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Basing {PRF}s on Constant-Query Weak {PRF}s: Minimizing Assumptions for Efficient Symmetric Cryptography

Ueli Maurer and Stefano Tessaro

Although it is well known that all basic private-key cryptographic primitives can be built from one-way functions, finding weak assumptions from which practical implementations of such primitives exist remains a challenging task. Towards this goal, this paper introduces the notion of a constant-query weak PRF}, a function with a secret key which is computationally indistinguishable from a truly random function when evaluated at a constant} number $s$ of known random inputs, where $s$ can be as small as two.

We provide iterated constructions of (arbitrary-input-length) PRFs from constant-query weak PRFs that even improve the efficiency of previous constructions based on the stronger assumption of a weak PRF (where polynomially many evaluations are allowed).

One of our constructions directly provides a new mode of operation using a constant-query weak PRF for IND-CPA symmetric encryption which is essentially as efficient as conventional PRF-based counter-mode encryption.

Furthermore, our constructions yield efficient modes of operation for keying hash functions (such as MD5 and SHA-1) to obtain iterated PRFs (and hence MACs) which rely solely on the assumption that the underlying compression function is a constant-query weak PRF, which is the weakest assumption ever considered in this context.