The GGM Function Family is Weakly One-Way

Aloni Cohen; Saleet Klein

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): PDF
Category: Foundations
Publication info: A minor revision of an IACR publication in TCC 2016
Keywords: Goldreich-Goldwasser-Micali (GGM)one-way functions pseudorandom 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

BibTeX

@misc{cryptoeprint:2016/610,
      author = {Aloni Cohen and Saleet Klein},
      title = {The {GGM} Function Family is Weakly One-Way},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/610},
      year = {2016},
      url = {https://eprint.iacr.org/2016/610}
}