A pseudorandom function family (PRF) can be made more usable and more secure by first hashing the input into a smaller domain. This approach is used to achieve ``PRF domain extension" using a short, e.g., fixed, input length PRF to get a variable-length PRF. Such reductions, however, are vulnerable to a ``birthday attack": after squareroot of of the range size 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 birthday attack barrier by replacing the above simple hashing approach with a variant of cuckoo hashing, a hashing paradigm typically used for resolving hash 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:
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