Memoryhard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on offtheshelf hardware (like x86 CPUs). MHFs have interesting cryptographic applications, most notably to password hashing and securing blockchains. Alwen and Serbinenko [STOC’15] define the cumulative memory complexity (cmc) of a function as the sum (over all timesteps) of the amount of memory required to compute the function. They advocate that a good MHF must have high cmc. Unlike previous notions, cmc takes into account thatmore »
DataIndependent Memory Hard Functions: New Attacks and Stronger Constructions
Memoryhard functions (MHFs) are a key cryptographic primitive underlying the design of moderately expensive password hashing algorithms and egalitarian proofs of work. Over the past few years several increasingly stringent goals for an MHF have been proposed including the requirement that the MHF have high sequential spacetime (ST) complexity, parallel spacetime complexity, amortized areatime (aAT) complexity and sustained space complexity. DataIndependent Memory Hard Functions (iMHFs) are of special interest in the context of password hashing as they naturally resist sidechannel attacks. iMHFs can be specified using a directed acyclic graph (DAG) $G$ with $N=2^n$ nodes and low indegree and the complexity of the iMHF can be analyzed using a pebbling game. Recently, Alwen et al. [CCS'17] constructed an DAG called DRSample which has aAT complexity at least $\Omega\left( N^2/\log N\right)$. Asymptotically DRSample outperformed all prior iMHF constructions including Argon2i, winner of the password hashing competition (aAT cost $\mathcal{O}\left(N^{1.767}\right)$), though the constants in these bounds are poorly understood. We show that the the greedy pebbling strategy of Boneh et al. [ASIACRYPT'16] is particularly effective against DRSample e.g., the aAT cost is $\mathcal{O}\left( N^2/\log N\right)$. In fact, our empirical analysis {\em reverses} the prior conclusion of Alwen et al. that DRSample provides more »
 Award ID(s):
 1755708
 Publication Date:
 NSFPAR ID:
 10092895
 Journal Name:
 Crypto
 ISSN:
 17902703
 Sponsoring Org:
 National Science Foundation
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Memoryhard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on offtheshelf hardware (like x86 CPUs). MHFs have interesting cryptographic applications, most notably to password hashing and securing blockchains. Alwen and Serbinenko [STOC'15] define the cumulative memory complexity (cmc) of a function as the sum (over all timesteps) of the amount of memory required to compute the function. They advocate that a good MHF must have high cmc. Unlike previous notions, cmc takes into account thatmore »

Memoryhard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on offtheshelf hardware (like x86 CPUs). MHFs have interesting cryptographic applications, most notably to password hashing and securing blockchains. Alwen and Serbinenko [STOC'15] define the cumulative memory complexity (cmc) of a function as the sum (over all timesteps) of the amount of memory required to compute the function. They advocate that a good MHF must have high cmc. Unlike previous notions, cmc takes into account thatmore »

Memory Hard Functions (MHFs) have been proposed as an answer to the growing inequality between the computational speed of general purpose CPUs and Application Specific Integrated Circuits (ASICs). MHFs have seen widespread applications including password hashing, key stretching and proofs of work. Several metrics have been proposed to quantify the “memory hardness” of a function. Cumulative memory complexity (CMC) [8] (or amortized Area × Time complexity [4]) attempts to quantify the cost to acquire/build the hardware to evaluate the function — after normalizing the time it takes to evaluate the function. By contrast, bandwidth hardness [30] attempts to quantify themore »

The cumulative pebbling complexity of a directed acyclic graph G is defined as cc(G) = min_P ∑_i P_i, where the minimum is taken over all legal (parallel) black pebblings of G and P_i denotes the number of pebbles on the graph during round i. Intuitively, cc(G) captures the amortized SpaceTime complexity of pebbling m copies of G in parallel. The cumulative pebbling complexity of a graph G is of particular interest in the field of cryptography as cc(G) is tightly related to the amortized AreaTime complexity of the DataIndependent MemoryHard Function (iMHF) f_{G,H} [Joël Alwen and Vladimir Serbinenko, 2015] definedmore »