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Efficient Fully Homomorphic Encryption from (Standard) LWE (2011)
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| Venue: | LWE, FOCS 2011, IEEE 52ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, IEEE |
| Citations: | 117 - 6 self |
BibTeX
@INPROCEEDINGS{Brakerski11efficientfully,
author = {Zvika Brakerski and Vinod Vaikuntanathan},
title = {Efficient Fully Homomorphic Encryption from (Standard) LWE},
booktitle = {LWE, FOCS 2011, IEEE 52ND ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE, IEEE},
year = {2011},
pages = {97--106},
publisher = {}
}
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Abstract
We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems ” on arbitrary lattices. Our construction improves on previous works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional assumptions. Our scheme has very short ciphertexts and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k · polylog(k) + log |DB | bits per single-bit query (here, k is a security parameter).
Keyphrases
efficient fully homomorphic encryption previous work homomorphic encryption arbitrary lattice homomorphic encryption scheme short ciphertexts security parameter worst-case hardness decryption complexity public-key model previous scheme single-bit query additional assumption log db various ring communication complexity new dimension-modulus reduction technique complexity assumption new relinearization technique short vector problem
