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Fully homomorphic encryption is faced with two problems now.One is candidate fully homomorphic encryption scheme is few.Another is that the efficiency of fully homomorphic encryption is a big question.We propose a fully homomorphic encryption scheme based on LWE,which has better key size.Our main contributions are:(1) according to the binary-LWE recently,we choose secret key from binary set and modify the basic encryption scheme proposed in LP10.We propose a fully homomorphic encryption scheme based on the new basic encryption scheme.We analyze the correctness and give the proof of the security of our scheme.The public key,evaluation keys and tensored ciphertext have better size in our scheme.(2) Estimating parameters for FHE scheme is an important work.We estimate the concert parameters for our scheme.These parameters include circuit depth L,dimension n,modulus q and Gaussian parameter r.From these parameters,we can obtain public key size,ciphertext size,the size of tensored ciphertext for multiplication and the size of key switching matrix.We compare these parameters between our scheme and Bra12 scheme.Our scheme have public key and private key that smaller by a factor of about logq than in Bra12 scheme.Tensored ciphertext in our scheme is smaller by a factor of about log2q than in Bra12 scheme.Key switching matrix in our scheme is smaller by a factor of about log3q than in Bra12 scheme.