CAREER: Design Principles for Cryptographic Hash Functions: Foundations, Primitives, and Transforms

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Cryptographic hash functions are ubiquitous in modern cryptography.They are an integral part of digital signature and public-keyencryption schemes, access control mechanisms, digital time-stampingroutines, message authentication codes, and file synchronizationutilities. They are implemented in point-of-sale terminals, ATMmachines, operating systems, web browsers, routers, and mobile phones,to name just a few. Yet the design and analysis of hash functions hasreceived relatively little attention from the cryptographic community,a shortcoming underscored by recent high-profile attacks on theoften-used MD5 and SHA-1 hash functions.This work aims to advance our understanding of cryptographic hashfunctions in theory and practice by developing three complementarythemes. First, it further solidifies the formal foundations ofhashing. This means establishing new and meaningful notions of whatmeans for a hash function to be "good". Additionally it explores thepowers and limitations of new analytic frameworks (for example,indifferentiability and human-ignorance), and search for a sharperview of design heuristics (in particular the random-oracle andideal-cipher models.) Second, it investigates the design of "small"hash functions, called compression functions, with small domains andfixed ranges. Designs based on permutations, blockciphers andtweakable blockciphers are especially interesting. Third, it developsmethods for transforming compression functions into "big" hashfunctions with flexible domains and ranges; traditionally, the rangeof a hash function is a string of a single fixed length. Alsotargetted is the problem of combining the outputs of multipleprimitives for the purpose of security preservation in the presence offaults.