Paper 2007/229
Domain Extension of Public Random Functions: Beyond the Birthday Barrier
Ueli Maurer and Stefano Tessaro
Abstract
A public random function is a random function that is accessible by all parties, including the adversary. For example, a (public) random oracle is a public random function $\{0,1\}^{*} \to \{0,1\}^n$. The natural problem of constructing a public random oracle from a public random function $\{0,1\}^{m} \to \{0,1\}^n$ (for some $m > n$) was first considered at Crypto 2005 by Coron et al.\ who proved the security of variants of the MerkleDamgård construction against adversaries issuing up to $O(2^{n/2})$ queries to the construction and to the underlying compression function. This bound is less than the square root of $n2^m$, the number of random bits contained in the underlying random function. In this paper, we investigate domain extenders for public random functions approaching optimal security. In particular, for all $\epsilon \in (0,1)$ and all functions $m$ and $\ell$ (polynomial in $n$), we provide a construction $\mathbf{C}_{\epsilon,m,\ell}(\cdot)$ which extends a public random function $\mathbf{R}: \{0,1\}^{n} \to \{0,1\}^n$ to a function $\mathbf{C}_{\epsilon,m,\ell}(\R): \{0,1\}^{m(n)} \to \{0,1\}^{\ell(n)}$ with timecomplexity polynomial in $n$ and $1/\epsilon$ and which is secure against adversaries which make up to $\Theta(2^{n(1\epsilon)})$ queries. A central tool for achieving high security are special classes of unbalanced bipartite expander graphs with small degree. The achievability of practical (as opposed to complexitytheoretic) efficiency is proved by a nonconstructive existence proof. Combined with the iterated constructions of Coron et al., our result leads to the first iterated construction of a hash function $\{0,1\}^{*} \to \{0,1\}^n$ from a component function $\{0,1\}^{n} \to \{0,1\}^n$ that withstands all recently proposed generic attacks against iterated hash functions, like Joux's multicollision attack, Kelsey and Schneier's secondpreimage attack, and Kelsey and Kohno's herding attacks.
Metadata
 Available format(s)
 PDF PS
 Publication info
 Published elsewhere. Appears at CRYPTO 2007. This is the full version.
 Keywords
 Hash FunctionsDomain ExtensionIndifferentiabilityBirthday Barrier
 Contact author(s)
 tessaros @ inf ethz ch
 History
 20070619: received
 Short URL
 https://ia.cr/2007/229
 License

CC BY
BibTeX
@misc{cryptoeprint:2007/229, author = {Ueli Maurer and Stefano Tessaro}, title = {Domain Extension of Public Random Functions: Beyond the Birthday Barrier}, howpublished = {Cryptology {ePrint} Archive, Paper 2007/229}, year = {2007}, url = {https://eprint.iacr.org/2007/229} }