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2017 | OriginalPaper | Buchkapitel

Tightly Secure IBE Under Constant-Size Master Public Key

verfasst von : Jie Chen, Junqing Gong, Jian Weng

Erschienen in: Public-Key Cryptography – PKC 2017

Verlag: Springer Berlin Heidelberg

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Abstract

Chen and Wee [CRYPTO, 2013] proposed the first almost tightly and adaptively secure IBE in the standard model and left two open problems which called for a tightly secure IBE with (1) constant-size master public key and/or (2) constant security loss. In this paper, we propose an IBE scheme with constant-size master public key and tighter security reduction. This (partially) solves Chen and Wee’s first open problem and makes progress on the second one. Technically, our IBE scheme is built based on Wee’s petit IBE scheme [TCC, 2016] in the composite-order bilinear group whose order is product of four primes. The sizes of master public key, ciphertexts, and secret keys are not only constant but also nearly optimal as Wee’s petit IBE. We can prove its adaptive security in the multi-instance, multi-ciphertext setting [PKC, 2015] based on the decisional subgroup assumption and a subgroup variant of DBDH assumption. The security loss is \({\mathcal {O}}(\log q)\) where q is the upper bound of the total number of secret keys and challenge ciphertexts per instance. It’s much smaller than those for all known adaptively secure IBE schemes in a concrete sense.

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Vorheriges Kapitel Scalable Multi-party Private Set-Intersection

Nächstes Kapitel Separating IND-CPA and Circular Security for Unbounded Length Key Cycles

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Let \(\lambda \) be the security parameter. In the common case that \(n = {\mathsf {poly}}(\lambda )\) and \(q = {\mathsf {poly}}(\lambda )\), we can see that \({\mathcal {O}}(n)\) and \({\mathcal {O}}(\log q)\) are equivalent to \({\mathcal {O}}(\lambda )\) and \({\mathcal {O}}(\log \lambda )\), respectively. Superficially, our reduction is also tighter in an asymptotical sense. However \({\mathcal {O}}(\log \lambda )\) here contains an adversarially-dependent constant while \({\mathcal {O}}(\lambda )\) is totally independent of adversary.

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Titel: Tightly Secure IBE Under Constant-Size Master Public Key
verfasst von: Jie Chen
Junqing Gong
Jian Weng
Verlag: Springer Berlin Heidelberg
Buch: Public-Key Cryptography – PKC 2017
Print ISBN: 978-3-662-54364-1

Electronic ISBN: 978-3-662-54365-8

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-662-54365-8_9

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