Search for: All records

Memory Hard Functions (MHFs) have been proposed as an answer to the growing inequality between the computational speed of general purpose CPUs and 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) quantifies the cost to acquire/build the hardware to evaluate the function repeatedly at a given rate. By contrast, bandwidth hardness quantifies the energy costs of evaluating this function. Ideally, a good MHF would be both bandwidth hard and have high CMC. While the CMC of leading MHF candidates is well understood, little is known about the bandwidth hardness of many prominent MHF candidates. Our contributions are as follows: First, we provide the first reduction proving that, in the parallel random oracle model (pROM), the bandwidth hardness of a data-independent MHF (iMHF) is described by the red-blue pebbling cost of the directed acyclic graph associated with that iMHF. Second, we show that the goals of designing an MHF with high CMC/bandwidth hardness are well aligned. Any function (data-independent or not) with high CMC also has relatively high bandwidth costs. Third, we prove that in the pROM the prominent iMHF candidates such as Argon2i, aATSample and DRSample are maximally bandwidth hard. Fourth, we prove the first unconditional tight lower bound on the bandwidth hardness of a prominent data-dependent MHF called Scrypt in the pROM. Finally, we show the problem of finding the minimum cost red–blue pebbling of a directed acyclic graph is NP-hard. 

In password security a defender would like to identify and warn users with weak passwords. Similarly, the defender may also want to predict what fraction of passwords would be cracked within B guesses as the attacker’s guessing budget B varies from small (online attacker) to large (offline attacker). Towards each of these goals the defender would like to quickly estimate the guessing number for each user password pwd assuming that the attacker uses a password cracking model M i.e., how many password guesses will the attacker check before s/he cracks each user password pwd. Since naïve brute-force enumeration can be prohibitively expensive when the guessing number is very large, Dell’Amico and Filippone [1] developed an efficient Monte Carlo algorithm to estimate the guessing number of a given password pwd. While Dell’Amico and Filippone proved that their estimator is unbiased there is no guarantee that the Monte Carlo estimates are accurate nor does the method provide confidence ranges on the estimated guessing number or even indicate if/when there is a higher degree of uncertainty.Our contributions are as follows: First, we identify theoretical examples where, with high probability, Monte Carlo Strength estimation produces highly inaccurate estimates of individual guessing numbers as well as the entire guessing curve. Second, we introduce Confident Monte Carlo Strength Estimation as an extension of Dell’Amico and Filippone [1]. Given a password our estimator generates an upper and lower bound with the guarantee that, except with probability δ, the true guessing number lies within the given confidence range. Our techniques can also be used to characterize the attacker’s guessing curve. In particular, given a probabilistic password cracking model M we can generate high confidence upper and lower bounds on the fraction of passwords that the attacker will crack as the guessing budget B varies. 

A central challenge in password security is to characterize the attacker's guessing curve i.e., what is the probability that the attacker will crack a random user's password within the first G guesses. A key challenge is that the guessing curve depends on the attacker's guessing strategy and the distribution of user passwords both of which are unknown to us. In this work we aim to follow Kerckhoffs's principal and analyze the performance of an optimal attacker who knows the password distribution. Let \lambda_G denote the probability that such an attacker can crack a random user's password within G guesses. We develop several statistically rigorous techniques to upper and lower bound \lambda_G given N independent samples from the unknown password distribution P. We show that our upper/lower bounds on \lambda_G hold with high confidence and we apply our techniques to analyze eight large password datasets. Our empirical analysis shows that even state-of-the-art password cracking models are often significantly less guess efficient than an attacker who can optimize its attack based on its (partial) knowledge of the password distribution. We also apply our statistical tools to re-examine different models of the password distribution i.e., the empirical password distribution and Zipf's Law. We find that the empirical distribution closely matches our upper/lower bounds on \lambda_G when the guessing number G is not too large i.e., G << N. However, for larger values of G our empirical analysis rigorously demonstrates that the empirical distribution (resp. Zipf's Law) overestimates the attacker's success rate. We apply our statistical techniques to upper/lower bound the effectiveness of password throttling mechanisms (key-stretching) which are used to reduce the number of attacker guesses G. Finally, if we are willing to make an additional assumption about the way users respond to password restrictions, we can use our statistical techniques to evaluate the effectiveness of various password composition policies which restrict the passwords that users may select. 

Abstract Much confusion exists on whether force‐ or energy‐based descriptions of cohesive‐particle interactions are more appropriate. We hypothesize a force‐based description is appropriate when enduring‐contacts dominate and an energy‐based description when contacts are brief in nature. Specifically, momentum is transferred through force‐chains when enduring‐contacts dominate and particles need to overcome a cohesive force to induce relative motion, whereas particles experiencing brief contacts transfer momentum through collisions and must overcome cohesion‐enhanced energy losses to avoid agglomeration. This hypothesis is tested via an attempt to collapse the dimensionless, dependent variable characterizing a given system against two dimensionless numbers: A generalized bond number, Bo_G–ratio of maximum cohesive force to the force driving flow, and a new Agglomerate number, Ag–ratio of critical cohesive energy to the granular energy. A gamut of experimental and simulation systems (fluidized bed, hopper, etc.), and cohesion sources (van der Waals, humidity, etc.), are considered. For enduring‐contact systems, collapse occurs with Bo_Gbut not Ag, and vice versa for brief‐contact systems, thereby providing support for the hypothesis. An apparent discrepancy with past work is resolved, and new insight into Geldart's classification is gleaned.