Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   introduce a new probabilistic lattice-based bounded homomorphic encryption scheme. For this scheme the sum of two encrypted messages is the encryption of the sum of two messages and the scheme is able to preserve a vector spave structure of the message. The size of the public key is rather large ap 3 Mb but the encryption and the decryption operations are very fast (of the same speed order than NTRU). The homomorphic operation, i.e. the addition of ciphertexts is dramatically fast compared to homomorphic schemes based on group theory like Paillier or El Gamal.
['Carlos Aguilar Melchor', 'Guilhem Castagnos', 'Philippe Gaborit']
I am writing a research paper on a idea Lattice-based homomorphic encryption of vector spaces
[{"from": "human", "value": "I am writing a research paper on a idea Lattice-based homomorphic encryption of vector spaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   introduce a new probabilistic lattice-based bounded homomorphic encryption scheme. For this scheme the sum of two encrypted messages is the encryption of the sum of two messages and the scheme is able to preserve a vector spave structure of the message. The size of the public key is rather large ap 3 Mb but the encryption and the decryption operations are very fast (of the same speed order than NTRU). The homomorphic operation, i.e. the addition of ciphertexts is dramatically fast compared to homomorphic schemes based on group theory like Paillier or El Gamal."}]