A mathematical problem for security analysis of hash functions and pseudorandom generators

Koji Nuida, Takuro Abe, Shizuo Kaji, Toshiaki Maeno, Yasuhide Numata

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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 con-crete 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 crypto-graphic applications of FDPs and on mathematical studies on FDPs themselves.

Original languageEnglish
Pages (from-to)169-194
Number of pages26
JournalInternational Journal of Foundations of Computer Science
Volume26
Issue number2
DOIs
Publication statusPublished - Feb 8 2015

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)

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