Practical fully homomorphic encryption over polynomial quotient rings

In this article we describe a simplified version of Polly Cracker-style fully homomorphic encryption scheme. The main feature of our scheme is an ability to define a strict upper bound of ciphertext size when performing calculations on it for both addition and multiplication. Combined with homomorphic properties of Polly Cracker it's able to reach high calculation performance without degrading in time. Another important aspect is utilization of large finite rings for calculations in untrusted environment, which prevents most of known attacks on Polly Cracker family.