Threshold Fully Homomorphic Encryption

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

Paper 2017/257

Threshold Fully Homomorphic Encryption

Aayush Jain, 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.

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

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Threshold Cryptography Fully Homomorphic Encryption Function Secret Sharing
Contact author(s): rasmussen @ cs ucla edu
History: 2017-09-30: revised; 2017-03-25: received; See all versions
Short URL: https://ia.cr/2017/257
License: CC BY

BibTeX

@misc{cryptoeprint:2017/257,
      author = {Aayush Jain and Peter M.  R.  Rasmussen and Amit Sahai},
      title = {Threshold Fully Homomorphic Encryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/257},
      year = {2017},
      url = {https://eprint.iacr.org/2017/257}
}