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Title:
The GGM Function Family is Weakly One-Way
Authors: Aloni Cohen, Saleet Klein
Abstract: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+\epsilon}-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.
ePrint: https://eprint.iacr.org/2016/610
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