Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A mathematical problem for security analysis of hash functions and
  pseudorandom generators   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.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci