Jeudi 6 avril 2017 à 16h00 en salle C48
Ilaria Chillotti (UVSQ)
Titre : Faster Fully Homomorphic Encryption: Bootstrapping in less than 0.1 Seconds
Résumé :
In this paper, we revisit fully homomorphic encryption (FHE) based on GSW and its ring variants.
We notice that the internal product of GSW can be replaced by a simpler external product between a GSW
and an LWE ciphertext. We show that the bootstrapping scheme FHEW of Ducas and Micciancio (Eurocrypt 2015)
can be expressed only in terms of this external product. As a result, we obtain a speed up from less than
1 second to less than 0.1 seconds. We also reduce the 1GB bootstrapping key size to 24MB, preserving the
same security levels, and we improve the noise propagation overhead by replacing exact decomposition
algorithms with approximate ones.
Moreover, our external product allows to explain the unique asymmetry in the noise propagation of GSW samples
and makes it possible to evaluate deterministic automata homomorphically as in (ePrint 2014/283) in an
efficient way with a noise overhead only linear in the length of the tested word.
Finally, we provide an alternative practical analysis of LWE based scheme, which directly relates the security
parameter to the error rate of LWE and the entropy of the LWE secret key.