2024-03-28T12:03:00Z
https://soar-ir.repo.nii.ac.jp/oai
oai:soar-ir.repo.nii.ac.jp:00019877
2022-12-14T03:45:51Z
1169:1170
A Mathematical Problem for Security Analysis of Hash Functions and Pseudorandom Generators
Nuida, Koji
Abe, Takuro
Kaji, Shizuo
Maeno, Toshiaki
Numata, Yasuhide
Function density problem
hash function
pseudorandom generator
security evaluation
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 FDFs, 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.
Article
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE. 26(2):169-194 (2015)
journal article
WORLD SCIENTIFIC PUBL CO PTE LTD
2015-02
application/pdf
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
2
26
169
194
0129-0541
AA10742015
https://soar-ir.repo.nii.ac.jp/record/19877/files/A_Mathematical_Problem_for_Security_Analysis_of_Hash_Functions_and_Pseudorandom_Generators.pdf
eng
10.1142/S0129054115500100
https://doi.org/10.1142/S0129054115500100
Electronic version of an article published as International Journal of Foundations of Computer Science, 26(2), 2015, 169-194 DOI: 10.1142/s0129054115500100. © World Scientific Publishing Company, https://doi.org/10.1142/s0129054115500100