We present a new theme for performing computations directly on encrypted data: the concept of homomorphic encryption, i.e., cryptosystems that allow a user to manipulate encrypted information even without knowing the secret key. In an attempt to alleviate the gap between cryptography which naturally operates on rings, groups, and fields, and signal processing which typically operates on real(complex)-valued data, we set the stage for distributed operations on encrypted data. We leverage advances in homomorphic encryption (such as the RSA, Paillier and Gentry cryptosystems), and in quantized signal processing and consensus to devise encryption-friendly distributed computing primitives. In specific, we show how to perform encrypted average consensus with finite-time convergence, using modular multiplication and exponentiation on encrypted information. We present the architecture for secure cloud computing and discuss its advantages and applicability to a wide range of data mining, signal processing and control operations over the cloud.