  The popularity of digital currencies, especially cryptocurrencies, has been
continuously growing since the appearance of Bitcoin. Bitcoin's security lies
in a proof-of-work scheme, which requires high computational resources at the
miners. Despite advances in mobile technology, existing cryptocurrencies cannot
be maintained by mobile devices due to their low processing capabilities.
Mobile devices can only accommodate mobile applications (wallets) that allow
users to exchange credits of cryptocurrencies. In this work, we propose
LocalCoin, an alternative cryptocurrency that requires minimal computational
resources, produces low data traffic and works with off-the-shelf mobile
devices. LocalCoin replaces the computational hardness that is at the root of
Bitcoin's security with the social hardness of ensuring that all witnesses to a
transaction are colluders. Localcoin features (i) a lightweight proof-of-work
scheme and (ii) a distributed blockchain. We analyze LocalCoin for double
spending for passive and active attacks and prove that under the assumption of
sufficient number of users and properly selected tuning parameters the
probability of double spending is close to zero. Extensive simulations on real
mobility traces, realistic urban settings, and random geometric graphs show
that the probability of success of one transaction converges to 1 and the
probability of the success of a double spending attempt converges to 0.
