Optimal Verification of Operations on Dynamic Sets

TitleOptimal Verification of Operations on Dynamic Sets
Publication TypeBook Chapters
Year of Publication2011
AuthorsPapamanthou C, Tamassia R, Triandopoulos N
EditorRogaway P
Book TitleAdvances in Cryptology – CRYPTO 2011
Series TitleLecture Notes in Computer Science
Pagination91 - 110
PublisherSpringer Berlin Heidelberg
ISBN Number978-3-642-22791-2, 978-3-642-22792-9
KeywordsComputer Communication Networks, computers and society, Data Encryption, Discrete Mathematics in Computer Science, Management of Computing and Information Systems, Systems and Data Security

We study the design of protocols for set-operation verification, namely the problem of cryptographically checking the correctness of outsourced set operations performed by an untrusted server over a dynamic collection of sets that are owned (and updated) by a trusted source. We present new authenticated data structures that allow any entity to publicly verify a proof attesting the correctness of primitive set operations such as intersection, union, subset and set difference. Based on a novel extension of the security properties of bilinear-map accumulators as well as on a primitive called accumulation tree, our protocols achieve optimal verification and proof complexity (i.e., only proportional to the size of the query parameters and the answer), as well as optimal update complexity (i.e., constant), while incurring no extra asymptotic space overhead. The proof construction is also efficient, adding a logarithmic overhead to the computation of the answer of a set-operation query. In contrast, existing schemes entail high communication and verification costs or high storage costs. Applications of interest include efficient verification of keyword search and database queries. The security of our protocols is based on the bilinear q-strong Diffie-Hellman assumption.