| This is a cryptography thesis, and the focus is on applications of cryptographic hash functions.;Hash functions, as a cryptographic primitive, are ubiquitous in their potential for application. In essence, a hash function distills data of any size into a fingerprint, where inverting this function is considered computationally infeasible.;After the introduction and preliminary work, the body of this paper is divided into chapters which report the results of three significant research problems.;The first problem is the study of building trapdoors into hash functions. How do we make a hash function that can be inverted with knowledge of a secret key? There are two main problems: the algorithm must not reveal the existence of the trapdoor, and use of the trapdoor must not reveal its existence. Finally, we offer a solution using elliptic curves.;The second problem is that of time-lock encryption, that is, how to encrypt a message such that it can not be opened before a given date. We start with the assumption of a centralized authority issuing time-lock encryption keys, and study ways for that party to certify intermediate authorities to do the same task, while retaining verifiability. We offer a solution using a structure developed for the Bitcoin wallet client.;The third is constructing a protocol for increased privacy for users on the Bitcoin network. A significant portion of this thesis is given over to the background of Bitcoin, as it also turned out to be helpful for our time-lock encryption solution. We construct a method for Bitcoin spending privacy using contracts, a simple but powerful mechanism for automating transactions and minimizing trust in the world of cryptocurrencies. |
