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1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Average Transaction Cost 1200 1000 800 600 400 200 0 BTC to USD Exchange Rate (Mt.Gox) Fig. 2: The average transaction fee per block per day. Data derived from http://blockchain.info/charts. ond, a standard reward is provided depending on how many blocks have been successfully calcu- lated. This reward started at B50 per block and is halved every 210,000 blocks. As of mid-March 2014, the reward is B25. The reward will eventu- ally reach B0; after such time it is imagined that the network of miners will continue mining but will do so in order to gain processing fees. This means that there is a limit on the number of Bitcoins which will be mined, but each Bitcoin is divisible up to 8 decimal places. The mean value of the transaction fee over a day is plotted for a range of days in Figure 2. As we can see the current standard reward, B25, is considerably larger than the current or historical average transaction fees. This may change in the future, as the standard reward continues to halve. III Hardware Arms Race The major limiting factors in Bitcoin mining are the hash rate of hardware and the cost of running this hardware. The hash rate, R, is typically mea- sured in millions of hashes per second or Mega- hashes (Mhash/s). This is combined with the power usage, P , of the hardware to get the energy efficiency of the hardware E = R/P (Mhash/J) which serves as a helpful statistic to compare hard- ware. Statistics are shown for a selection of hard- ware in Table 1. Initially mining took place on normal2 comput- ers. As Bitcoin gained popularity, there was some- thing akin to an arms race as miners attempted to increase their hash rate. Graphics Process- ing Units (GPUs) which can perform many par- allel calculations are well-adapted to Bitcoin min- ing. Standard programming interfaces, such as OpenCL or CUDA, made GPUs popular among 2Where ‘normal’ is defined as a general purpose com- puter, such as an IBM PC type architecture with an x86 CPU. Fig. 3: The exchange rate between Bitcoin and Dollars, based on aggregate statistics [6]. Bitcoin miners. Their higher hash rate compared with their lower energy footprint made them bet- ter suited to mining than normal CPUs. As the use of GPUs became more widespread, people were forced to look for alternatives to keep ahead of the crowd. Field Programmable Gate Arrays (FPGA) came into vogue for a brief pe- riod before Application Specific Integrated Cir- cuits (ASIC) came onto the scene. ASICS can per- form the Bitcoin hash at higher rates but with a much smaller energy requirement. The evolution of hardware for Bitcoin mining is described in de- tail in [7]. IV Energy Cost/Reward Trade Off Bitcoin is similar to other currencies, in that the exchange rate between Bitcoin and other curren- cies fluctuates over time. This in turn impacts on the viability of Bitcoin mining: if the value of a Bitcoin is less than the cost of the energy required to generated it then there is a disincentive to con- tinue mining. The exchange rate to US dollars is shown in Figure 3. On the other hand, as the number of people min- ing Bitcoin increases and the difficulty of mining follows suit, so the likelihood of discovering a valid block decreases. To overcome this, more powerful hardware is required to achieve the same success rate. However, since the cost of energy is a limiting factor, newer hardware will have to have a higher hash rate and a lower energy footprint. Thus, there is a trade off between two time vary- ing factors: first, the energy cost of discovering a block, Ce = E[t]PU ≈ D232PU = D232U RE where U is the unit cost for a Joule of energy; sec- ond is the cash reward for discovering the block, which is simply the reward for the block, in B, BTC USD Apr 2013 May 2013 Jun 2013 Jul 2013 Aug 2013 Sep 2013 Oct 2013 Nov 2013 Dec 2013 Jan 2014 Feb 2014 Mar 2014 Nov 2010 Mar 2011 Jul 2011 Nov 2011 Mar 2012 Jul 2012 Nov 2012 Mar 2013 Jul 2013 Nov 2013 Mar 2014PDF Image | Bitcoin Mining and its Energy Footprint
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