Vector Encoding over Lattices and Its Applications

Daniel Apon, Xiong Fan, and Feng-Hao Liu

Abstract

In this work, we design a new lattice encoding structure for vectors. Our encoding can be used to achieve a packed FHE scheme that allows some SIMD operations and can be used to improve all the prior IBE schemes and signatures in the series. In particular, with respect to FHE setting, our method improves over the prior packed GSW structure of Hiromasa et al. (PKC '15), as we do not rely on a circular assumption as required in their work. Moreover, we can use the packing and unpacking method to extract each single element, so that the homomorphic operation supports element-wise and cross-element-wise computation as well. In the IBE scenario, we improves over previous constructions supporting $O(\Lambda)$-bit length identity from lattices substantially, such as Yamada (Eurocrypt '16), Katsumata, Yamada (Asiacrypt '16) and Yamada (Crypto '17), by shrinking the master public key to three matrices from standard Learning With Errors assumption. Additionally, our techniques from IBE can be adapted to construct a compact digital signature scheme, which achieves existential unforgeability under the standard Short Integer Solution (SIS) assumption with small polynomial parameters.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. Minor revision.
Contact author(s)
xfan @ cs cornell edu
History
2017-06-15: last of 2 revisions
See all versions
Short URL
https://ia.cr/2017/455

CC BY

BibTeX

@misc{cryptoeprint:2017/455,
author = {Daniel Apon and Xiong Fan and Feng-Hao Liu},
title = {Vector Encoding over Lattices and Its Applications},
howpublished = {Cryptology ePrint Archive, Paper 2017/455},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/455}},
url = {https://eprint.iacr.org/2017/455}
}

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