Cryptology ePrint Archive: Report 2017/257

Threshold Fully Homomorphic Encryption

Aayush Jain and Peter M. R. Rasmussen and Amit Sahai

Abstract: We formally define and give the first construction of (leveled) threshold fully homomorphic encryption for any access structure induced by a monotone boolean formula and in particular for the threshold access structure. Our construction is based on the learning with errors assumption and can be instantiated with any existing homomorphic encryption scheme that satisfies fairly general conditions, such as Gentry, Sahai, Waters (CRYPTO 2013) and Brakerski, Gentry, Vaikuntanathan (ITCS 2012).

From threshold homomorphic encryption, we construct function secret sharing and distributed pseudorandom functions for the aforementioned access structures. No such constructions were known prior to this work.

Category / Keywords: public-key cryptography / Threshold Cryptography, Fully Homomorphic Encryption, Function Secret Sharing

Date: received 20 Mar 2017, last revised 30 Sep 2017

Contact author: rasmussen at cs ucla edu

Available format(s): PDF | BibTeX Citation

Note: This work is subsumed by ePrint report 2017/956.

Version: 20170930:212718 (All versions of this report)

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