TY - GEN
T1 - Optimal Oblivious Parallel RAM
AU - Asharov, Gilad
AU - Komargodski, Ilan
AU - Lin, Wei Kai
AU - Peserico, Enoch
AU - Shi, Elaine
N1 - Publisher Copyright: Copyright © 2022 by SIAM.
PY - 2022
Y1 - 2022
N2 - An oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (STOC '87 and J. ACM '96), is a technique for hiding RAM's access pattern. That is, for every input the distribution of the observed locations accessed by the machine is essentially independent of the machine's secret inputs. Recent progress culminated in a work of Asharov et al. (EUROCRYPT '20), obtaining an ORAM with (amortized) logarithmic overhead in total work, which is known to be optimal. Oblivious Parallel RAM (OPRAM) is a natural extension of ORAM to the (more realistic) parallel setting where several processors make concurrent accesses to a shared memory. It is known that any OPRAM must incur logarithmic work overhead (in the balls and bins model). Despite the significant recent advances for constructing ORAM, there is still a significant gap for OPRAM: all existing OPRAM schemes incur a poly- logarithmic overhead either in total work or in depth. Our main result closes the aforementioned gap and provides an optimal OPRAM. Specifically, assuming one-way functions, we show that any Parallel RAM with memory capacity N can be obliviously simulated in space O(N), incurring only O(logN) blowup in (amortized) total work as well as in depth. Our transformation supports all PRAMs in the CRCW (concurrent read, concurrent write) mode and the resulting simulation is in the CRCW mode as well.
AB - An oblivious RAM (ORAM), introduced by Goldreich and Ostrovsky (STOC '87 and J. ACM '96), is a technique for hiding RAM's access pattern. That is, for every input the distribution of the observed locations accessed by the machine is essentially independent of the machine's secret inputs. Recent progress culminated in a work of Asharov et al. (EUROCRYPT '20), obtaining an ORAM with (amortized) logarithmic overhead in total work, which is known to be optimal. Oblivious Parallel RAM (OPRAM) is a natural extension of ORAM to the (more realistic) parallel setting where several processors make concurrent accesses to a shared memory. It is known that any OPRAM must incur logarithmic work overhead (in the balls and bins model). Despite the significant recent advances for constructing ORAM, there is still a significant gap for OPRAM: all existing OPRAM schemes incur a poly- logarithmic overhead either in total work or in depth. Our main result closes the aforementioned gap and provides an optimal OPRAM. Specifically, assuming one-way functions, we show that any Parallel RAM with memory capacity N can be obliviously simulated in space O(N), incurring only O(logN) blowup in (amortized) total work as well as in depth. Our transformation supports all PRAMs in the CRCW (concurrent read, concurrent write) mode and the resulting simulation is in the CRCW mode as well.
UR - http://www.scopus.com/inward/record.url?scp=85130731896&partnerID=8YFLogxK
U2 - https://doi.org/10.1137/1.9781611977073.98
DO - https://doi.org/10.1137/1.9781611977073.98
M3 - منشور من مؤتمر
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 2459
EP - 2521
BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
T2 - 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Y2 - 9 January 2022 through 12 January 2022
ER -