Vector Encoding over Lattices and Its Applications

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(λ)-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. ∗University of Maryland, Email: [email protected] work was supported in part by financial assistance award 70NANB15H328 from the U.S. Department of Commerce, National Institute of Standards and Technology. †Cornell University, Email: [email protected] material is based upon work supported by IBM under Agreement 4915013672. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsors. ‡Florida Atlantic University, Email: [email protected].