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

  • Shuichi KatsumataEmail author
  • Shota Yamada
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11443)

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 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.

Notes

Acknowledgement

The first author was partially supported by JST CREST Grant Number JPMJCR1302 and JSPS KAKENHI Grant Number 17J05603. The second author was supported by JST CREST Grant Number JPMJCR1688 and JSPS KAKENHI Grant Number 16K16068.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.The University of TokyoTokyoJapan
  2. 2.National Institute of Advanced Industrial Science and Technology (AIST)TokyoJapan

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