Fully Homomorphic symmetric scheme without bootstrapping

Capability of operating over encrypted data makes Fully Homomorphic Encryption(FHE)the Holy Grail for secure data processing applications. Though many applications need only secret keys, FHE has not been achieved properly through symmetric cryptography. Major hurdle is the need to refresh noisy ciphertexts which essentially requires public key and bootstrapping. We introduce a refreshing procedure to make a somewhat homomorphic scheme, fully homomorphic without requiring bootstrapping. Our scheme uses symmetric keys and has performance superior to existing public-key schemes.