@inproceedings{1652,
abstract = {We develop new theoretical tools for proving lower-bounds on the (amortized) complexity of certain functions in models of parallel computation. We apply the tools to construct a class of functions with high amortized memory complexity in the parallel Random Oracle Model (pROM); a variant of the standard ROM allowing for batches of simultaneous queries. In particular we obtain a new, more robust, type of Memory-Hard Functions (MHF); a security primitive which has recently been gaining acceptance in practice as an effective means of countering brute-force attacks on security relevant functions. Along the way we also demonstrate an important shortcoming of previous definitions of MHFs and give a new definition addressing the problem. The tools we develop represent an adaptation of the powerful pebbling paradigm (initially introduced by Hewitt and Paterson [HP70] and Cook [Coo73]) to a simple and intuitive parallel setting. We define a simple pebbling game Gp over graphs which aims to abstract parallel computation in an intuitive way. As a conceptual contribution we define a measure of pebbling complexity for graphs called cumulative complexity (CC) and show how it overcomes a crucial shortcoming (in the parallel setting) exhibited by more traditional complexity measures used in the past. As a main technical contribution we give an explicit construction of a constant in-degree family of graphs whose CC in Gp approaches maximality to within a polylogarithmic factor for any graph of equal size (analogous to the graphs of Tarjan et. al. [PTC76, LT82] for sequential pebbling games). Finally, for a given graph G and related function fG, we derive a lower-bound on the amortized memory complexity of fG in the pROM in terms of the CC of G in the game Gp.},
author = {Alwen, Joel F and Serbinenko, Vladimir},
booktitle = {Proceedings of the 47th annual ACM symposium on Theory of computing},
location = {Portland, OR, United States},
pages = {595 -- 603},
publisher = {ACM},
title = {{High parallel complexity graphs and memory-hard functions}},
doi = {10.1145/2746539.2746622},
year = {2015},
}