A mathematical problem for security analysis of hash functions and pseudorandom generators
This work addresses foundational security issues in cryptography for researchers, but it is incremental as it builds on existing concepts without delivering practical outcomes.
The paper tackles the problem of theoretical security analysis for hash functions and pseudorandom generators by introducing Function Density Problems (FDPs) and connecting them to these cryptographic topics, aiming to propose new frameworks rather than providing concrete results.
In this paper, we specify a class of mathematical problems, which we refer to as "Function Density Problems" (FDPs, in short), and point out novel connections of FDPs to the following two cryptographic topics; theoretical security evaluations of keyless hash functions (such as SHA-1), and constructions of provably secure pseudorandom generators (PRGs) with some enhanced security property introduced by Dubrov and Ishai [STOC 2006]. Our argument aims at proposing new theoretical frameworks for these topics (especially for the former) based on FDPs, rather than providing some concrete and practical results on the topics. We also give some examples of mathematical discussions on FDPs, which would be of independent interest from mathematical viewpoints. Finally, we discuss possible directions of future research on other cryptographic applications of FDPs and on mathematical studies on FDPs themselves.