### Non-Zero Inner Product Encryption Schemes from Various Assumptions: LWE, DDH and DCR

##### Abstract

In non-zero inner product encryption (NIPE) schemes, ciphertexts and secret keys are associated with vectors and decryption is possible whenever the inner product of these vectors does not equal zero. So far, much effort on constructing bilinear map-based NIPE schemes have been made and this has lead to many efficient schemes. However, the constructions of NIPE schemes without bilinear maps are much less investigated. The only known other NIPE constructions are based on lattices, however, they are all highly inefficient due to the need of converting inner product operations into circuits or branching programs. To remedy our rather poor understanding regarding NIPE schemes without bilinear maps, we provide two methods for constructing NIPE schemes: a direct construction from lattices and a generic construction from functional encryption schemes for inner products (LinFE). For our first direct construction, it highly departs from the traditional lattice-based constructions and we rely heavily on new tools concerning Gaussian measures over multi-dimensional lattices to prove security. For our second generic construction, using the recent constructions of LinFE schemes as building blocks, we obtain the first NIPE constructions based on the DDH and DCR assumptions. In particular, we obtain the first NIPE schemes without bilinear maps or lattices.

Available format(s)
Publication info
A major revision of an IACR publication in Pkc 2019
Keywords
Non-zero inner product encryptionlatticesgeneric constructionsfunctional encryption for inner products
Contact author(s)
shuichi katsumata000 @ gmail com
shota yamada enc @ gmail com
History
Short URL
https://ia.cr/2019/036

CC BY

BibTeX

@misc{cryptoeprint:2019/036,
author = {Shuichi Katsumata and Shota Yamada},
title = {Non-Zero Inner Product Encryption Schemes from Various Assumptions: LWE, DDH and DCR},
howpublished = {Cryptology ePrint Archive, Paper 2019/036},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/036}},
url = {https://eprint.iacr.org/2019/036}
}

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