Homomorphic Encryption without Gaussian Noise

Abstract

We propose a Somewhat Homomorphic Encryption (SHE) scheme based on the Learning With Rounding (LWR) problem. The LWR problem is somewhat similar to the more classical Learning With Errors (LWE) and was proposed as a deterministic variant of it and setting up an LWR instance does not require the generation of gaussian noise. Thus our SHE scheme can be instantiated without the need for expensive Gaussian noise sampling. Our initial scheme provides lower ciphertext sizes for small plaintext spaces than existing leading schemes such as BGV