conference paper
Efficiently computing data-independent memory-hard functions
LNCS
published
yes
Joel F
Alwen
author 2A8DFA8C-F248-11E8-B48F-1D18A9856A87
Jeremiah
Blocki
author
KrPi
department
CRYPTO: International Cryptology Conference
A memory-hard function (MHF) f is equipped with a space cost σ and time cost τ parameter such that repeatedly computing fσ,τ on an application specific integrated circuit (ASIC) is not economically advantageous relative to a general purpose computer. Technically we would like that any (generalized) circuit for evaluating an iMHF fσ,τ has area × time (AT) complexity at Θ(σ2 ∗ τ). A data-independent MHF (iMHF) has the added property that it can be computed with almost optimal memory and time complexity by an algorithm which accesses memory in a pattern independent of the input value. Such functions can be specified by fixing a directed acyclic graph (DAG) G on n = Θ(σ ∗ τ) nodes representing its computation graph. In this work we develop new tools for analyzing iMHFs. First we define and motivate a new complexity measure capturing the amount of energy (i.e. electricity) required to compute a function. We argue that, in practice, this measure is at least as important as the more traditional AT-complexity. Next we describe an algorithm A for repeatedly evaluating an iMHF based on an arbitrary DAG G. We upperbound both its energy and AT complexities per instance evaluated in terms of a certain combinatorial property of G. Next we instantiate our attack for several general classes of DAGs which include those underlying many of the most important iMHF candidates in the literature. In particular, we obtain the following results which hold for all choices of parameters σ and τ (and thread-count) such that n = σ ∗ τ. -The Catena-Dragonfly function of [FLW13] has AT and energy complexities O(n1.67). -The Catena-Butterfly function of [FLW13] has complexities is O(n1.67). -The Double-Buffer and the Linear functions of [CGBS16] both have complexities in O(n1.67). -The Argon2i function of [BDK15] (winner of the Password Hashing Competition [PHC]) has complexities O(n7/4 log(n)). -The Single-Buffer function of [CGBS16] has complexities O(n7/4 log(n)). -Any iMHF can be computed by an algorithm with complexities O(n2/ log1 −ε(n)) for all ε > 0. In particular when τ = 1 this shows that the goal of constructing an iMHF with AT-complexity Θ(σ2 ∗ τ ) is unachievable. Along the way we prove a lemma upper-bounding the depth-robustness of any DAG which may prove to be of independent interest.
Springer2016Santa Barbara, CA, USA
eng
10.1007/978-3-662-53008-5_9
9815241 - 271
J.F. Alwen, J. Blocki, in:, Springer, 2016, pp. 241–271.
Alwen, Joel F, and Jeremiah Blocki. “Efficiently Computing Data-Independent Memory-Hard Functions,” 9815:241–71. Springer, 2016. <a href="https://doi.org/10.1007/978-3-662-53008-5_9">https://doi.org/10.1007/978-3-662-53008-5_9</a>.
Alwen JF, Blocki J. 2016. Efficiently computing data-independent memory-hard functions. CRYPTO: International Cryptology Conference, LNCS, vol. 9815, 241–271.
Alwen, J. F., & Blocki, J. (2016). Efficiently computing data-independent memory-hard functions (Vol. 9815, pp. 241–271). Presented at the CRYPTO: International Cryptology Conference, Santa Barbara, CA, USA: Springer. <a href="https://doi.org/10.1007/978-3-662-53008-5_9">https://doi.org/10.1007/978-3-662-53008-5_9</a>
Alwen JF, Blocki J. Efficiently computing data-independent memory-hard functions. In: Vol 9815. Springer; 2016:241-271. doi:<a href="https://doi.org/10.1007/978-3-662-53008-5_9">10.1007/978-3-662-53008-5_9</a>
J. F. Alwen and J. Blocki, “Efficiently computing data-independent memory-hard functions,” presented at the CRYPTO: International Cryptology Conference, Santa Barbara, CA, USA, 2016, vol. 9815, pp. 241–271.
Alwen, Joel F., and Jeremiah Blocki. <i>Efficiently Computing Data-Independent Memory-Hard Functions</i>. Vol. 9815, Springer, 2016, pp. 241–71, doi:<a href="https://doi.org/10.1007/978-3-662-53008-5_9">10.1007/978-3-662-53008-5_9</a>.
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