# Gentry: „Fully Homomorphic Encryption using Ideal Lattices“

## 15.05.2019, 10:00 – 11:00

15.05.2019 10:00-11:00

Speaker: Philipp Muth | Location: Mornewegstraße 32 (S4|14), Room 5.3.01, Darmstadt

Organizer: Christian Janson**Abstract**

This talk is the second one in the seminar series „Reading the Crypto Classics“ for the summer term 2019. The idea of this seminar is to jointly read classical milestone papers in the area of cryptography, to discuss their impact and understand their relevance for current research areas. The seminar is running as an Oberseminar, but at the same time meant to be a joint reading group seminar of the CROSSING Special Interest Group on Advanced Cryptography with all interested CROSSING members being invited to participate.

This issue will cover the paper

with the following abstract:

„We propose a fully homomorphic encryption scheme -- i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result -- that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable.

Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable.

Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits.

Unfortunately, our initial scheme is not quite bootstrappable -- i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem.“

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