## Cryptology ePrint Archive: Report 2019/720

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

Zvika Brakerski and Nico Döttling and Sanjam Garg and Giulio Malavolta

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) $1-\sigma$ for $\sigma = o(1)$. Our scheme is based on the hardness of the Learning with Errors (LWE) problem and $\sigma$ 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.

Category / Keywords: public-key cryptography / Fully-Homomorphic Encryption, High-Rate, Time-Lock Puzzles

Date: received 17 Jun 2019, last revised 18 Jun 2019

Contact author: giulio malavolta at hotmail it, nico doettling at gmail com, sanjamg at berkeley edu, zvika brakerski at weizmann ac il

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/720

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