CT-ISG: On the Design of Secure Hash Functions and Privacy-Preserving Protocols

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While the mathematical study of cryptography has yielded a rich theory, and while the use of cryptography has become quite widespread, there is unfortunately still a significant gap between the theory and practice of cryptography. The goal of this research is to try to bridge this gap. The emphasis is on the design and analysis of fundamental cryptographic primitives that are practical yet theoretically sound. This research focuses on two specific areas: the design and use of secure hash functions, and the design of more efficient privacy-preserving protocols. Because of recently discovered weaknesses in industry-standard hash functions, there is renewed interest and urgency to study the basic design principles of hash functions, as well as how such hash functions should be appropriately used in applications. Indeed, although hash functions were originally designed to serve as message digests, which should provide a form of security known as collision resistance, they are actually used in many different types of applications where the security requirements may be somewhat different: sometimes the security requirement of the hash function in a given application may be weaker than, stronger than, or perhaps just incomparable to collision resistance. This project investigates new methodologies for constructing hash functions that satisfy the various security requirements required in applications, as well as how the applications themselves may be adapted so as to minimize the security requirements placed on the hash function. With the widespread use of computers and the Internet in daily transactions, concerns about privacy issues have taken on new urgency. One key aspect of privacy is deniability: if a user runs a protocol, it should not be possible for an eavesdropper, or even another participant in the protocol, to convince a third party that the transaction actually occurred. While there are compelling reasons to focus on this area for its own sake, there are also a number of technical issues that arise that overlap with some of the subproblems associated with hash functions.