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Paper 2016/610
The GGM Function Family is Weakly One-Way
Aloni Cohen and 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.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- A minor revision of an IACR publication in TCC 2016
- Keywords
- Goldreich-Goldwasser-Micali (GGM)one-way functionspseudorandom functions
- Contact author(s)
- aloni @ mit edu; saleet @ mit edu
- History
- 2016-09-12: last of 3 revisions
- 2016-06-14: received
- See all versions
- Short URL
- https://ia.cr/2016/610
- License
-
CC BY