This paper uses a variant of the notion of \emph{inaccessible entropy} (Haitner, Reingold, Vadhan and Wee, STOC 2009), to give an alternative construction and proof for the fundamental result, first proved by Rompel (STOC 1990), that \emph{Universal One-Way Hash Functions (UOWHFs)} can be based on any one-way functions. We observe that a small tweak of any one-way function $f$ is already a weak form of a UOWHF: consider the function $F(x,i)$ that returns the $i$-bit-long prefix of $f(x)$. If $F$ were a UOWHF then given a random $x$ and $i$ it would be hard to come up with $x'\neq x$ such that $F(x,i)=F(x',i)$. While this may not be the case, we show (rather easily) that it is hard to sample $x'$ with almost full entropy among all the possible such values of $x'$. The rest of our construction simply amplifies and exploits this basic property.Combined with other recent work, the construction of three fundamental cryptographic primitives (Pseudorandom Generators, Statistically Hiding Commitments and UOWHFs) out of one-way functions is now to a large extent unified. In particular, all three constructions rely on and manipulate computational notions of entropy in similar ways. Pseudorandom Generators rely on the well-established notion of pseudoentropy, whereas Statistically Hiding Commitments and UOWHFs rely on the newer notion of inaccessible entropy.

中文翻译：

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不可访问的熵II：IE功能和通用单向哈希

本文使用\ emph {inaccessible entropy}概念的变体（Haitner，Reingold，Vadhan和Wee，STOC，2009年）为基本结果提供了另一种构造和证明，首先由Rompel证明（STOC，1990年）， \ emph {通用单向哈希函数（UOWHF）}可以基于任何单向函数。我们观察到任何单向函数$ f $的细微调整已经是UOWHF的一种弱形式：考虑函数$ F（x，i）$返回$ i $位长前缀$ f（ x）$。如果$ F $是一个UOWHF，则给定一个随机的$ x $和$ i $，将很难得出$ x'\ neq x $使得$ F（x，i）= F（x'，i） $。尽管可能并非如此，但我们（相当容易）证明，在所有可能的$ x'$值中几乎没有完全熵的情况下很难对$ x'$进行采样。我们其余的构造只是简单地放大和利用了这一基本特性。结合最近的其他工作，单向函数构造了三个基本的密码基元（伪随机数生成器，统计隐藏承诺和UOWHF），现在已在很大程度上统一了。特别地，所有这三种构造都以相似的方式依赖和操纵熵的计算概念。伪随机生成器依赖于公认的伪熵概念，而统计隐藏承诺和UOWHF依赖于不可访问的熵的新概念。这三种构造都以类似的方式依赖和操纵熵的计算概念。伪随机生成器依赖于公认的伪熵概念，而统计隐藏承诺和UOWHF依赖于不可访问的熵的新概念。这三种构造都以类似的方式依赖和操纵熵的计算概念。伪随机生成器依赖于公认的伪熵概念，而统计隐藏承诺和UOWHF依赖于不可访问的熵的新概念。