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A Tag Based Encoding: An Efficient Encoding for Predicate Encryption in Prime Order Groups Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Non-zero Inner Product Encryption with Short Ciphertexts and Private Keys

Authors : Jie Chen, Benoît Libert, Somindu C. Ramanna

Published in: Security and Cryptography for Networks

Publisher: Springer International Publishing

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Abstract

We describe two constructions of non-zero inner product encryption (NIPE) systems in the public index setting, both having ciphertexts and secret keys of constant size. Both schemes are obtained by tweaking the Boneh-Gentry-Waters broadcast encryption system (Crypto 2005) and are proved selectively secure under previously considered assumptions in groups with a bilinear map. Our first realization builds on prime-order bilinear groups and is proved secure under the Decisional Bilinear Diffie-Hellman Exponent assumption, which is parameterized by the length n of vectors over which the inner product is defined. By moving to composite order bilinear groups, we are able to obtain security under static subgroup decision assumptions following the Déjà Q framework of Chase and Meiklejohn (Eurocrypt 2014) and its extension by Wee (TCC 2016). Our schemes are the first NIPE systems to achieve such parameters, even in the selective security setting. Moreover, they are the first proposals to feature optimally short private keys, which only consist of one group element. Our prime-order-group realization is also the first one with a deterministic key generation mechanism.

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previous chapter A Tag Based Encoding: An Efficient Encoding for Predicate Encryption in Prime Order Groups
next chapter Attribute-Based Encryption for Range Attributes
Footnotes
1
One may object saying the linear-length vector \(\varvec{x}\) still has to be appended to the ciphertext. Nevertheless, in many applications the description of \(\varvec{x}\) can be very short. For example, in an ordinary (i.e., non-identity-based) broadcast encryption scheme for n users, \(\varvec{x}\) is uniquely determined by the n-bit word that specifies which users are in the revoked set. In this case, our ciphertexts reduce the communication overhead from \(O(n \lambda )\) to \(O(n+\lambda )\) bits if \(\lambda \) is the security parameter.
 
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Metadata
Title
Non-zero Inner Product Encryption with Short Ciphertexts and Private Keys
Authors
Jie Chen
Benoît Libert
Somindu C. Ramanna
Copyright Year
2016
Book
Security and Cryptography for Networks

Print ISBN: 978-3-319-44617-2

Electronic ISBN: 978-3-319-44618-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-44618-9_2

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