How to compute the inner product on encrypted vector by using a third party? I want to compute the inner product of two vectors on a third party, i.e. 
$f(x) \cdot f(y) = x \cdot y$
where $x$ and $y$ are two vectors. However, I do not want the third party knows the real value of the two vectors.

So is there any encryption scheme that can do this?
One possible way to calculate the inner product is by using fully homomorphic encryption schemes.
First, you encrypt each vector $$x = (x_1,x_2,\ldots,x_n), \quad y = (y_1,y_2,\ldots,y_n)$$
with your public key $$X = Enc_{pub}(x) \text{ and } Y = Enc_{pub}(y)$$ where $$X = (X_1,X_2,\ldots,X_n), \quad Y = (Y_1,Y_2,\ldots,Y_n)$$ and $$X_i = Enc_{pub}(x_i) \text{ and } Y_i = Enc_{pub}(y_i)$$
Now, you can send $X$ and $y$ to the server to calculate the inner product, IP, under FHE.
$$IP = \langle X,Y \rangle = X_1 \odot  Y_1 \oplus X_1 \odot Y_1 \oplus \cdots \oplus X_n \odot Y_n$$ when the server send you back the result, use your public key to decrypt the result. Where $\odot$ represent homomorphic multiplication and $\oplus$ represent homomoprhic addition.
$$res = \langle x,y \rangle = Dec_{priv}(IP)$$
Note 1 : You have to assume the server semi-honest. Here, there is no integrity against a malicious server.
Note 2 : For the implementation, you can use TFHE: Fast Fully Homomorphic Encryption over the Torus or Helib
Note 3 :  You can also use 2DNF by Boneh et.al, which support one multiplication but many additions. This work is enough for the calculation of the inner product under 2DNF encryption. The decryption, however, is not straightforward. As noted on page 4 of the paper;

To recover $m$, it suffices to compute the discrete log of $C^{q_1}$ of base $\hat{q}$
Note that decryption in this system takes polynomial time in the size of the message space T.
Therefore, the system as described above can only be used to encrypt short messages

Note 4: there is an article titled as Design and Implementation of Low Depth Pairing-based
Homomorphic Encryption Scheme by Herbert at. al that that

can handle the homomorphic evaluation of polynomials of degree at most 4.
and uses Elliptic Curves. And, they have an implementation posted on github.