anonymity is gaining increased interest and importance. Examples of such new applications are innovative payment systems, digital notaries, electronic voting, documents sharing, electronic auctions, medical applications, and many others. In addition to anonymity, these applications and transactions also require standard security services: identification, authentication, and authorization of users and protection of their transactions. Providing those services in combination with anonymity is an especially challenging issue, because all security services require explicit user identification and authentication. To solve this issue and enable applications with security and also anonymity we introduce a new type of cryptographically encapsulated objects called BIX certificates. “BIX” is an abbreviation for “Blockchain Information Exchange.” Their purpose is equivalent to X.509 certificates: to support security services for users and transactions, but also enhanced with anonymity. This paper describes the structure and attributes of BIX certificate objects and all related protocols for their creation, distribution, and use. The BIX Certification Infrastructure (BCI) as a distributed public ledger is also briefly described.