Hardness-Preserving Reductions via Cuckoo Hashing

Itay Berman, Iftach Haitner, Ilan Komargodski*, Moni Naor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The focus of this work is hardness-preserving transformations of somewhat limited pseudorandom functions families (PRFs) into ones with more versatile characteristics. Consider the problem of 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 |U| queries to the resulting PRF, a collision (i.e., two distinct inputs having the same hash value) is very likely to occur. As a consequence, the resulting PRF is 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 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 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 security-preserving reduction from non-adaptive to adaptive PRFs.

Original languageEnglish
Pages (from-to)361-392
Number of pages32
JournalJournal of Cryptology
Issue number2
StatePublished - 15 Apr 2019


FundersFunder number
Check Point Institute for Information Security
Israel Science Foundation
Defense Advanced Research Projects Agency
Weizmann Institute of Science
David and Lucile Packard Foundation
Air Force Office of Scientific ResearchFA9550-15-1-0262
National Science FoundationCNS-1413920, CNS-1350619
Horizon 2020 Framework Programme638121
Israeli Centers for Research Excellence4/11
Army Research OfficeW911NF-15-C-0236, W911NF-15-C-0226


    • Cuckoo hashing
    • Hardness preserving reductions
    • Pseudorandom functions


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