Welcome to the resource topic for
**2019/561**

**Title:**

Faster Bootstrapping of FHE over the integers with large prime message space

**Authors:**
Zhizhu Lian, Yupu Hu, Hu Chen, Baocang Wang

**Abstract:**

Bootstrapping of FHE over the integer with large message is a open problem, which is to evaluate double modulo (c ~\text{mod}~ p )~\mod~ Q arithmetic homomorphically for large Q. In this paper, we express this double modulo reduction circuit as a arithmetic circuit of degree at most \theta^2 \log^2\theta/2, with O(\theta \log^2\theta) multiplication gates, where \theta= \frac{\lambda}{\log \lambda} and \lambda is the security parameter. The complexity of decryption circuit is independent of the message space size Q with a constraint Q> \theta \log^2\theta/2.

**ePrint:**
https://eprint.iacr.org/2019/561

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