Difference between revisions of "GSW"
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== Overview of the GSW scheme == | == Overview of the GSW scheme == | ||
| − | We follow the exposition in <ref | + | We follow the exposition in <ref name = "GSW" /> |
The description of this scheme is strikingly simple. GSW achieves homomorphic encryption based on [[LWE]] | The description of this scheme is strikingly simple. GSW achieves homomorphic encryption based on [[LWE]] | ||
== References == | == References == | ||
Revision as of 10:58, 4 June 2020
Around 2013, Gentry, Sahai and Waters [1] proposed a new way of building FHE schemes whose homomorphic multiplication algorithms are more natural than those presented in BFV or BGV. A distinguished feature of the scheme we are about to present is an asymmetric formula for the growth of the noise when multiplying two ciphertexts. Due to this feature, certain types of circuits have a very slow noise growth rate. Based on this asymmetry, Alperin-Sheriff and Peikert [2] found a very efficient bootstrapping technique for the GSW scheme.
More efficient FHE schemes based on ring variants of GSW have been proposed since then. These achieve very fast bootstrapping via various optimisation techniques, such as "refreshing the ciphertexts" after every single homomorphic operation. To our knowledge, among the schemes based on GSW (and not only), TFHE [3] holds the record for fastest bootstrapping. In the literature, the schemes based on the aformentioned work of Gentry, Sahai and Waters are commonly referred to as "third generation FHE". Their security is based on the so-called approximate eigenvector problem.
Overview of the GSW scheme
We follow the exposition in [1]
The description of this scheme is strikingly simple. GSW achieves homomorphic encryption based on LWE
References
- ↑ 1.0 1.1 C. Gentry, A. Sahai, and B. Waters. Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based. In CRYPTO 2013 (Springer). https://eprint.iacr.org/2013/340
- ↑ J. Alperin-Sheriff and C. Peikert. Faster Bootstrapping with Polynomial Error. In CRYPTO 2014 (Springer). https://eprint.iacr.org/2014/094
- ↑ I. Chillotti, N. Gama, M. Georgieva, and M. Izabachène. TFHE: Fast Fully Homomorphic Encryptionover the Torus. In Journal of Cryptology, volume 33, pages 34–91 (2020). https://eprint.iacr.org/2018/421
