How to construct random functions
Journal of the ACM (JACM)
Pseudo-random permutation generators and cryptographic composition
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Expanding Pseudorandom Functions; or: From Known-Plaintext Security to Chosen-Plaintext Security
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Indistinguishability of Random Systems
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
A Fast and Key-Efficient Reduction of Chosen-Ciphertext to Known-Plaintext Security
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
The security of triple encryption and a framework for code-based game-playing proofs
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Expanding weak PRF with small key size
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
A Fast and Key-Efficient Reduction of Chosen-Ciphertext to Known-Plaintext Security
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Weak Pseudorandom Functions in Minicrypt
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Basing PRFs on Constant-Query Weak PRFs: Minimizing Assumptions for Efficient Symmetric Cryptography
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A Leakage-Resilient Mode of Operation
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Leakage-resilient RFID authentication with forward-privacy
RFIDSec'10 Proceedings of the 6th international conference on Radio frequency identification: security and privacy issues
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We investigate a general class of (black-box) constructions for range extension of weak pseudorandom functions: a construction based on mindependent functions F1,...,Fmis given by a set of strings over {1,...,m}*, where for example $\{\langle{2}\rangle, \langle{1,2}\rangle\}$ corresponds to the function X驴[F2(X),F2(F1(X))]. All efficient constructions for range expansion of weak pseudorandom functions that we are aware of are of this form.We completely classify such constructions as good, bador ugly, where the good constructions are those whose security can be proven via a black-box reduction, the bad constructions are those whose insecurity can be proven via a black-box reduction, and the ugly constructions are those which are neither good nor bad.Our classification shows that the range expansion from [10] is optimal, in the sense that it achieves the best possible expansion (2m驴 1 when using mkeys).Along the way we show that for weak quasirandomfunctions (i.e. in the information theoretic setting), all constructions which are not bad --- in particular all the ugly ones --- are secure.