Paper 2017/442
On the DepthRobustness and Cumulative Pebbling Cost of Argon2i
Jeremiah Blocki and Samson Zhou
Abstract
Argon2i is a dataindependent memory hard function that won the password hashing competition. The password hashing algorithm has already been incorporated into several open source crypto libraries such as libsodium. In this paper we analyze the cumulative memory cost of computing Argon2i. On the positive side we provide a lower bound for Argon2i. On the negative side we exhibit an improved attack against Argon2i which demonstrates that our lower bound is nearly tight. In particular, we show that (1) An Argon2i DAG is $\left(e,O\left(n^3/e^3\right)\right))$reducible. (2) The cumulative pebbling cost for Argon2i is at most $O\left(n^{1.768}\right)$. This improves upon the previous best upper bound of $O\left(n^{1.8}\right)$ [Alwen and Blocki, EURO S&P 2017]. (3) Argon2i DAG is $\left(e,\tilde{\Omega}\left(n^3/e^3\right)\right))$depth robust. By contrast, analysis of [Alwen et al., EUROCRYPT 2017] only established that Argon2i was $\left(e,\tilde{\Omega}\left(n^2/e^2\right)\right))$depth robust. (4) The cumulative pebbling complexity of Argon2i is at least $\tilde{\Omega}\left( n^{1.75}\right)$. This improves on the previous best bound of $\Omega\left( n^{1.66}\right)$ [Alwen et al., EUROCRYPT 2017] and demonstrates that Argon2i has higher cumulative memory cost than competing proposals such as Catena or Balloon Hashing. We also show that Argon2i has high {\em fractional} depthrobustness which strongly suggests that datadependent modes of Argon2 are resistant to spacetime tradeoff attacks.
Metadata
 Available format(s)
 Category
 Secretkey cryptography
 Publication info
 Published by the IACR in TCC 2017
 Keywords
 Argon2iMemory Hard FunctionsDepthRobustness
 Contact author(s)
 jblocki @ purdue edu
 History
 20170922: last of 4 revisions
 20170523: received
 See all versions
 Short URL
 https://ia.cr/2017/442
 License

CC BY
BibTeX
@misc{cryptoeprint:2017/442, author = {Jeremiah Blocki and Samson Zhou}, title = {On the DepthRobustness and Cumulative Pebbling Cost of Argon2i}, howpublished = {Cryptology ePrint Archive, Paper 2017/442}, year = {2017}, note = {\url{https://eprint.iacr.org/2017/442}}, url = {https://eprint.iacr.org/2017/442} }