UC San Diego

Cryptographic hash functions deterministically generate a short digest225}0s̀ummary'' of an input message. Their functionality and perceived security properties have contributed to their use in a wide variety of applications. Unfortunately, traditional design approaches for hash functions target only a single application. This gap between use and design has lead to hash functions not providing the security properties required by certain uses, and, in turn, to vulnerabilities in applications. This thesis argues for the construction of multi-property hash functions. Such a function should enjoy strong guarantees that it simultaneously provides multiple, disparate security properties, while remaining efficient and easy to use. That is, these hash functions are built to reflect the diverse needs of applications. Towards this end, we introduce the notion of a multi-property-preserving domain extension transform, which formalizes the goal of multi- property hashing for a key step in hash design. By analyzing existing transforms from the lense of multi- property-preservation, we explain the inability of traditional hash designs to be multi-property. We propose new domain extension transforms, provide new techniques for their formal analysis in modern cryptography's framework of provable security, and use the techniques to show that the proposed constructions provide the multi- property-preservation guarantees needed to build the next generation of hash functions