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Hardness-Preserving Reductions via Cuckoo Hashing
arXiv - CS - Cryptography and Security Pub Date : 2021-05-04 , DOI: arxiv-2105.01409
Itay Berman, Iftach Haitner, Ilan Komargodski, Moni Naor

The focus of this work is \emph{hardness-preserving} transformations of somewhat limited pseudorandom functions families (PRFs) into ones with more versatile characteristics. Consider the problem of \emph{domain extension} of pseudorandom functions: given a PRF that takes as input elements of some domain $U$, we would like to come up with a PRF over a larger domain. Can we do it with little work and without significantly impacting the security of the system? One approach is to first hash the larger domain into the smaller one and then apply the original PRF. Such a reduction, however, is vulnerable to a "birthday attack": after $\sqrt{\size{U}}$ queries to the resulting PRF, a collision (\ie two distinct inputs having the same hash value) is very likely to occur. As a consequence, the resulting PRF is \emph{insecure} against an attacker making this number of queries. In this work we show how to go beyond the aforementioned birthday attack barrier by replacing the above simple hashing approach with a variant of \textit{cuckoo hashing}, a hashing paradigm that resolves collisions in a table by using two hash functions and two tables, cleverly assigning each element to one of the two tables. We use this approach to obtain: (i) a domain extension method that requires {\em just two calls} to the original PRF, can withstand as many queries as the original domain size, and has a distinguishing probability that is exponentially small in the amount of non-cryptographic work; and (ii) a {\em security-preserving} reduction from non-adaptive to adaptive PRFs.

中文翻译:

通过布谷鸟哈希来减少硬度

这项工作的重点是将某些有限的伪随机函数族(PRF)转换为具有更通用特性的\ emph {hardness-preserving}转换。考虑一下伪随机函数\ emph {domain extension}的问题:给定一个PRF作为某些域$ U $的输入元素,我们想在一个更大的域上提出一个PRF。我们可以在不花大功夫的情况下做到这一点,而又不会显着影响系统的安全性吗?一种方法是先将较大的域散列为较小的域,然后再应用原始PRF。但是,这种减少很容易受到“生日攻击”的影响:在对生成的PRF进行$ \ sqrt {\ size {U}} $查询之后,很可能发生冲突(即两个具有相同哈希值的不同输入)发生。作为结果,针对攻击者进行此数量的查询后,最终的PRF为\ emph {insecure}。在这项工作中,我们展示了如何通过使用\ textit {cuckoo hashing}的变体替换上述简单的哈希方法来超越上述的生日攻击障碍,该变体是通过使用两个哈希函数和两个表来解决表中的冲突的哈希范式,巧妙地将每个元素分配给两个表之一。我们使用这种方法来获得:(i)一种域扩展方法,它需要对原始PRF进行{\ em两次调用},可以承受与原始域大小一样多的查询,并且在非加密工作量;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。在这项工作中,我们展示了如何通过使用\ textit {cuckoo hashing}的变体替换上述简单的哈希方法来超越上述的生日攻击障碍,该变体是通过使用两个哈希函数和两个表来解决表中的冲突的哈希范式,巧妙地将每个元素分配给两个表之一。我们使用这种方法来获得:(i)一种域扩展方法,该方法需要对原始PRF进行{\ em两次调用},可以承受与原始域大小一样多的查询,并且在非加密工作量;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。在这项工作中,我们展示了如何通过使用\ textit {cuckoo hashing}的变体替换上述简单的哈希方法来超越上述的生日攻击障碍,该变体是通过使用两个哈希函数和两个表来解决表中的冲突的哈希范式,巧妙地将每个元素分配给两个表之一。我们使用这种方法来获得:(i)一种域扩展方法,它需要对原始PRF进行{\ em两次调用},可以承受与原始域大小一样多的查询,并且在非加密工作量;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。哈希范式,它通过使用两个哈希函数和两个表来解决表中的冲突,并将每个元素巧妙地分配给两个表之一。我们使用这种方法来获得:(i)一种域扩展方法,它需要对原始PRF进行{\ em两次调用},可以承受与原始域大小一样多的查询,并且在非加密工作量;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。一个哈希表范式,它通过使用两个哈希函数和两个表来解决表中的冲突,并巧妙地将每个元素分配给两个表之一。我们使用这种方法来获得:(i)一种域扩展方法,它需要对原始PRF进行{\ em两次调用},可以承受与原始域大小一样多的查询,并且在非加密工作量;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。并且在非加密工作量方面的区分概率极小;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。并且在非加密工作量方面的区分概率极小;(ii){\ em security-preserving}从非自适应PRF减少到自适应PRF。
更新日期:2021-05-05
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