On the provable security of an efficient RSA-based pseudorandom generator

Ron Steinfeld*, Josef Pieprzyk, Huaxiong Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

19 Citations (Scopus)

Abstract

Pseudorandom Generators (PRGs) based on the RSA inversion (one-wayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSA-based generators output asymptotically only at most O(logn) bits per multiply modulo an RSA modulus of bitlength n, and hence are too slow to be used in many practical applications. To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSA-based PRG, which shows that one can obtain an RSA-based PRG which outputs Ω(n) bits per multiply and has provable pseudorandomness security assuming the hardness of a well-studied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate O(logn) bits per multiply at the cost of a reasonable assumption on RSA inversion.

Original languageEnglish
Title of host publicationAdvances in Cryptology - ASIACRYPT 2006 - 12th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
EditorsXuejia Lai, Kefei Chen
Place of PublicationBerlin ; London
PublisherSpringer, Springer Nature
Pages194-209
Number of pages16
Volume4284 LNCS
ISBN (Print)3540494758, 9783540494751
DOIs
Publication statusPublished - 2006
Event12th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2006 - Shanghai, China
Duration: 3 Dec 20067 Dec 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4284 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2006
CountryChina
CityShanghai
Period3/12/067/12/06

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