# From Non-adaptive to Adaptive Pseudorandom Functions

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## Abstract

Unlike the standard notion of pseudorandom functions (PRF), a *non-adaptive* PRF is only required to be indistinguishable from a random function in the eyes of a *non-adaptive* distinguisher (i.e., one that prepares its oracle calls in advance). A recent line of research has studied the possibility of a *direct* construction of adaptive PRFs from non-adaptive ones, where direct means that the constructed adaptive PRF uses only few (ideally, constant number of) calls to the underlying non-adaptive PRF. Unfortunately, this study has only yielded negative results (e.g., Myers in Advances in Cryptology – EUROCRYPT 2004, pp. 189–206, 2004; Pietrzak in Advances in Cryptology – CRYPTO 2005, pp. 55–65, 2005).

We give an affirmative answer to the above question, presenting a direct construction of adaptive PRFs from non-adaptive ones. The suggested construction is extremely simple, a composition of the non-adaptive PRF with an appropriate pairwise independent hash function.

## Keywords

Function Family Message Authentication Code Pseudorandom Generator Pseudorandom Function Oracle Access## Notes

### Acknowledgements

We are very grateful to Omer Reingold for very useful discussions, and for challenging the second author with this research question a long while ago. We also thank the anonymous referees for their useful comments.

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