  Anonymity in Bitcoin, a peer-to-peer electronic currency system, is a
complicated issue. Within the system, users are identified by public-keys only.
An attacker wishing to de-anonymize its users will attempt to construct the
one-to-many mapping between users and public-keys and associate information
external to the system with the users. Bitcoin tries to prevent this attack by
storing the mapping of a user to his or her public-keys on that user's node
only and by allowing each user to generate as many public-keys as required. In
this chapter we consider the topological structure of two networks derived from
Bitcoin's public transaction history. We show that the two networks have a
non-trivial topological structure, provide complementary views of the Bitcoin
system and have implications for anonymity. We combine these structures with
external information and techniques such as context discovery and flow analysis
to investigate an alleged theft of Bitcoins, which, at the time of the theft,
had a market value of approximately half a million U.S. dollars.
