A public key size homomorphic encryption scheme based on the sum of sparse subsets and integers

The paper proposes a homomorphic encryption scheme with public key size based on summation integer of sparse subset. The full-homomorphic encryption scheme that applies the batch processing technology to the integer can homomorphically process and encrypt a plaintext vector in a ciphertext to improve the efficiency of the original scheme, yet its size of the public key is Õ(λ8). In an effort to reduce the size of public key for this scheme, we combine quadric form of public key elements and ciphertext compression to present SomeWhat homomorphic public key scheme, which reduces the security of public key scheme into the approximate integer GCD problem, thereby converting the homomorphic encryption scheme into full homomorphic encryption scheme. For the proposed homomorphic encryption scheme with public key size based on summation integer of sparse subset, the public key size for improve scheme is Õ(λ5.5), a smaller size. Lastly, the scheme is proved to be semantically secure.