This thesis has been realized for the Master of Science in Mathematical Engineering at Politecnico di Milano.
Insufficient privacy is recognized to be one of the major vulnerabilities of the Bitcoin's protocol, even because it undermines its fungibility. Bitcoin eliminates the need for a trusted third party, but mainly faces users' privacy by hiding them behind pseudonymous addresses. This work aims at presenting Confidential Transactions, the first proposal for a transaction format with encrypted amounts in Bitcoin, which would strongly increase value privacy. It exploits homomorphic encryption which does not remarkably hurt universal validation of transactions, a crucial premise for the achievement of a distributed consensus on the order of valid transactions.