590 

   591 \noindent Here is an interesting problem: You are part of a lottery

   592 pool, if you chip in some of the money to buy a lottery ticket. In

   593 this setting it is clear when you are in or outside of the pool. But

   594 how do you make sure people work hard in a mining pool in order to

   595 justify a fraction of any reward? If evil me had its way, I would just

   596 claim I do work and then sit back and relax. Or even if I do some work

   597 for a mining pool and I happen to find a correct salt, I would keep it

   598 secret and submit it to the bitcoin network on the ``side''. Actually,

   599 the idea of mining pools has opened up a full can of interesting

   600 problems.

   601 

   602 

   963 

   964 Ken Shirrif in his blog at

   965 

   966 \begin{center}\small

   967 \url{http://www.righto.com/2014/02/bitcoin-mining-hard-way-algorithms.html}

   968 \end{center}  

   969 

   970 \noindent writes that every day the electricity consumption of mining

   971 for bitcoins is roughly 15 Mega Watts---the energy consumption of a country

   972 like Cambodia. He writes:

   973 

   974 \begin{quote}

   975   \it{}``The difficulty of mining a block is astounding. At the

   976   current difficulty, the chance of a hash succeeding is a bit less

   977   than one in $10^{19}$. Finding a successful hash is harder than

   978   finding a particular grain of sand from all the grains of sand on

   979   Earth. To find a hash every ten minutes, the Bitcoin hash rate needs

   980   to be insanely large. Currently, the miners on the Bitcoin network

   981   are doing about 25 million gigahashes per second. That is, every

   982   second about 25,000,000,000,000,000 blocks gets hashed. I estimate

   983   (very roughly) that the total hardware used for Bitcoin mining cost

   984   tens of millions of dollars and uses as much power as the country of

   985   Cambodia.''

   986 \end{quote}