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The GGM function family is a weakly one-way family of functions. (English) Zbl 1369.94527
Hirt, Martin (ed.) et al., Theory of cryptography. 14th international conference, TCC 2016-B, Beijing, China, October 31 – November 3, 2016. Proceedings. Part I. Berlin: Springer (ISBN 978-3-662-53640-7/pbk; 978-3-662-53641-4/ebook). Lecture Notes in Computer Science 9985, 84-107 (2016).
Summary: We give the first demonstration of the cryptographic hardness of the Goldreich-Goldwasser-Micali (GGM) function family when the secret key is exposed. We prove that for any constant \(\epsilon >0\), the GGM family is a \(1/n^{2+\varepsilon}\)-weakly one-way family of functions, when the lengths of secret key, inputs, and outputs are equal. Namely, any efficient algorithm fails to invert GGM with probability at least \(1/n^{2+\epsilon}\) – even when given the secret key.{
} Additionally, we state natural conditions under which the GGM family is strongly one-way.
For the entire collection see [Zbl 1347.94003].
MSC:
94A60 Cryptography
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