We introduce the notion of malleable smooth projective hash function, which is an extension of the smooth projective hash function (SPHF) introduced by Cramer and Shoup (Eurocrypt'02) with the new properties of key malleability and element rerandomizability. We demonstrate the feasibility of our new notion using graded rings proposed by Benhamouda et al. (Crypto'13), and present an instantiation from the k-linear assumption. Moreover, we show that the malleable SPHF can also be based on other standard assumptions.
We show how to generically construct CRFs via malleable SPHFs in a modular way for some widely used cryptographic protocols. Specifically, we propose generic constructions of CRFs for the unkeyed message-transmission protocol and the oblivious signature-based envelope (OSBE) protocol of Blazy, Pointcheval and Vergnaud (TCC'12). We also present a new malleable SPHFfrom the linear encryption of valid signatures for instantiating the OSBE protocol with CRFs.
We further study the two-pass oblivious transfer (OT) protocol and show that the malleable SPHF does not suffice for its CRF constructions. We then develop a new OT framework from graded rings and show how to construct OT-CRFs by modifying the malleable SPHF framework. This new framework encompasses the DDH-based OT-CRF constructions proposed by Mironov and Stephens-Davidowitz (Eurocrypt'15), and yields a new construction under the $k$-linear assumption.Category / Keywords: Cryptographic reverse firewall, malleable smooth projective hash function, oblivious signature-based envelope, oblivious transfer Original Publication (in the same form): IACR-ASIACRYPT-2016 Date: received 6 Sep 2016, last revised 11 Sep 2016 Contact author: rc517 at uowmail edu au Available format(s): PDF | BibTeX Citation Version: 20160911:130506 (All versions of this report) Short URL: ia.cr/2016/873 Discussion forum: Show discussion | Start new discussion