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Paper: Threshold Cryptosystems from Threshold Fully Homomorphic Encryption

Authors:
Dan Boneh
Rosario Gennaro
Steven Goldfeder
Aayush Jain
Sam Kim
Peter M. R. Rasmussen
Amit Sahai
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DOI: 10.1007/978-3-319-96884-1_19
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Conference: CRYPTO 2018
Abstract: We develop a general approach to adding a threshold functionality to a large class of (non-threshold) cryptographic schemes. A threshold functionality enables a secret key to be split into a number of shares, so that only a threshold of parties can use the key, without reconstructing the key. We begin by constructing a threshold fully-homomorphic encryption scheme (ThFHE) from the learning with errors (LWE) problem. We next introduce a new concept, called a universal thresholdizer, from which many threshold systems are possible. We show how to construct a universal thresholdizer from our ThFHE. A universal thresholdizer can be used to add threshold functionality to many systems, such as CCA-secure public-key encryption (PKE), signature schemes, pseudorandom functions, and others primitives. In particular, by applying this paradigm to a (non-threshold) lattice signature system, we obtain the first single-round threshold signature scheme from LWE.
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BibTeX
@inproceedings{crypto-2018-28851,
  title={Threshold Cryptosystems from Threshold Fully Homomorphic Encryption},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={10991},
  pages={565-596},
  doi={10.1007/978-3-319-96884-1_19},
  author={Dan Boneh and Rosario Gennaro and Steven Goldfeder and Aayush Jain and Sam Kim and Peter M. R. Rasmussen and Amit Sahai},
  year=2018
}