---
_id: '1652'
abstract:
- lang: eng
text: 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:
- first_name: Joel F
full_name: Alwen, Joel F
id: 2A8DFA8C-F248-11E8-B48F-1D18A9856A87
last_name: Alwen
- first_name: Vladimir
full_name: Serbinenko, Vladimir
last_name: Serbinenko
citation:
ama: 'Alwen JF, Serbinenko V. High parallel complexity graphs and memory-hard functions.
In: *Proceedings of the 47th Annual ACM Symposium on Theory of Computing*.
ACM; 2015:595-603. doi:10.1145/2746539.2746622'
apa: 'Alwen, J. F., & Serbinenko, V. (2015). High parallel complexity graphs
and memory-hard functions. In *Proceedings of the 47th annual ACM symposium
on Theory of computing* (pp. 595–603). Portland, OR, United States: ACM. https://doi.org/10.1145/2746539.2746622'
chicago: Alwen, Joel F, and Vladimir Serbinenko. “High Parallel Complexity Graphs
and Memory-Hard Functions.” In *Proceedings of the 47th Annual ACM Symposium
on Theory of Computing*, 595–603. ACM, 2015. https://doi.org/10.1145/2746539.2746622.
ieee: J. F. Alwen and V. Serbinenko, “High parallel complexity graphs and memory-hard
functions,” in *Proceedings of the 47th annual ACM symposium on Theory of computing*,
Portland, OR, United States, 2015, pp. 595–603.
ista: 'Alwen JF, Serbinenko V. 2015. High parallel complexity graphs and memory-hard
functions. Proceedings of the 47th annual ACM symposium on Theory of computing.
STOC: Symposium on the Theory of Computing, 595–603.'
mla: Alwen, Joel F., and Vladimir Serbinenko. “High Parallel Complexity Graphs and
Memory-Hard Functions.” *Proceedings of the 47th Annual ACM Symposium on Theory
of Computing*, ACM, 2015, pp. 595–603, doi:10.1145/2746539.2746622.
short: J.F. Alwen, V. Serbinenko, in:, Proceedings of the 47th Annual ACM Symposium
on Theory of Computing, ACM, 2015, pp. 595–603.
conference:
end_date: 2015-06-17
location: Portland, OR, United States
name: 'STOC: Symposium on the Theory of Computing'
start_date: 2015-06-14
corr_author: '1'
date_created: 2018-12-11T11:53:16Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2024-10-09T20:56:13Z
day: '01'
department:
- _id: KrPi
doi: 10.1145/2746539.2746622
ec_funded: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://eprint.iacr.org/2014/238
month: '06'
oa: 1
oa_version: Submitted Version
page: 595 - 603
project:
- _id: 258C570E-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '259668'
name: Provable Security for Physical Cryptography
publication: Proceedings of the 47th annual ACM symposium on Theory of computing
publication_status: published
publisher: ACM
publist_id: '5498'
quality_controlled: '1'
scopus_import: 1
status: public
title: High parallel complexity graphs and memory-hard functions
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...