Generically speeding-up repeated squaring is equivalent to factoring: Sharp thresholds for all generic-ring delay functions

Lior Rotem*, Gil Segev

*Corresponding author for this work

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

5 Scopus citations

Abstract

Despite the fundamental importance of delay functions, repeated squaring in RSA groups (Rivest, Shamir and Wagner ’96) is the only candidate offering both a useful structure and a realistic level of practicality. Somewhat unsatisfyingly, its sequentiality is provided directly by assumption (i.e., the function is assumed to be a delay function). We prove sharp thresholds on the sequentiality of all generic-ring delay functions relative to an RSA modulus based on the hardness of factoring in the standard model. In particular, we show that generically speeding-up repeated squaring (even with a preprocessing stage and any polynomial number parallel processors) is equivalent to factoring. More generally, based on the (essential) hardness of factoring, we prove that any generic-ring function is in fact a delay function, admitting a sharp sequentiality threshold that is determined by our notion of sequentiality depth. Moreover, we show that generic-ring functions admit not only sharp sequentiality thresholds, but also sharp pseudorandomness thresholds.

Original languageAmerican English
Title of host publicationAdvances in Cryptology - CRYPTO 2020 - 40th Annual International Cryptology Conference, Proceedings
EditorsDaniele Micciancio, Thomas Ristenpart
PublisherSpringer
Pages481-509
Number of pages29
ISBN (Print)9783030568764
DOIs
StatePublished - 2020
Event40th Annual International Cryptology Conference, CRYPTO 2020 - Santa Barbara, United States
Duration: 17 Aug 202021 Aug 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12172 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference40th Annual International Cryptology Conference, CRYPTO 2020
Country/TerritoryUnited States
CitySanta Barbara
Period17/08/2021/08/20

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2020.

Fingerprint

Dive into the research topics of 'Generically speeding-up repeated squaring is equivalent to factoring: Sharp thresholds for all generic-ring delay functions'. Together they form a unique fingerprint.

Cite this