**On the Memory-Hardness of Data-Independent Password-Hashing Functions**

*Joël Alwen and Peter Gaži and Chethan Kamath and Karen Klein and Georg Osang and Krzysztof Pietrzak and Leonid Reyzin and Michal Rolínek and Michal Rybár*

**Abstract: **We show attacks on five data-independent memory-hard functions (iMHF)
that were submitted to the password hashing competition. Informally, an MHF is a
function which cannot be evaluated on dedicated hardware, like ASICs, at
significantly lower energy and/or hardware cost than evaluating a single
instance on a standard single-core architecture. Data-independent means the
memory access pattern of the function is independent of the input; this makes
iMHFs harder to construct than data-dependent ones, but the latter can be
attacked by various side-channel attacks.

Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a good measure for the cost of evaluating the iMHF on an ASIC. If n denotes the number of nodes of a DAG (or equivalently, the number of operations --- typically hash function calls --- of the underlying iMHF), its pebbling complexity must be close to n^2 for the iMHF to be memory-hard. We show that the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit can be attacked with complexity O(n^{1.75}); the data-independent phase of Pomelo (a finalist of the password hashing competition) and Lyra2 (also a finalist) can be attacked with complexity O(n^{1.83}) and O(n^{1.67}), respectively.

For our attacks we use and extend the technique developed by [Alwen-Blocki'16], who show that the pebbling complexity of a DAG can be upper bounded in terms of its depth-robustness.

**Category / Keywords: **password hashing, memory hardness

**Date: **received 16 Aug 2016, last revised 22 Aug 2016

**Contact author: **peter gazi at ist ac at

**Available format(s): **PDF | BibTeX Citation

**Version: **20160822:100323 (All versions of this report)

**Short URL: **ia.cr/2016/783

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