Samson Zhou

On the Depth-Robustness and Cumulative Pebbling Cost of Argon2i

Argon2i is a data-independent 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

Nearly optimal sparse group testing

Group testing is the process of pooling arbitrary subsets from a set of n items so as to identify, with a minimal number of disjunctive tests, a “small” subset of d defective items. In “classical” non-adaptive group testing, it is known that when d = o(n^1−δ) for any δ > 0, θ(d log(n)) tests are both information-theoretically necessary, and sufficient to guarantee recovery with high probability. Group testing schemes in the literature meeting this bound require most items to be tested Ω(log(n)) times, and most tests to incorporate Ω(n/d) items. Motivated by physical considerations, we study group testing models in which the testing procedure is constrained to be “sparse”. Specifically, we consider (separately) scenarios in which (a) items are finitely divisible and hence may participate in at most γ tests; and (b) tests are size-constrained to pool no more than ρ items per test. For both scenarios we provide information-theoretic lower bounds on the number of tests required to guarantee high probability recovery. In particular, one of our main results shows that γ-finite divisibility of items forces any group testing algorithm with probability of recovery error at most ϵ to perform at least Ω(γ(n/d)^{(1−2ϵ)/((1+2ϵ)γ)}) tests. Analogously, for ρ-sized constrained tests, we show an information-theoretic lower bound of Ω(n log(n/d)/(ρ log(n/ρd))). In both scenarios we provide both randomized constructions (under both ϵ-error and zero-error reconstruction guarantees) and explicit constructions of computationally efficient group-testing algorithms (under ϵ-error reconstruction guarantees) that require a number of tests that are optimal up to constant factors in some regimes of n, d, γ and ρ. We also investigate the effect of unreliability/noise in test outcomes.

Periodicity in Data Streams with Wildcards

We investigate the problem of detecting periodic trends within a string

Structural Results on Matching Estimation with Applications to Streaming

S

Streaming Weighted Matchings: Optimal Meets Greedy.

of length

On the Economics of Offline Password Cracking

n

Streaming Periodicity with Mismatches.

, arriving in the streaming model, containing at most

Estimating Weighted Matchings in o(n) Space.

k

Bandwidth-Hard Functions: Reductions and Lower Bounds

wildcard characters, where

Optimal Parametric Search for Path and Tree Partitioning.

k=o(n)