Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Attribute-Based Encryption, Post-Quantum Crypto., Isogeny

Date: received 7 Dec 2016

Contact author: Takashima Katsuyuki at aj MitsubishiElectric co jp

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Version: 20161214:185829 (All versions of this report)

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