Composition does not imply adaptive security Conference Paper

Author(s): Pietrzak, Krzysztof
Title: Composition does not imply adaptive security
Title Series: LNCS
Abstract: We study the question whether the sequential or parallel composition of two functions, each indistinguishable from a random function by non-adaptive distinguishers is secure against adaptive distinguishers. The sequential composition of F and G is the function G(F()), the parallel composition is F G where ⋆ is some group operation. It has been shown that composition indeed gives adaptive security in the information theoretic setting, but unfortunately the proof does not translate into the more interesting computational case. In this work we show that in the computational setting composition does not imply adaptive security: If there is a prime order cyclic group where the decisional Diffie-Hellman assumption holds, then there are functions F and G which are indistinguishable by non-adaptive polynomially time-bounded adversaries, but whose parallel composition can be completely broken (i.e. we recover the key) with only three adaptive queries. We give a similar result for sequential composition. Interestingly, we need a standard assumption from the asymmetric (aka. public-key) world to prove a negative result for symmetric (aka. private-key) systems.
Conference Title: CRYPTO: International Cryptology Conference
Volume: 3621
Conference Dates: August 14-18, 2005
Conference Location: Santa Barbara, CA
Publisher: Springer  
Date Published: 2005-09-12
Start Page: 55
End Page: 65
Copyright Statement: ⓒ International Association for Cryptologic Research 2005
Sponsor: Supported by the Swiss National Science Foundation, project No. 200020-103847/1.
DOI: 10.1007/11535218_4
Open access: no
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