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--- a/handouts/ho08.tex	Thu Jun 29 16:48:10 2017 +0100
+++ b/handouts/ho08.tex	Thu Jul 06 13:51:18 2017 +0100
@@ -588,6 +588,19 @@
 \url{https://blockchain.info/pools}
 \end{center}
 
+\noindent Here is an interesting problem: You are part of a lottery
+pool, if you chip in some of the money to buy a lottery ticket. In
+this setting it is clear when you are in or outside of the pool. But
+how do you make sure people work hard in a mining pool in order to
+justify a fraction of any reward? If evil me had its way, I would just
+claim I do work and then sit back and relax. Or even if I do some work
+for a mining pool and I happen to find a correct salt, I would keep it
+secret and submit it to the bitcoin network on the ``side''. Actually,
+the idea of mining pools has opened up a full can of interesting
+problems.
+
+
+
 \subsubsection*{Bitcoins for Real}
 
 Let us now turn to the nitty gritty details. As a participant
@@ -944,10 +957,34 @@
 \end{center}
 
 \noindent where the author proposes ways of publishing information
-that is censor resistant as part of the blockchain. The idea is that
+that is censor-resistant as part of the blockchain. The idea is that
 if a government wants to use Bitcoins, it would also have to put up
 with plain-text data that can be included in a transaction.
 
+Ken Shirrif in his blog at
+
+\begin{center}\small
+\url{http://www.righto.com/2014/02/bitcoin-mining-hard-way-algorithms.html}
+\end{center}  
+
+\noindent writes that every day the electricity consumption of mining
+for bitcoins is roughly 15 Mega Watts---the energy consumption of a country
+like Cambodia. He writes:
+
+\begin{quote}
+  \it{}``The difficulty of mining a block is astounding. At the
+  current difficulty, the chance of a hash succeeding is a bit less
+  than one in $10^{19}$. Finding a successful hash is harder than
+  finding a particular grain of sand from all the grains of sand on
+  Earth. To find a hash every ten minutes, the Bitcoin hash rate needs
+  to be insanely large. Currently, the miners on the Bitcoin network
+  are doing about 25 million gigahashes per second. That is, every
+  second about 25,000,000,000,000,000 blocks gets hashed. I estimate
+  (very roughly) that the total hardware used for Bitcoin mining cost
+  tens of millions of dollars and uses as much power as the country of
+  Cambodia.''
+\end{quote}  
+
 \end{document}
 
 bit coin

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