Paper 2017/257

Threshold Fully Homomorphic Encryption

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


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.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Threshold CryptographyFully Homomorphic EncryptionFunction Secret Sharing
Contact author(s)
rasmussen @ cs ucla edu
2017-09-30: revised
2017-03-25: received
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Creative Commons Attribution


      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},
      note = {\url{}},
      url = {}
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