Information dispersal algorithms (IDA) are used for distributed data storage because they simultaneously provide security, reliability and space efficiency, constituting a trustworthy computing framework for many critical applications, such as cloud computing, in the information society. In the most general sense, this is achieved by dividing data into smaller pieces and then storing these pieces on different servers such that access to a stored piece reveals only a very limited amount of information about the original data. The effectiveness of IDA is predicated on spreading of risk across servers that provides protection against loss of data due to disasters and intrusion. The main objective of this dissertation is to develop new information dispersal techniques together with efficient reconstruction algorithms that will perform well in the presence of adversaries and erratic servers. The new techniques consider a general model of risk distribution that is appropriate for situations related to cloud computing, sensor networks, information hiding, and internet voting. We develop verifiable IDA algorithms so that a client can distribute the data among a set of servers, of which a certain subset might be faulty or compromised, in such a way that the client can always recover the stored data correctly, independent of the behavior of the faulty servers, and not have the data compromised to an adversary. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]