Paper 2016/1138
Pairing Cryptography Meets Isogeny: A New Framework of Isogenous Pairing Groups
Takeshi Koshiba and Katsuyuki Takashima
Abstract
We put forth a new mathematical framework called Isogenous Pairing Groups (IPG) and new intractable assumptions in the framework, the Isogenous DBDH (Isog-DBDH) assumption and its variants. Three operations, i.e., exponentiation, pairing and isogeny on elliptic curves are treated under a unified notion of trapdoor homomorphisms, and combinations of the operations have potential new cryptographic applications, in which the compatibility of pairing and isogeny is a main ingredient in IPG. As an example, we present constructions of (small and large universe) key-policy attribute-based encryption (KP-ABE) schemes secure against pre-challenge quantum adversaries in the quantum random oracle model (QROM). Note that our small universe KP-ABE has asymptotically the same efficiency as Goyal et al.'s small universe KP-ABE, which has only classical security. As a by-product, we also propose practical (hierarchical) identity-based encryption ((H)IBE) schemes secure against pre-challenge quantum adversaries in the QROM from isogenies, which are based on the Boneh-Franklin IBE and the Gentry-Silverberg HIBE, respectively.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Attribute-Based EncryptionPost-Quantum Crypto.Isogeny
- Contact author(s)
- Takashima Katsuyuki @ aj mitsubishielectric co jp
- History
- 2016-12-14: received
- Short URL
- https://ia.cr/2016/1138
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2016/1138,
author = {Takeshi Koshiba and Katsuyuki Takashima},
title = {Pairing Cryptography Meets Isogeny: A New Framework of Isogenous Pairing Groups},
howpublished = {Cryptology {ePrint} Archive, Paper 2016/1138},
year = {2016},
url = {https://eprint.iacr.org/2016/1138}
}