Cuckoo Hashing in Cryptography: Optimal Parameters, Robustness and Applications

Cuckoo hashing is a powerful primitive that enables storing items using small space with efficient querying. At high level, cuckoo maps n into b entries at most $$\ell $$ such each item placed one of k randomly chosen entries. Additionally, there an overflow stash can store s items. Many cryptographic primitives rely upon to privately embed and query data where it integral ensure failure probability when constructing tables as directly relates the privacy guarantees. As our main result, we present more query-efficient construction hash functions. For $$\epsilon , overhead scheme $$O(1 + \sqrt{\log (1/\epsilon )/\log n})$$ . Our has quadratically smaller than prior works for any target We also prove lower bounds matching construction. improvements come from new understanding locality failures sets initiate study robust input set may be knowledge functions $$\tilde{O}(\log \lambda )$$ against $$\textsf{poly}(\lambda adversaries. Furthermore, showing this tight extending previous approaches large stashes or cannot obtain robustness except $$\varOmega (n)$$ overhead. applications results, improved constructions batch codes PIR. In particular, explicit code blackbox reduction single-query PIR