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. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Maurer, U., & Tessaro, S. (2008). Basing PRFs on constant-query weak PRFs: Minimizing assumptions for efficient symmetric cryptography. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5350 LNCS, pp. 161–178). https://doi.org/10.1007/978-3-540-89255-7_11
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