## Cryptology ePrint Archive: Report 2012/310

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

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

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 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.

Category / Keywords: foundations / foundations; hash functions; pseudo-randomness; cryptanalysis

Date: received 31 May 2012, last revised 28 Aug 2014

Contact author: k nuida at aist go jp

Available format(s): PDF | BibTeX Citation

Note: A preliminary version of this paper was presented at The 6th International Workshop on Security (IWSEC 2011), November 8-10, 2011

Short URL: ia.cr/2012/310

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