## Cryptology ePrint Archive: Report 2016/488

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

Short URL: ia.cr/2016/488

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