All the existing fully homomorphic encryption schemes are based on three different problems, namely bounded distance decoding problem over ideal lattice, approximate greatest common divisor problem over integers and learning with error
problem. In this paper, we unify the first two families of problems by introducing a new class of problems, which can be reduced from both problems. Based on this new problem, namely the bounded distance decoding over hidden ideal lattice, we present a new fully homomorphic encryption scheme. Since it is a combination of the two problems to some extent, the performance of our scheme lies between the ideal lattice based schemes and the integer based schemes. Furthermore, we also show a lower and upper bound of the problem our scheme is based on. As a result, we present a security conjecture. Assuming this security conjecture holds, we can incorporate smaller parameters, which will result in a scheme that is more efficient than both lattice based and integer based schemes. Hence, our scheme makes a perfect alternative to the state-ofart ring learning with error based schemes.