Fully homomorphic encryption

The notion of a fully homomorphic encryption scheme over integers with public key compression has been proposed by Coron. The main attractive feature of this scheme is the reduction of the public key size, which is obtained by encrypting the plaintext with a quadratic form in the public key elements instead of in a linear form. In this work, we adopt this technique and apply it to the hidden ideal lattice scheme to acquire a more efficient scheme based on the hidden ideal lattice. The security of our scheme is based on the bounded distance decoding over the hidden ideal lattice. Additionally, we also describe a variant of the scheme with higher degrees. The scheme shows a better level of efficiency in comparison to the original scheme.