Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles

Zvika Brakerski; Nico Döttling; Sanjam Garg; Giulio Malavolta

doi:10.1007/978-3-030-36033-7_16

Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles

Zvika Brakerski, Nico Döttling, Sanjam Garg, Giulio Malavolta

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

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

Abstract

We show how to combine a fully-homomorphic encryption scheme with linear decryption and a linearly-homomorphic encryption schemes to obtain constructions with new properties. Specifically, we present the following new results. (1)Rate-1 Fully-Homomorphic Encryption: We construct the first scheme with message-to-ciphertext length ratio (i.e., rate) (formula presented). Our scheme is based on the hardness of the Learning with Errors (LWE) problem and(formula presented) is proportional to the noise-to-modulus ratio of the assumption. Our building block is a construction of a new high-rate linearly-homomorphic encryption.One application of this result is the first general-purpose secure function evaluation protocol in the preprocessing model where the communication complexity is within additive factor of the optimal insecure protocol.(2)Fully-Homomorphic Time-Lock Puzzles: We construct the first time-lock puzzle where one can evaluate any function over a set of puzzles without solving them, from standard assumptions. Prior work required the existence of sub-exponentially hard indistinguishability obfuscation.

Original language	English
Title of host publication	Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings
Editors	Dennis Hofheinz, Alon Rosen
Publisher	Springer Verlag
Pages	407-437
Number of pages	31
ISBN (Electronic)	978-3-030-36033-7
ISBN (Print)	9783030360320
DOIs	https://doi.org/10.1007/978-3-030-36033-7_16
State	Published - 2019
Event	17th International Conference on Theory of Cryptography, TCC 2019 - Nuremberg, Germany Duration: 1 Dec 2019 → 5 Dec 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11892 LNCS

Conference

Conference	17th International Conference on Theory of Cryptography, TCC 2019
Country/Territory	Germany
City	Nuremberg
Period	1/12/19 → 5/12/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-36033-7_16

Cite this

Brakerski, Z., Döttling, N., Garg, S., & Malavolta, G. (2019). Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles. In D. Hofheinz, & A. Rosen (Eds.), Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings (pp. 407-437). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11892 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-36033-7_16

Brakerski, Zvika ; Döttling, Nico ; Garg, Sanjam et al. / Leveraging Linear Decryption : Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles. Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. editor / Dennis Hofheinz ; Alon Rosen. Springer Verlag, 2019. pp. 407-437 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles",

abstract = "We show how to combine a fully-homomorphic encryption scheme with linear decryption and a linearly-homomorphic encryption schemes to obtain constructions with new properties. Specifically, we present the following new results. (1)Rate-1 Fully-Homomorphic Encryption: We construct the first scheme with message-to-ciphertext length ratio (i.e., rate) (formula presented). Our scheme is based on the hardness of the Learning with Errors (LWE) problem and(formula presented) is proportional to the noise-to-modulus ratio of the assumption. Our building block is a construction of a new high-rate linearly-homomorphic encryption.One application of this result is the first general-purpose secure function evaluation protocol in the preprocessing model where the communication complexity is within additive factor of the optimal insecure protocol.(2)Fully-Homomorphic Time-Lock Puzzles: We construct the first time-lock puzzle where one can evaluate any function over a set of puzzles without solving them, from standard assumptions. Prior work required the existence of sub-exponentially hard indistinguishability obfuscation.",

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Brakerski, Z, Döttling, N, Garg, S & Malavolta, G 2019, Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles. in D Hofheinz & A Rosen (eds), Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11892 LNCS, Springer Verlag, pp. 407-437, 17th International Conference on Theory of Cryptography, TCC 2019, Nuremberg, Germany, 1/12/19. https://doi.org/10.1007/978-3-030-36033-7_16

Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles. / Brakerski, Zvika; Döttling, Nico; Garg, Sanjam et al.
Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. ed. / Dennis Hofheinz; Alon Rosen. Springer Verlag, 2019. p. 407-437 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11892 LNCS).

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

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AU - Brakerski, Zvika

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AU - Malavolta, Giulio

PY - 2019

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N2 - We show how to combine a fully-homomorphic encryption scheme with linear decryption and a linearly-homomorphic encryption schemes to obtain constructions with new properties. Specifically, we present the following new results. (1)Rate-1 Fully-Homomorphic Encryption: We construct the first scheme with message-to-ciphertext length ratio (i.e., rate) (formula presented). Our scheme is based on the hardness of the Learning with Errors (LWE) problem and(formula presented) is proportional to the noise-to-modulus ratio of the assumption. Our building block is a construction of a new high-rate linearly-homomorphic encryption.One application of this result is the first general-purpose secure function evaluation protocol in the preprocessing model where the communication complexity is within additive factor of the optimal insecure protocol.(2)Fully-Homomorphic Time-Lock Puzzles: We construct the first time-lock puzzle where one can evaluate any function over a set of puzzles without solving them, from standard assumptions. Prior work required the existence of sub-exponentially hard indistinguishability obfuscation.

AB - We show how to combine a fully-homomorphic encryption scheme with linear decryption and a linearly-homomorphic encryption schemes to obtain constructions with new properties. Specifically, we present the following new results. (1)Rate-1 Fully-Homomorphic Encryption: We construct the first scheme with message-to-ciphertext length ratio (i.e., rate) (formula presented). Our scheme is based on the hardness of the Learning with Errors (LWE) problem and(formula presented) is proportional to the noise-to-modulus ratio of the assumption. Our building block is a construction of a new high-rate linearly-homomorphic encryption.One application of this result is the first general-purpose secure function evaluation protocol in the preprocessing model where the communication complexity is within additive factor of the optimal insecure protocol.(2)Fully-Homomorphic Time-Lock Puzzles: We construct the first time-lock puzzle where one can evaluate any function over a set of puzzles without solving them, from standard assumptions. Prior work required the existence of sub-exponentially hard indistinguishability obfuscation.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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PB - Springer Verlag

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ER -

Brakerski Z, Döttling N, Garg S, Malavolta G. Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles. In Hofheinz D, Rosen A, editors, Theory of Cryptography - 17th International Conference, TCC 2019, Proceedings. Springer Verlag. 2019. p. 407-437. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-36033-7_16

Leveraging Linear Decryption: Rate-1 Fully-Homomorphic Encryption and Time-Lock Puzzles

Abstract

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All Science Journal Classification (ASJC) codes

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