In the past decade, cloud computing has emerged as an economical and practical alternative to in-house datacenters. But due to security concerns, many enterprises are still averse to adopting third party clouds. To mitigate these concerns, several authors have proposed to use partially homomorphic encryption (PHE) to achieve practical levels of confidentiality while enabling computations in the cloud. However, these approaches are either not performant or not versatile enough. We present two novel PHE schemes, an additive and a multiplicative homomorphic encryption scheme, which, unlike previous schemes, are symmetric. We prove the security of our schemes and show they are more efficient than state-of-the-art asymmetric PHE schemes, without compromising the expressiveness of homomorphic operations they support. The main intuition behind our schemes is to trade strict ciphertext compactness for good "relative" compactness in practice, while in turn reaping improved performance. We build a prototype system called Symmetria that uses our proposed schemes and demonstrate its performance improvements over previous work. Symmetria achieves up to 7× average speedups on standard benchmarks compared to asymmetric PHE-based systems.