Exposure-resilient functions and all-or-nothing transforms

Ran Canetti, Yevgeniy Dodis, Shai Halevi, Eyal Kushilevitz, Amit Sahai

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

123 Scopus citations

Abstract

We study the problem of partial key exposure. Standard cryptographic definitions and constructions do not guarantee any security even if a tiny fraction of the secret key is compromised. We show how to build cryptographic primitives that remain secure even when an adversary is able to learn almost all of the secret key. The key to our approach is a new primitive of independent interest, which we call an Exposure-Resilient Function (ERF) – a deterministic function whose output appears random (in a perfect, statistical or computational sense) even if almost all the bits of the input are known. ERF’s by themselves efficiently solve the partial key exposure problem in the setting where the secret is simply a random value, like in private-key cryptography. They can also be viewed as very secure pseudorandom generators, and have many other applications. To solve the general partial key exposure problem, we use the (generalized) notion of an All-Or-Nothing Transform (AONT), an invertible (randomized) transformation T which, nevertheless, reveals “no information” about x even if almost all the bits of T(x) are known. By applying an AONT to the secret key of any cryptographic system, we obtain security against partial key exposure. To date, the only known security analyses of AONT candidates were made in the random oracle model. We show how to construct ERF’s and AONT’s with nearly optimal parameters. Our computational constructions are based on any one-way function. We also provide several applications and additional properties concerning these notions.

Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 2000 - International Conference on the Theory and Application of Cryptographic Techniques, Proceedings
EditorsBart Preneel
PublisherSpringer Verlag
Pages453-469
Number of pages17
ISBN (Print)9783540675174
DOIs
StatePublished - 2000
Externally publishedYes
Event19th International Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 2000 - Bruges, Belgium
Duration: 14 May 200018 May 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1807
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on the Theory and Application of Cryptographic Techniques, EUROCRYPT 2000
Country/TerritoryBelgium
CityBruges
Period14/05/0018/05/00

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