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2018 | OriginalPaper | Chapter

Threshold Cryptosystems from Threshold Fully Homomorphic Encryption

Authors : Dan Boneh, Rosario Gennaro, Steven Goldfeder, Aayush Jain, Sam Kim, Peter M. R. Rasmussen, Amit Sahai

Published in: Advances in Cryptology – CRYPTO 2018

Publisher: Springer International Publishing

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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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previous chapter On the Local Leakage Resilience of Linear Secret Sharing Schemes

next chapter Multi-Input Functional Encryption for Inner Products: Function-Hiding Realizations and Constructions Without Pairings

In the weaker model where the set of t servers that will respond to the combiner is known ahead of time, there exist simple methods to preserve correctness. In this work, we work in the traditional model of threshold cryptography where the combiner does not know the set of t servers ahead of time.

We describe the precise trade-offs between the two methods in [12].

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Title: Threshold Cryptosystems from Threshold Fully Homomorphic Encryption
Authors: Dan Boneh
Rosario Gennaro
Steven Goldfeder
Aayush Jain
Sam Kim
Peter M. R. Rasmussen
Amit Sahai
Publisher: Springer International Publishing
Book: Advances in Cryptology – CRYPTO 2018
Print ISBN: 978-3-319-96883-4

Electronic ISBN: 978-3-319-96884-1

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-96884-1_19

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