Range extension for weak PRFs the good the bad and the ugly

K.Z. Pietrzak, J. Sjödin, in:, Springer, 2007, pp. 517–533.

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Abstract
We investigate a general class of (black-box) constructions for range extension of weak pseudorandom functions: a construction based on m independent functions F 1,...,F m is given by a set of strings over {1,...,m}*, where for example {〈2〉, 〈1,2〉} corresponds to the function X ↦[F 2(X),F 2(F 1(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, bad or 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 (2 m  − 1 when using m keys). Along the way we show that for weak quasirandom functions (i.e. in the information theoretic setting), all constructions which are not bad – in particular all the ugly ones – are secure.
Publishing Year
Date Published
2007-06-12
Acknowledgement
This work was partially supported by the Zurich Information Security Center. It represents the views of the authors.
Volume
4515
Page
517 - 533
Conference
EUROCRYPT: Theory and Applications of Cryptographic Techniques
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Pietrzak KZ, Sjödin J. Range extension for weak PRFs the good the bad and the ugly. In: Vol 4515. Springer; 2007:517-533. doi:10.1007/978-3-540-72540-4_30
Pietrzak, K. Z., & Sjödin, J. (2007). Range extension for weak PRFs the good the bad and the ugly (Vol. 4515, pp. 517–533). Presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, Springer. https://doi.org/10.1007/978-3-540-72540-4_30
Pietrzak, Krzysztof Z, and Johan Sjödin. “Range Extension for Weak PRFs the Good the Bad and the Ugly,” 4515:517–33. Springer, 2007. https://doi.org/10.1007/978-3-540-72540-4_30.
K. Z. Pietrzak and J. Sjödin, “Range extension for weak PRFs the good the bad and the ugly,” presented at the EUROCRYPT: Theory and Applications of Cryptographic Techniques, 2007, vol. 4515, pp. 517–533.
Pietrzak KZ, Sjödin J. 2007. Range extension for weak PRFs the good the bad and the ugly. EUROCRYPT: Theory and Applications of Cryptographic Techniques, LNCS, vol. 4515. 517–533.
Pietrzak, Krzysztof Z., and Johan Sjödin. Range Extension for Weak PRFs the Good the Bad and the Ugly. Vol. 4515, Springer, 2007, pp. 517–33, doi:10.1007/978-3-540-72540-4_30.

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