Threshold cryptosystems from threshold fully homomorphic encryption

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

doi:10.1007/978-3-319-96884-1_19

Threshold cryptosystems from threshold fully homomorphic encryption

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

^*Corresponding author for this work

34 Citations (Scopus)

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.

Original language	English
Title of host publication	Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings
Editors	Alexandra Boldyreva, Hovav Shacham
Number of pages	32
Publisher	Springer
Publication date	2018
Pages	565-596
ISBN (Print)	9783319968834
DOIs	https://doi.org/10.1007/978-3-319-96884-1_19
Publication status	Published - 2018
Externally published	Yes
Event	38th Annual International Cryptology Conference, CRYPTO 2018 - Santa Barbara, United States Duration: 19 Aug 2018 → 23 Aug 2018

Conference

Conference	38th Annual International Cryptology Conference, CRYPTO 2018
Country/Territory	United States
City	Santa Barbara
Period	19/08/2018 → 23/08/2018

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10991 LNCS
ISSN	0302-9743

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10.1007/978-3-319-96884-1_19

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Boneh, D., Gennaro, R., Goldfeder, S., Jain, A., Kim, S., Rasmussen, P. M. R., & Sahai, A. (2018). Threshold cryptosystems from threshold fully homomorphic encryption. In A. Boldyreva, & H. Shacham (Eds.), Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings (pp. 565-596). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 10991 LNCS https://doi.org/10.1007/978-3-319-96884-1_19

Threshold cryptosystems from threshold fully homomorphic encryption. / Boneh, Dan; Gennaro, Rosario; Goldfeder, Steven et al.

Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings. ed. / Alexandra Boldyreva; Hovav Shacham. Springer, 2018. p. 565-596 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10991 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Boneh, D, Gennaro, R, Goldfeder, S, Jain, A, Kim, S, Rasmussen, PMR & Sahai, A 2018, Threshold cryptosystems from threshold fully homomorphic encryption. in A Boldyreva & H Shacham (eds), Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10991 LNCS, pp. 565-596, 38th Annual International Cryptology Conference, CRYPTO 2018, Santa Barbara, United States, 19/08/2018. https://doi.org/10.1007/978-3-319-96884-1_19

Boneh D, Gennaro R, Goldfeder S, Jain A, Kim S, Rasmussen PMR et al. Threshold cryptosystems from threshold fully homomorphic encryption. In Boldyreva A, Shacham H, editors, Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings. Springer. 2018. p. 565-596. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10991 LNCS). doi: 10.1007/978-3-319-96884-1_19

Boneh, Dan ; Gennaro, Rosario ; Goldfeder, Steven et al. / Threshold cryptosystems from threshold fully homomorphic encryption. Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings. editor / Alexandra Boldyreva ; Hovav Shacham. Springer, 2018. pp. 565-596 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 10991 LNCS).

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AB - 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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ER -

Threshold cryptosystems from threshold fully homomorphic encryption

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