**Efficient Homomorphic Integer Polynomial Evaluation based on GSW FHE**

*Husen Wang and Qiang Tang*

**Abstract: **We introduce new methods to evaluate integer polynomials with GSW FHE, which has much slower noise growth and per integer multiplication cost $O((\log k/k)^{4.7454}/n)$ times the original GSW, where $k$ is the input plaintext width, $n$ is the LWE dimention parameter. Basically we reduce the integer multiplication noise by performing the evaluation between two kinds of ciphertexts, one in $\mathbb{Z}_q$ and another in $\mathbb{F}_2^{\lceil \log q \rceil}$. The conversion between two ciphertexts can be achieved by the integer bootstrapping. We also propose to solve the ciphertext expansion problem by symmetric encryption with stream ciphers.

**Category / Keywords: **GSW, Homomorphic Encryption, integer multiplication, Polyno- mial, bootstrapping, packing

**Date: **received 20 May 2016, last revised 23 Dec 2016

**Contact author: **wanghs thu at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20161223:133710 (All versions of this report)

**Short URL: **ia.cr/2016/488

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